Journal articles: 'Material and Geometrical Nonlinearity Effects'

1

Budiman, H. T., and P. A. Lagace. "Nondimensional Parameters for Geometric Nonlinear Effects in Pressurized Cylinders With Axial Cracks." Journal of Applied Mechanics 64, no. 2 (June 1, 1997): 401–7. http://dx.doi.org/10.1115/1.2787322.

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The effects of geometric nonlinearity on the response of axially cracked cylindrical shells under internal pressure are investigated in a general way. Using the Donnell-Mushtari-Vlasov nonlinear shell equations, the nonlinear response is shown to depend on two nondimensional parameters: the geometrical parameter λ, which is a function of the cylinder geometries and crack length, and the loading parameter η, which depends on the applied pressure, material properties, and cylinder geometries. To assess the applicability of such parameters, nonlinear analyses of different cylindrical configurations were performed using the STAGS finite element code. The results show that the two parameters are able to characterize the nonlinear response of such cylinders. Effects of nonlinearity are then presented in the form of an iso-nonlinear plot showing the percentage difference between the linear and nonlinear stress intensification factors. Using the iso-nonlinear plot, the importance of geometric nonlinearity can thus be assessed once the cylinder geometries, loading parameters, and material properties are known.

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2

Luo, Xu, Xin Sha Fu, Li Xiong Gu, and Lu Rong Cai. "Nonlinear Stability Analysis of Long-Span Suspension Bridge Cable Tower." Advanced Materials Research 1030-1032 (September 2014): 802–6. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.802.

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The cable tower is the bearing component of long-span suspension bridges, and its structure is very high and bear large force, which determines the stability and is the key of safety control. As for the height of the main tower of a long-span suspension bridge up to 195.3 m, the finite element software ANSYS is used to establish a three-dimensional finite element model (FEM), and the effects of geometric nonlinearity and material nonlinearity on the stability of the main tower are analyzed. The calculation results show that geometrical nonlinearity and material defects have significant influence on the main tower stability, and the nonlinear stability should be considered under wind load in the design calculation.

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3

Phuong, Nguyen Thi, Vu Hoai Nam, Nguyen Thoi Trung, Vu Minh Duc, and Pham Van Phong. "Nonlinear Stability of Sandwich Functionally Graded Cylindrical Shells with Stiffeners Under Axial Compression in Thermal Environment." International Journal of Structural Stability and Dynamics 19, no. 07 (June 26, 2019): 1950073. http://dx.doi.org/10.1142/s0219455419500731.

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The geometrically nonlinear response of sandwich functionally graded cylindrical shells reinforced by orthogonal and/or spiral stiffeners and subjected to axial compressive loads is investigated in this paper. Two types of sandwich functionally graded material models are considered. The formulations are based on the Donnell shell theory considering geometrical nonlinearity and Pasternak’s elastic foundation. The improved Lekhnitskii’s smeared stiffener technique is used to account for the stiffener effects with both mechanical and thermal stresses. The results obtained indicate that the spiral stiffeners have significantly beneficial influences in comparison with orthogonal stiffeners on the nonlinear buckling behavior of shells. The relatively large effects of temperature change, geometrical and material parameters are also demonstrated in the numerical investigations.

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4

Brunesi, Emanuele, and Roberto Nascimbene. "Effects of structural openings on the buckling strength of cylindrical shells." Advances in Structural Engineering 21, no. 16 (March 15, 2018): 2466–82. http://dx.doi.org/10.1177/1369433218764625.

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Computational models, which follow numerical assessment strategies codified by current European rules for shell buckling, were developed so as to study the buckling and post-buckling response of a large set of cylindrical steel thin-shell prototypes with structural openings. Behavioural changes as a consequence of variations in the cutout configuration, that is, shape, size, location and number, were predicted and the obtained numerical estimates were related to the test data of previous experiments in order to explore critical design aspects. Damage modes and axial force–axial displacement response curves were presented and discussed, decoupling the roles played by material nonlinearity and geometrical nonlinearity, as well as the contribution of initial geometrical imperfections to the buckling mechanism of axially compressed cylindrical thin shells.

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5

Cong, Pham Hong, Pham Thi Ngoc An, and Nguyen Dinh Duc. "Nonlinear stability of shear deformable eccentrically stiffened functionally graded plates on elastic foundations with temperature-dependent properties." Science and Engineering of Composite Materials 24, no. 3 (May 1, 2017): 455–69. http://dx.doi.org/10.1515/secm-2015-0225.

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AbstractThis article investigates the nonlinear stability of eccentrically stiffened moderately thick plates made of functionally graded materials (FGM) subjected to in-plane compressive, thermo-mechanical loads. The equilibrium and compatibility equations for the moderately thick plates are derived by using the first-order shear deformation theory of plates, taking into account both the geometrical nonlinearity in the von Karman sense and initial geometrical imperfections, temperature-dependent properties with Pasternak type elastic foundations. By applying the Galerkin method and using a stress function, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations, boundary conditions, and eccentric stiffeners on the buckling and post-buckling loading capacity of the eccentrically stiffened moderately thick FGM plates in thermal environments are analyzed and discussed.

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Feng, Xiu Ling, Meng Shen, Xiang Ya Kong, Jie Zhang, and Peng Fei Luo. "Study on Flexural Stiffness Reduction Factor of Reinforced Concrete Column with Equiaxial T Shaped Section." Applied Mechanics and Materials 351-352 (August 2013): 319–24. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.319.

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The reduced stiffness method had been adopted to evaluate the material nonlinearity characteristics of reinforced concrete structures to be in compliance with concrete structure standards of the United States, New Zealand and Canada. Concrete structure design code in China also accepts the reduced stiffness method as a supplementary method of considering the second-order effects problem. However, the concrete structure with specially shaped columns code of China still use amplified coefficients of eccentricity to consider nonlinearity characteristics of reinforced concrete structure with special shaped columns. Based on the numerical integral method, a flexural stiffness reduction factor is proposed to consider characteristics of material nonlinearity and geometrical nonlinearity of reinforced concrete columns with equiaxial T shaped section.

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Marius, Foguieng Wembe, Mambou Ngueyep Luc Leroy, and Ngapgue François. "Modeling and Numerical Analysis in 3D of Anisotropic and Nonlinear Mechanical Behavior of Tournemire Argillite under High Temperatures and Dynamic Loading." Scientific World Journal 2020 (June 23, 2020): 1–20. http://dx.doi.org/10.1155/2020/2978257.

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This work proposes a model that takes into account the anisotropy of material with its inhomogeneity and geometrical and material nonlinearities. According to Newton’s second law, the investigations were carried out on the simultaneous effects of mechanical load and thermal treatment on the Tournemire argillite material. The finite difference method was used for the numerical resolution of the problem by the MATLAB 2015a software in order to determine the peak stress and strain of argillite as a function of material nonlinearity and demonstrated the inhomogeneity parameter Ω. The critical temperature from which the material damage was pronounced is 500°C. Indeed, above this temperature, the loss of rigidity of argillite reduced significantly the mechanical performance of this rock. Therefore, after 2.9 min, the stress reduction in X or Y direction was 75.5% with a peak stress value of 2500 MPa, whereas in Z direction, the stress reduction was 74.1% with a peak stress value of 1998 MPa. Meanwhile, knowing that the material inhomogeneity was between 2995 and 3256.010, there was an increase in peak stress of about 75%. However, the influence of the material nonlinearity was almost negligible. Thus, the geometrical nonlinearity allows having the maximal constant strain of about 1.25 in the direction of the applied dynamic mechanical force.

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8

Tzou, H. S., and Y. Bao. "Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part 1: Nonlinear Anisotropic Piezothermoelastic Shell Laminates." Journal of Vibration and Acoustics 119, no. 3 (July 1, 1997): 374–81. http://dx.doi.org/10.1115/1.2889733.

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Nonlinear characteristics, either material or geometrical nonlinearity, and temperature variations can significantly influence the performance and reliability of piezoelectric sensors, actuators, structures, and systems. This paper is intended to examine the nonlinear piezothermoelastic characteristics and temperature effects of piezoelectric laminated systems, and it is divided into two parts. Part 1 is concerned with a mathematical modeling of nonlinear anisotropic piezothermoelastic shell laminates and Part 2 is a study of static and dynamic control of a nonlinear piezoelectric laminated circular plate subjected to mechanical, electric, and temperature excitations. Geometric nonlinearity induced by large deformations is considered in both parts. A generic nonlinear piezothermoelastic shell lamination theory is proposed and its nonlinear thermo-electromechanical equations are derived based on Hamilton’s principle. Thermo-electromechanical couplings among the elastic, electric, and temperature fields are discussed, and nonlinear components identified. Applications of the nonlinear theory to other materials, continua, sensors, actuators, and linear systems are discussed.

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9

Thi Phuong, Nguyen, Vu Hoai Nam, and Dang Thuy Dong. "Nonlinear vibration of functionally graded sandwich shallow spherical caps resting on elastic foundations by using first-order shear deformation theory in thermal environment." Journal of Sandwich Structures & Materials 22, no. 4 (June 12, 2018): 1157–83. http://dx.doi.org/10.1177/1099636218782645.

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A semi-analytical approach to investigate the nonlinear vibration axisymmetric analysis of functionally graded sandwich shallow spherical caps under external pressure resting on elastic foundation in thermal environment is presented. The governing equations are derived by using the first-order shear deformation theory taking into account von Karman geometrical nonlinearity and Pasternak’s two-parameter elastic foundation. The motion equations are determined by Galerkin method and the obtained equation is numerically solved by using Runge–Kutta method. Results of nonlinear dynamic responses show the effects of foundation, material, geometric parameters, and temperature change on the nonlinear vibration of shells.

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10

Zhang, Zheng, Jin Ping Zhuang, Xue Chao Chen, and Zhi Bin Wang. "Analysis on In-Plane Seismic Performance of Aluminium Beams under Cyclic Bending." Advanced Materials Research 1049-1050 (October 2014): 365–68. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.365.

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The in-plane mechanical properties of aluminium beams under cyclic bending were analyzed and contrasted to those of steel beams. In order to carry out research on in-plane seismic performance of aluminium beams, a finite element analysis method was presented. The method was based on general FEA software, ANSYS. The analysis method considered the effects of material nonlinearity and geometrical nonlinearity. On this basis, hysteretic curves and reversal skeleton curves of 6061-T6 aluminium beams, 6061-T4 aluminium beams and Q235 steel beams under cyclic bending were get and contrasted. The analysis shows that the in-plane seismic performance of the aluminium beams is similar with the low carbon steel beams and is notably influenced by material properties.

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11

Bich, Dao Huy, Nguyen Xuan Nguyen, and Hoang Van Tung. "Postbuckling of functionally graded cylindrical shells based on improved Donnell equations." Vietnam Journal of Mechanics 35, no. 1 (April 10, 2013): 1–15. http://dx.doi.org/10.15625/0866-7136/35/1/2894.

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This paper presents an analytical approach to investigate the buckling and postbuckling of functionally graded cylindrical shells subjected to axial and transversemechanical loads incorporating the effects of temperature. Material properties are assumed to be temperature independent, and graded in the thickness direction accordingto a simple power law distribution in terms of the volume fractions of constituents. Equilibrium equations for perfect cylindrical shells are derived by using improved Donnell shell theory taking into account geometrical nonlinearity. One-term approximate solution is assumed to satisfy simply supported boundary conditions and closed-form expressions of buckling loads and load-deflection curves are determined by Galerkin method. Analysis shows the effects of material and the geometric parameters, buckling mode, pre-existent axial compressive and thermal loads on the nonlinear response of the shells.

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12

Van Tung, Hoang. "Nonlinear thermomechanical response of pressure-loaded doubly curved functionally graded material sandwich panels in thermal environments including tangential edge constraints." Journal of Sandwich Structures & Materials 20, no. 8 (January 2, 2017): 974–1008. http://dx.doi.org/10.1177/1099636216684312.

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This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail.

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13

Zhang, Zheng, and Gui Yun Yan. "Study on T-Section Aluminium Beam-Columns with Web in Compression." Advanced Materials Research 250-253 (May 2011): 1786–89. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1786.

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Parameter analysis based on finite element methods was executed to study the in-plane stability capacity of extruded T-section aluminium beam-columns with the tip of the web in bigger compression. The analysis methods considered the effects of material nonlinearity, geometrical nonlinearity, and initial imperfection. The comparisons of calculate results of three kinds of T-sections of weak hardening alloy and strong hardening alloy between GB 50429, proposed formula and numerical methods were executed. And the analytical results show that GB 50429 is safe and suitable, and the modification formula based on GB 50429 is also safe enough and more exact than the former.

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14

Zhang, Zheng, Xue Chao Chen, Yong Chao Ma, and Zhi Bin Wang. "Analysis on Out-of-Plane Seismic Stability Performance of Aluminium Beams under Cyclic Bending." Advanced Materials Research 1049-1050 (October 2014): 369–73. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.369.

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The out-of-plane mechanical properties of aluminium beams under cyclic bending were studied and contrasted to those of steel beams. In order to carry out research on out-of-plane seismic stability performance of aluminium beams, a method by finite element analysis was proposed. The method was based on FEA software, ANSYS. The analysis methods considered the effects of material nonlinearity, geometrical nonlinearity and initial imperfection. Based on above, hysteretic curves, reversal skeleton curves and stiffness degradation curves of 6061-T6 aluminium beams, 6061-T4 aluminium beams and Q235 steel beams under cyclic bending were get and contrasted. Results show that the out-of-plane seismic stability performance of the aluminium beams is lower than the low carbon steel beams and is significantly influenced by material properties.

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15

Munoz, Miguel, Michele Iuliano, and Bruno Briseghella. "A Calculation Method of Coupled Nonlinearities in Slender Bridge Piers." Applied Mechanics and Materials 847 (July 2016): 431–39. http://dx.doi.org/10.4028/www.scientific.net/amm.847.431.

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In some cases, due to particular conditions, the project of a bridge requires the construction of high piers. The study of these structural elements needs to go beyond a simple linear analysis, especially considering the second order effects, that contemplate the possibility of instability of the pier due to the slenderness it. In this paper a toolbox that considers the geometrical nonlinearity, the nonlinearity mechanical behaviour of the materials and the time dependent properties of the concrete is presented. The assessment of the pier starts with the possibility of cracking in the section (material non linearity) with consequent loses of stiffness. The second step takes into account the increment of bending moment caused by the P-d effect (geometrical non linearity) and strictly related to the slenderness of the member. The last step is the evaluation of the increment of deformation caused by permanent loads, mainly due to the loss of the concrete stiffness in time for creep effect of concrete. In this paper, a detailed explanation of the automatic procedure is provided and finally the application to a real case of a bridge pier under a critical stage construction condition is presented.

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16

Zhang, Chuntao, and Ian D. Moore. "Nonlinear Finite Element Analysis for Thermoplastic Pipes." Transportation Research Record: Journal of the Transportation Research Board 1624, no. 1 (January 1998): 225–30. http://dx.doi.org/10.3141/1624-26.

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Thermoplastic pipes are being used increasingly for water supply lines, storm sewers, and leachate collection systems in landfills. To facilitate limit states design for buried polymer pipes, nonlinear constitutive models have recently been developed to characterize the highly nonlinear and time-dependent material behavior of high-density polyethylene (HDPE). These models have been implemented in a finite element program to permit structural analysis for buried HDPE pipes and to provide information regarding performance limits of the structures. Predictions of HDPE pipe response under parallel plate loading and hoop compression in a soil cell are reported and compared with pipe response measured in laboratory tests. Effects on the structural performance of pipe material nonlinearity, geometrical nonlinearity, and backfill soil properties were investigated. Good correlations were found between the finite element predictions and the experimental measurements. The models can be used to predict pipe response under many different load histories (not just relaxation or creep). Work is ongoing to develop nonlinear constitutive models for polyvinylchloride and polypropylene to extend the predictive capability of the finite element model to these materials.

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17

Nam, Vu Hoai, Dang Thuy Dong, Nguyen Thi Phuong, and Ho Duc Tuan. "Nonlinear thermo-mechanical stability of multilayer-FG plates reinforced by orthogonal and oblique stiffeners according to FSDT." Journal of Reinforced Plastics and Composites 38, no. 11 (February 24, 2019): 521–36. http://dx.doi.org/10.1177/0731684419831650.

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This paper presents an analytical approach to investigate the nonlinear stability of multilayer-functionally graded plates stiffened by orthogonal and/or oblique functionally graded stiffeners subjected to axial compression and/or thermal load. The equilibrium equation system is established by using the first-order shear deformation plate theory taking into account the plate–foundation interaction, geometrical nonlinearity in von Kármán sense and initial geometrical imperfection. An improved Lekhnitskii’s smeared stiffener technique is applied for oblique stiffeners with thermal terms and shear deformation of stiffeners. The governing equations are solved by Galerkin procedure to obtain the explicit expressions of buckling loads and postbuckling load–deflection curves. Results show the effects of material and geometrical properties, boundary conditions, elastic foundation parameters and initial imperfection on the buckling and postbuckling load-carrying capacity of plates.

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18

Thi Phuong, Nguyen, Dang Thanh Luan, Vu Hoai Nam, and Pham Thanh Hieu. "Nonlinear approach on torsional buckling and postbuckling of functionally graded cylindrical shells reinforced by orthogonal and spiral stiffeners in thermal environment." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 6 (June 6, 2018): 2091–106. http://dx.doi.org/10.1177/0954406218780523.

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A new nonlinear approach on the buckling and postbuckling of functionally graded orthogonal and/or spiral-stiffened circular cylindrical shells subjected to torsional loads is proposed in this paper. The shells skin are stiffened by eccentrically rings, stringers, and/or spiral stiffeners at the surface of shells assuming that the material distribution laws of shell skin and stiffeners are graded by two distribution models. Lekhnitskii’s smeared stiffeners technique is improved for spiral stiffeners with effect of thermal terms. This is the significant novelty and scientific contribution of this paper. Theoretical formulations were established by using the Donnell shell theory taking into account the geometrical nonlinearity of von Kármán. The obtained results investigated in numerical forms show effects of volume fraction exponent of shell skin and stiffeners, geometrical parameter and stiffeners on the torsional buckling, and postbuckling behavior of functionally graded cylindrical shells. Especially, very large effects of spiral stiffeners on torsional stability behavior are obtained in comparison with same quantity material of orthogonal stiffeners.

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19

Zhang, Zheng, Yong Qian Zheng, Xue Chao Chen, and Zhi Bin Wang. "Finite Element Analysis on Hysteretic Behavior of Aluminium Columns under Cyclic Loading." Advanced Materials Research 1049-1050 (October 2014): 264–67. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.264.

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The mechanical properties of axial compression aluminium members under cyclic loading were studied and compared with those of steel columns. In order to proceed to theoretical study on hysteretic behavior of aluminium columns, a method by finite element analysis was proposed. The method was based on FEA software, ANSYS. The analysis methods considered the effects of material nonlinearity, geometrical nonlinearity and initial imperfection. On this basis, hysteretic curves, reversal skeleton curves and stiffness degradation curves of 6061-T6 aluminium columns, 6061-T4 aluminium columns and Q235 steel columns under axial cyclic loading were obtained and compared. Results show that the hysteretic behavior of the aluminium columns is similar with the low carbon steel columns and is significantly influenced by constitutive relationship.

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20

Cattani, Carlo. "Signorini Cylindrical Waves and Shannon Wavelets." Advances in Numerical Analysis 2012 (June 26, 2012): 1–24. http://dx.doi.org/10.1155/2012/731591.

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Hyperelastic materials based on Signorini’s strain energy density are studied by using Shannon wavelets. Cylindrical waves propagating in a nonlinear elastic material from the circular cylindrical cavity along the radius are analyzed in the following by focusing both on the main nonlinear effects and on the method of solution for the corresponding nonlinear differential equation. Cylindrical waves’ solution of the resulting equations can be easily represented in terms of this family of wavelets. It will be shown that Hankel functions can be linked with Shannon wavelets, so that wavelets can have some physical meaning being a good approximation of cylindrical waves. The nonlinearity is introduced by Signorini elastic energy density and corresponds to the quadratic nonlinearity relative to displacements. The configuration state of elastic medium is defined through cylindrical coordinates but the deformation is considered as functionally depending only on the radial coordinate. The physical and geometrical nonlinearities arising from the wave propagation are discussed from the point of view of wavelet analysis.

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21

Gordaninejad, F., N. G. Chalhoub, A. Ghazavi, and Q. Lin. "Nonlinear Deformation of a Shear-Deformable Laminated Composite-Material Flexible Robot Arm." Journal of Mechanical Design 114, no. 1 (March 1, 1992): 96–102. http://dx.doi.org/10.1115/1.2916932.

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In this work a general procedure to derive a nonlinear dynamic model for a three-link revolute flexible robot arm constructed from laminated fiber-reinforced composite materials is presented. The effects of geometric nonlinearity as well as rotary inertia and shear deformation are included to study the dynamic response of robotic manipulators made of moderately thick beams under large deformations. Hamilton’s principle is used to derive the equations of motion. A displacement finite element model based on the Timoshenko beam theory is implemented to approximate the solution. The digital simulation studies examine the combined effects of geometric nonlinearity, rotary inertia, and shear deformation on the arm’s end effector displacements. Furthermore, the effects of angle of fiber orientation and material orthotropy on the end-of-the-arm displacements and maximum normal bending stresses, are assessed.

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22

Hoa, Le Kha, Nguyen-Thoi Trung, Pham Van Hoan, and Pham Le Ben. "Nonlinear Instability Analysis of Functionally Graded Sandwich Truncated Conical Shells Reinforced by Stiffeners Resting on Elastic Foundations." International Journal of Structural Stability and Dynamics 19, no. 08 (August 2019): 1950082. http://dx.doi.org/10.1142/s0219455419500822.

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This paper investigates the nonlinear instability of eccentrically stiffened functionally graded (ES-FG) sandwich truncated conical shells subjected to the axial compressive load. The core of the FG sandwich truncated conical shells, assumed to be thin, is made of pure metal or ceramic materials and the two skin layers are made of a FG material. The shell reinforced by orthogonal stiffeners (stringers) is also made of FG materials. The change of spacing between the stringers in the meridional direction is considered. The governing equations are derived using the Donnell shell theory with von Karman geometrical nonlinearity along with the smeared technique for stiffeners. The resulting coupled set of three nonlinear partial differential equations with variable coefficients in terms of displacement components are solved by the Galerkin’s method. The closed-form expressions for determining the critical buckling load and for analyzing the postbucking load–deflection curves are obtained. The accuracy of present formulation is verified by comparing the results obtained with available ones in the literature. The effects of various parameters such stiffeners, foundations, material properties, geometric dimensions on the stability of the shells are studied in detail.

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Dung, Dao Van, and Le Kha Hoa. "Solving nonlinear stability problem of imperfect functionally graded circular cylindrical shells under axial compression by Galerkin's method." Vietnam Journal of Mechanics 34, no. 3 (September 4, 2012): 139–56. http://dx.doi.org/10.15625/0866-7136/34/3/2356.

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This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection. Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper [13] which were solved by Ritz energy method.

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Sun, Shuang Shuang, and Xian Ce Jiang. "Nonlinear Analysis of Actuation Performance of NiTi/Si Composite Film." Applied Mechanics and Materials 437 (October 2013): 572–76. http://dx.doi.org/10.4028/www.scientific.net/amm.437.572.

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The NiTi shape memory alloy (SMA) composite film with Si substrate subjected to thermal loads was modeled by the method of mechanics of materials. The governing equation was obtained by combining static equilibrium equations, geometric and physical equations. Both the material nonlinearity of SMA and the geometric nonlinearity of bending deformation of SMA composite film were considered. By simulating the actuation performance of the SMA composite film during a cooling-heating thermal cycle, it is found that the final cooling temperature and the thickness of SMA film have significant effects on the actuation performance of the SMA composite film. Besides, the maximum deflection of the SMA composite film is affected obviously by the geometric nonlinearity of bending deformation when the thickness of SMA film is very large.

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Tung, Hoang Van. "Thermomechanical postbuckling of thick FGM plates resting on elastic foundations with tangential edge constraints." Vietnam Journal of Mechanics 38, no. 1 (March 15, 2016): 63–79. http://dx.doi.org/10.15625/0866-7136/38/1/7036.

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This paper investigates the effects of tangential edge constraints and elastic foundations on the buckling and postbuckling behavior of thick FGM rectangular plates resting on elastic foundations and subjected to thermal and thermomechanical loading conditions. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Governing equations are based on the higher order shear deformation plate theory incorporating the von Karman geometrical nonlinearity, initial geometrical imperfection, tangential edge constraints and Pasternak type elastic foundations. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and load-deflection relations. In thermal postbuckling analysis, an iteration algorithm is employed to determine critical buckling temperatures and postbuckling temperature-deflection equilibrium paths. The separate and simultaneous effects of tangential edge restraints, elastic foundations and temperature dependence of material properties on the buckling and postbuckling responses of higher order shear deformable FGM plates are analyzed and discussed.

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Tung, Hoang Van. "Postbuckling of thick FGM cylindrical panels with tangential edge constraints and temperature dependent properties." Vietnam Journal of Mechanics 38, no. 2 (June 24, 2016): 123–40. http://dx.doi.org/10.15625/0866-7136/38/2/7066.

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This paper investigates postbuckling behavior of thick FGM cylindrical panels resting on elastic foundations and subjected to thermal, mechanical and thermomechanical loading conditions. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Governing equations are based on higher order shear deformation shell theory incorporating von Karman-Donnell geometrical nonlinearity, initial geometrical imperfection, tangential edge constraints and Pasternak type elastic foundations. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and load-deflection relations. In thermal postbuckling analysis, an iteration algorithm is employed to determine critical buckling temperatures and postbuckling temperature-deflection equilibrium paths. The separate and simultaneous effects of tangential edge restraints, elastic foundations and temperature dependence of material properties on the buckling and postbuckling responses of higher order shear deformable FGM cylindrical panels are analyzed and discussed.

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Khoa, Nguyen Minh, and Hoang Van Tung. "Nonlinear thermo-mechanical stability of shear deformable FGM sandwich shallow spherical shells with tangential edge constraints." Vietnam Journal of Mechanics 39, no. 4 (December 27, 2017): 351–64. http://dx.doi.org/10.15625/0866-7136/9810.

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This paper presents an analytical approach to investigate the nonlinear axisymmetric response of moderately thick FGM sandwich shallow spherical shells resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. Material properties are assumed to be temperature independent, and effective properties of FGM layer are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations and various degree of tangential constraint of boundary edge into consideration. Approximate solutions are assumed to satisfy clamped boundary condition and Galerkin method is applied to derive closed-form expressions of critical buckling loads and nonlinear load-deflection relation. Effects of geometrical parameters, thickness of face sheets, foundation stiffness, imperfection, thermal environments and degree of tangential edge constraints on the nonlinear stability of FGM sandwich shallow spherical shells are analyzed and discussed.

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Zaami, Amin, and Ali Shokuhfar. "Investigating Effects of Losing Fluid on Nonlinear Structural Behavior of Rabbit ACL." Journal of Biomimetics, Biomaterials and Biomedical Engineering 26 (February 2016): 45–59. http://dx.doi.org/10.4028/www.scientific.net/jbbbe.26.45.

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This study is conducted to investigate the effects of losing fluid during extension of rabbit ACL (Anterior Cruciate Ligament) on its nonlinear behavior. The incompressible Neo-Hookean model is employed for modeling the mechanical response of ACL under the uniaxial loading. The material properties of the ligament are characterized by measuring the deformation of a continuum element regarding to two assumptions, the exact and near incompressible cases. In the near incompressible assumption, it is assumed that some fluids exit during ligament extension which influence the nonlinear structural response of the ACL. Finally, considering the nonlinearity of the ligament due to the material behavior and geometrical effect, the ligament behavior is modeled using the nonlinear FEM solution. This study provides a new insight based on the model incompressibility for the ACL of the rabbit knee. These findings help researchers to predict the patterns of injuries that occur in the ligament for different amount of losing fluid by developing the computational model to assess the nonlinear response

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Goulbourne, Nakhiah, Eric Mockensturm, and Mary Frecker. "A Nonlinear Model for Dielectric Elastomer Membranes." Journal of Applied Mechanics 72, no. 6 (April 21, 2005): 899–906. http://dx.doi.org/10.1115/1.2047597.

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The material and geometrical nonlinearities of novel dielectric elastomer actuators make them more difficult to model than linear materials used in traditional actuators. To accurately model dielectric elastomers, a comprehensive mathematical formulation that incorporates large deformations, material nonlinearity, and electrical effects is derived using Maxwell-Faraday electrostatics and nonlinear elasticity. The analytical model is used to numerically solve for the resultant behavior of an inflatable dielectric elastomer membrane, subject to changes in various system parameters such as prestrain, external pressure, applied voltage, and the percentage electroded membrane area. The model can be used to predict acceptable ranges of motion for prescribed system specifications. The predicted trends are qualitatively supported by experimental work on fluid pumps [A. Tews, K. Pope, and A. Snyder, Proceedings SPIE, 2003)]. For a potential cardiac pump application, it is envisioned that the active dielectric elastomer membrane will function as the motive element of the device.

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Wei, Liu, Shu Ganping, and Chan Siulai. "Research on Advanced Analysis Method of Semi-Rigid Steel Frames." Open Construction and Building Technology Journal 9, no. 1 (May 29, 2015): 12–16. http://dx.doi.org/10.2174/1874836801509010012.

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The advanced analysis method used to analyze semi-rigid steel frames is introduced, and the method could take account of many factors influencing structure mechanical performance. These factors include: initial imperfect mode of structure and members, geometrical nonlinearity (P-∆, P-δ effects), material nonlinearity and semi-rigid connections. The Curved Stability Function (CSF) element is built to take account of initial imperfect state, semi-rigid connections and plastic hinge, and derivatives of the second-order element stiffness matrix to extend the spatial element stiffness matrix. The nonlinearity behavior of semi-rigid connections and plastic hinge are simulated by the spring element. Judgment criteria of plastic hinge and spring stiffness values are determined, as well as of the structure failure. The three semirigid steel frames are directly analyzed by the program named NIDA, and the results of NIDA are comparatively analyzed with test results. It is indicated that the results of NIDA are better compared to the test results, verifying validity and reliability of the advanced analysis method used to analyze semi-rigid steel frames.

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Sun, Shuangshuang, and Xiance Jiang. "Nonlinear Analysis of Actuation Performance of Shape Memory Alloy Composite Film Based on Silicon Substrate." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/728950.

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The mechanical model of the shape memory alloy (SMA) composite film with silicon (Si) substrate was established by the method of mechanics of composite materials. The coupled action between the SMA film and Si substrate under thermal loads was analyzed by combining static equilibrium equations, geometric equations, and physical equations. The material nonlinearity of SMA and the geometric nonlinearity of bending deformation were both considered. By simulating and analyzing the actuation performance of the SMA composite film during one cooling-heating thermal cycle, it is found that the final cooling temperature, boundary condition, and the thickness of SMA film have significant effects on the actuation performance of the SMA composite film. Besides, the maximum deflection of the SMA composite film is affected obviously by the geometric nonlinearity of bending deformation when the thickness of SMA film is very large.

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Van Phu, Khuc, Dao Huy Bich, and Le Xuan Doan. "Nonlinear thermal vibration and dynamic buckling of eccentrically stiffened sandwich-FGM cylindrical shells containing fluid." Journal of Reinforced Plastics and Composites 38, no. 6 (December 1, 2018): 253–66. http://dx.doi.org/10.1177/0731684418814636.

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The governing equations for analysing thermal vibration and dynamic buckling of eccentrically stiffened sandwich functionally graded cylindrical shells full filled with fluid and surrounded by elastic foundations in thermal environment are derived by using the classical shell theory, the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Pasternak’s foundation model. Solutions of the problem are established according to the Galerkin’s method and Runge–Kutta method. The effects of fluid pressure, stiffeners, geometrical ratios, temperature and elastic foundation on the dynamic responses of shells are investigated.

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Ziaee, Sima. "Postbuckling and nonlinear free vibration of size-dependent prestressed FG nanobeams resting on elastic foundation based on nonlocal Euler-Bernoulli beam theory." Journal of the Mechanical Behavior of Materials 24, no. 3-4 (August 1, 2015): 91–103. http://dx.doi.org/10.1515/jmbm-2015-0011.

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AbstractVibrations of micro/nanobeams that are subjected to initial stresses due to mismatch between different materials or thermal stresses are important in some devices. The present study is an attempt to present nonlinear free vibration of simply supported size-dependent functionally graded (FG) nanobeams resting on elastic foundation and under precompressive axial force. It is assumed that the material properties of FG materials are graded in the thickness direction. The partial differential equation of motion, which is simplified into an ordinary differential equation using the Galerkin method, is derived based on Euler-Bernoulli beam theory, von Karman geometric nonlinearity, and Eringen’s nonlocal elasticity theory. The final ordinary differential equation is solved using the variational iteration method. The effects of geometrical parameters, small-scale parameter, elastic coefficient of foundation, precompressive axial force, and neutral axis location on dimensionless nonlinear natural frequencies are investigated. In this study, the buckling and postbuckling behavior of FG nanobeams and the effect of neutral axis location on buckling behavior are investigated as well. Results show that the effects of small scale on FG nanobeam frequencies change with the aspect ratio, the values of radius of gyration, and the values of compressive axial force. It is also found that the influence of neutral axis location on the nonlinear fundamental frequency of prestressed FG nanobeams is more than that of prestressed FG nanobeams resting on elastic foundation.

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34

Nageswara Rao, B., and G. Venkateswara Rao. "Large deflection analysis of cantilever beams of symmetrical cross-section subjected to a rotational distributed loading including the effect of material nonlinearity." Aeronautical Journal 92, no. 916 (July 1988): 230–34. http://dx.doi.org/10.1017/s0001924000016171.

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AbstractCombined effects of geometrical and material non-linearities on a cantilever beam having symmetrical cross-section about its central axis with a rotational distributed loading are studied. It is assumed that the stress-strain relation in compression is identical to that in tension. Due to this, the neutral axis coincides with the central axis of the beam. The problem is formulated by means of an integral equation which is suitably converted to a system of nonlinear ordinary differential equations which are solved using a simple and accurate numerical method. Details of the load deflection characteristics for an I-beam and for a beam of rectangular cross-section are presented.

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Sathyamoorthy, M. "Nonlinear Vibrations of Plates: An Update of Recent Research Developments." Applied Mechanics Reviews 49, no. 10S (October 1, 1996): S55—S62. http://dx.doi.org/10.1115/1.3101977.

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This paper comprises a survey on the nonlinear vibration analysis of plates, with emphasis on research carried out since 1987. Most of the research reviewed here deals with the effects of geometric nonlinearity on the vibration behavior of plates. Complicating factors such as material nonlinearity, geometric imperfections, transverse shear and rotatory inertia effects, and magnetic fields on the vibration behavior are included. Recent developments in the analytical and numerical methods of solution of isotropic, orthotropic as well as laminated, composite plates are presented. Experimental, analytical, and numerical investigations are included for all the cases reviewed and some general remarks are presented along with suggestions for future research directions.

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Savard, M., D. Beaulieu, and M. Fafard. "Nonlinear finite element analysis of three-dimensional frames." Canadian Journal of Civil Engineering 21, no. 3 (June 1, 1994): 461–70. http://dx.doi.org/10.1139/l94-050.

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This paper presents a numerical model for the nonlinear analysis of three-dimensional frames using the finite element method. The model is based on a general variational formulation for thin-walled beams with open or closed sections; the mathematical development uses an updated Lagrangian description for shallow arches, taking into account geometrical and material nonlinearities, residual stresses, member initial imperfections, warping, and connection flexibility. The model has been used to evaluate second-order effects and the influence of residual stresses and joint flexibility on the behavior of plane frames. A semirigid space frame has been analyzed and the gain in rigidity offered by a horizontal rigid diaphragm has been evaluated. Key words: analysis, connection, finite element, nonlinearity, residual stress, thin-walled beams, warping.

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Nam, Vu Hoai, Nguyen Thi Phuong, Cao Van Doan, and Nguyen Thoi Trung. "Nonlinear Thermo-Mechanical Stability Analysis of Eccentrically Spiral Stiffened Sandwich Functionally Graded Cylindrical Shells Subjected to External Pressure." International Journal of Applied Mechanics 11, no. 05 (June 2019): 1950045. http://dx.doi.org/10.1142/s1758825119500455.

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A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners subjected to external pressure is presented in this paper. By employing the Donnell shell theory, the geometrical nonlinearity in Von Kármán sense and developed Lekhnitskii’s smeared stiffener technique, the governing equations of sandwich functionally graded circular cylindrical shells are derived. Resulting equations are solved by applying the Galerkin method to obtain the explicit expression of critical buckling external pressure load and postbuckling load–deflection curve. Effects of spiral stiffeners, thermal environment, external pressure, and geometrical parameters on nonlinear buckling behavior of sandwich functionally graded circular cylindrical shells are shown in numerical results.

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Oliveira, C. E. M., E. A. P. Batelo, P. Z. Berke, R. A. M. Silveira, and T. J. Massart. "Nonlinear analysis of the progressive collapse of reinforced concrete plane frames using a multilayered beam formulation." Revista IBRACON de Estruturas e Materiais 7, no. 5 (October 2014): 845–55. http://dx.doi.org/10.1590/s1983-41952014000500007.

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This work investigates the response of two reinforced concrete (RC) plane frames after the loss of a column and their potential resistance for progressive collapse. Nonlinear dynamic analysis is performed using a multilayered Euler/Bernoulli beam element, including elasto-viscoplastic effects. The material nonlinearity is represented using one-dimensional constitutive laws in the material layers, while geometrical nonlinearities are incorporated within a corotational beam formulation. The frames were designed in accordance with the minimum requirements proposed by the reinforced concrete design/building codes of Europe (fib [1-2], Eurocode 2 [3]) and Brazil (NBR 6118 [4]). The load combinations considered for PC analysis follow the prescriptions of DoD [5]. The work verifies if the minimum requirements of the considered codes are sufficient for enforcing structural safety and robustness, and also points out the major differences in terms of progressive collapse potential of the corresponding designed structures.

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Wu, Jianqiang, Lunting Chen, Ruixian Wu, and Xiaochao Chen. "Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam." Shock and Vibration 2021 (March 27, 2021): 1–13. http://dx.doi.org/10.1155/2021/6675125.

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The nonlinear forced vibration of bidirectional functionally graded porous material beams where the material components gradient change in both thickness and axial directions are studied in this study. Combining von Karman’s geometric nonlinearity and first-order shear deformation theory, the governing equations describing the coupled deformations are formulated as a system of nonlinear partial differential equations. Utilizing the Galerkin method, the formulated continuous model is transformed to a coupled nonlinear ordinary differential dynamic system. By accomplishing bifurcation calculation for periodic response of the discrete system using pseudoarclength technique, the vibration response curves are obtained by extracting the max-min amplitude of periodic motions. To highlight the effect of nonlinearity, the linear and nonlinear dynamic responses of beam are demonstrated. It is found that the periodic motion of beam may undergo cyclic-fold bifurcation. Numerical results are presented to examine the effects of the system parameters, e.g., gradient indexes, porosity, damping coefficients, and aspect ratio.

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Chen, Ling, Dong Hui Chan, and Xiang Qiao. "How to Select the Fire-Resistant Calculation Model for the Completed Steel Structure." Applied Mechanics and Materials 290 (February 2013): 25–30. http://dx.doi.org/10.4028/www.scientific.net/amm.290.25.

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Finite element model of the three-dimension steel frame of sorbic alcohol warehouse is built to study the response of the steel structure on fire. The material nonlinearity and geometrical nonlinearity being aroused by high-temperature are taken into account adequately during this computation. Shell elements are used to model the concrete floor slab，beams as well as columns. The rigid connection and flexible connection between the beams and column are considered respectively. In order to reduce the computing amount, the effects of the completed structure and the neighboring span have been explored under the local fire. It turns out that it has more effects on stresses and deflections in the neighboring span than that in others when the whole structure is under local fire. It has greater deflections when using the rigid connection than using flexible connection between the components. Meanwhile, according to the rules of the stresses and the deflections of the structure, the method of selecting the effective and reasonable simulating areas under the local fire is concluded. The conclusions are important for building the reasonable simulating areas on fire and for further studying the mechanical behaviors of the steel structure, also significant for providing references for the fire-resistant calculation of the completed steel structure.

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Li, Q. S., and J. M. Chen. "Nonlinear Analysis of Single-Layer Reticulated Spherical Shells Under Static and Dynamic Loads." Journal of Vibration and Control 10, no. 5 (May 2004): 731–54. http://dx.doi.org/10.1177/1077546304040236.

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A nonlinear finite element technique is developed for analyzing the nonlinear static and dynamic responses as well as the nonlinear stability of single-layer reticulated shells under external loads, in which the nonlinear three-dimensional beam elements are employed. Using the updated Lagrangian formulation, we derive a tangent stiffness matrix of three-dimensional beam element, considering the geometric nonlinearity of the element. Moreover, the modified Newton-Raphson method is employed for the solution of the nonlinear equilibrium equations, and the Newmark-β method is adopted for determining the seismic response of single-layer reticulated shells. An improved arc-length method, in which the current stiffness parameter is used to reflect the nonlinear degree of such space structures, is presented for determining the load increment for the structural stability analysis. In addition, an accurate incremental method is developed for computing the large rotations of the space structures. The developed approach is presented in matrix form, which is particularly convenient for developing a computer program. Numerical examples are presented to illustrate the application of the present method and to investigate the effects of the geometrical nonlinearity of the space structures.

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Mortazavi, S. M. R., M. Ghassemieh, and M. S. Ghobadi. "Research on the Behavior of the Steel Plated Shear Wall by Finite Element Method." Journal of Structures 2013 (May 30, 2013): 1–9. http://dx.doi.org/10.1155/2013/756253.

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From the early’ 70s till today, steel shear walls have been used as the primary lateral force resisting system in some of the significant buildings around the world. To assist understanding the behavior of this system, there have been research programs in USA, Canada, Japan, and UK. This research presents the dynamic and cyclic behavior of steel plated shear wall. In order to simulate the behavior of such a wall structure, finite element method of analysis is implemented. Several analytical models are implemented, in order to obtain the dynamic as well as cyclic behavior of such system. The material nonlinearity as well as geometrical nonlinearity along with the postbuckling behavior of steel plate subjected to cyclic loading has also been employed. The hysteresis diagrams of steel shear wall system in terms of storey shear drift are presented. The results obtained from the analyses are compared to some experimental results reported by other researchers previously. The nonlinear time history analysis of such system is carried out for different seismic response spectra. Finally, the significant factors and parameters of the steel plated shear wall which affect the overall behavior of such system are acknowledged and their effects were recognized.

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Jiang, Zheng Rong, Kai Rong Shi, Xiao Nan Gao, and Qing Jun Chen. "Analysis of Nonlinear Buckling of a Long-Span Elliptic Paraboloid Suspended Dome Structure." Advanced Materials Research 639-640 (January 2013): 191–97. http://dx.doi.org/10.4028/www.scientific.net/amr.639-640.191.

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The suspended dome structure, which is a new kind of hybrid spatial one composed of the upper single layer latticed shell and the lower cable-strut system, generally has smaller rise-to-span ratio, thus the overall stability is one of the key factors to the design of the structure. The nonlinear buckling behavior of an elliptic paraboloid suspended dome structure of span 110m80m is investigated by introducing geometric nonlinearity, initial geometric imperfection, material elastic-plasticity and half-span distribution of live loads. The study shows that the coefficient of stable bearing capacity usually is not minimal when the initial geometric imperfection configuration is taken as the first order buckling mode. The unsymmetrical loading distribution and the material nonlinearity might have significant effects on the coefficient. The structure is sensitive to the changes of initial geometric imperfection, and the consistent mode imperfection method is not fully applicable to the stability analysis of suspended dome structure.

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Hieu, Pham Thanh, and Hoang Van Tung. "Thermomechanical nonlinear buckling of pressure-loaded carbon nanotube reinforced composite toroidal shell segment surrounded by an elastic medium with tangentially restrained edges." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 9 (September 30, 2018): 3193–207. http://dx.doi.org/10.1177/0954406218802942.

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Buckling and postbuckling behaviors of toroidal shell segment reinforced by single-walled carbon nanotubes, surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes are reinforced into matrix phase by uniform distribution or functionally graded distribution along the thickness direction. Material properties of constituents are assumed to be temperature dependent, and the effective properties of carbon nanotube reinforced composite are estimated by extended mixture rule through a micromechanical model. Governing equations for toroidal shell segments are based on the classical thin shell theory taking into account geometrical nonlinearity, surrounding elastic medium, and varying degree of tangential constraints of edges. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to derive nonlinear load–deflection relation from which buckling loads and postbuckling equilibrium paths are determined. Analysis shows that tangential edge restraints have significant effects on nonlinear buckling of carbon nanotube reinforced composite toroidal shell segments. In addition, the effects of carbon nanotube volume fraction, distribution types, geometrical ratios, elastic foundation, and thermal environments on the buckling and postbuckling behaviors of carbon nanotube reinforced composite toroidal shell segments are analyzed and discussed.

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Chang, Tai Ping. "Stochastic Nonlinear Vibration of Fluid-Loaded Double-Walled Carbon Nanotubes." Applied Mechanics and Materials 284-287 (January 2013): 362–66. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.362.

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This paper investigates the stochastic dynamic behaviors of nonlinear vibration of the fluid-loaded double-walled carbon nanotubes (DWCNTs) by considering the effects of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force. The nonlinear governing equations of the fluid-conveying DWCNTs are formulated based on the Hamilton’s principle. The Young’s modulus of elasticity of the DWCNTs is assumed as stochastic with respect to the position to actually describe the random material properties of the DWCNTs. By utilizing the perturbation technique, the nonlinear governing equations of the fluid-conveying can be decomposed into two sets of nonlinear differential equations involving the mean value of the displacement and the first variation of the displacement separately. Then we adopt the harmonic balance method in conjunction with Galerkin’s method to solve the nonlinear differential equations successively. Some statistical dynamic response of the DWCNTs such as the mean values and standard deviations of the amplitude of the displacement are computed. It is concluded that the mean value and standard deviation of the amplitude of the displacement increase nonlinearly with the increase of the frequencies.

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Nam, Vu Hoai, Nguyen Thi Phuong, Dang Thuy Dong, Nguyen Thoi Trung, and Nguyen Van Tue. "Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 17 (July 8, 2019): 6177–96. http://dx.doi.org/10.1177/0954406219861658.

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In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

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Ji, Ri Chen, Jun He, and Ming Xing Shi. "Stability Analysis of Single-Track Railway Long Span Combination Bridge of Arch and Beam." Advanced Materials Research 383-390 (November 2011): 6079–84. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.6079.

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For the single-track railway concrete-filled steel tube tied-arch bridge, since restrictions of the bridge width will inevitably lead to a relatively smaller ratio of width to span using long span.The stability is a very prominent issue in design and construction. Taking a 136m span through concrete filled steel tube tied-arch bridge as an object, considering the influence of geometric and material nonlinearity of arch rib, its space stability analysis of the whole bridge is made using finite element program. Its stability factor and the instabil-ity mode are given under the most unfavourable load condition. Instability of the structure is mainly shown in out-plane instability of arch rib. Elastic buckling factor is greater than the general requirement, which satisfies the requirement of the bridge elastic stability. The effect of geometric nonlinearity on stability of the bridge is smaller while the effect of material nonlinearity is greater, which should be considered in the stability analysis of long span arch bridge. After the arch ribs are progressively loaded, the ultimate loads of the arch ribs are obtained. Effects and variation law of transverse brace layout, arch rib inclination angle and ratio of height to span of the arch to the stability of this bridge are revealed.

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Zamani Alavije, Rasool, and Mohsen Botshekanan Dehkordi. "Nonlinear bending analysis of shape memory alloy beam considering both material and geometric nonlinearity effects." Journal of Intelligent Material Systems and Structures 30, no. 6 (December 23, 2018): 823–43. http://dx.doi.org/10.1177/1045389x18818781.

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This study examined the nonlinear super-elastic bending of shape memory alloy beam considering the material and geometric nonlinearity effects that coupled together. Shape memory alloy properties change instantaneously at different points in the beam, while they are unknown at the same time. In other words, coupling of the governing and kinetic equations of the shape memory alloy beams together results in a more complicated analysis. In this study, the governing equations were extracted through using the Timoshenko beam theory and applying the principle of virtual work. For achieving this goal, von Karman strains were applied to consider large deflections. The Boyd–Lagoudas three-dimensional constitutive model and return mapping algorithm were also used for shape memory alloy modeling. Furthermore, in order to obtain the characteristics of finite element beam, the Galerkin weighted-residual method was used by developing the iterative nonlinear finite element model. Considering the different supporting conditions and forces for the shape memory alloy beam, this study examined their effects on the distribution of martensitic volume fraction, stress distribution, and changes in the location of the neutral axis. The obtained results revealed that as loading increases, the magnitude of martensitic volume fraction and the level of hysteresis increase, which in turn would result in reduction of the modulus of elasticity and the strength of the material and consequently increases the deflection of shape memory alloy beam. The findings suggested the necessity of nonlinear strain field in this modeling by which the stress distribution and volume fraction become asymmetric along the beam thickness. The results were presented in the forms of loading and unloading diagrams for different support and force conditions, and the martensitic volume fraction along the length and through the thickness of the shape memory alloy beam were also shown. To validate the proposed formulation, the results were compared with other experimental findings in this regard suggesting that there is an acceptable and satisfying level of agreement between them.

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Tung, Hoang Van, Nguyen Dinh Kien, and Le Thi Nhu Trang. "Thermal postbuckling analysis of FG-CNTRC doubly curved panels with elastically restrained edges using Reddy's higher order shear deformation theory." Vietnam Journal of Mechanics 42, no. 3 (September 27, 2020): 307–20. http://dx.doi.org/10.15625/0866-7136/15309.

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For the first time, postbuckling behavior of thick doubly curved panels made of carbon nanotube reinforced composite (CNTRC), under preexisting external pressure and subjected to uniform temperature rise is analyzed in this paper. Carbon nanotubes (CNTs) are reinforced into matrix through functionally graded (FG) distribution patterns, and effective properties of CNTRC are determined according to extended rule of mixture. Formulations are based on a higher order shear deformation theory including Von Karman-Donnell nonlinearity, initial geometrical imperfection and elasticity of tangential constraints of boundary edges. Analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain nonlinear load-deflection relation. Taking into account temperature dependence of material properties, postbuckling temperature-deflection paths are traced through an iteration process. The effects of preexisting external pressure, CNT volume fraction, tangential edge constraints, initial geometrical imperfection and curvature ratios on thermal postbuckling behavior of CNTRC doubly curved panels are analyzed through numerical examples. The study reveals that thermally loaded panels experiences a quasi-bifurcation response due to the presence of preexisting external pressure. For the most part, perfect panels are deflected toward convex side at the onset of undergoing thermal load. Particularly, imperfect panels may exhibit a bifurcation type buckling response when imperfection size satisfy a special condition.

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Panagiotidou, Andriani I., George Gazetas, and Nikos Gerolymos. "Pushover and Seismic Response of Foundations on Stiff Clay: Analysis with P-Delta Effects." Earthquake Spectra 28, no. 4 (November 2012): 1589–618. http://dx.doi.org/10.1193/1.4000084.

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Finite-element analyses are performed for the response to lateral monotonic, slow-cyclic, and seismic loading of rigid footings carrying tall slender structures and supported on stiff clay. The response involves mainly footing rotation under the action of overturning moments from the horizontal external force on—or the developing inertia at—the mass of the structure, as well as from the aggravating contribution of its weight (P-delta effect). Emphasis is given to the conditions for collapse of the soil-foundation-structure system. Two interconnected mechanisms of nonlinearity are considered: detachment from the soil with subsequent uplifting of the foundation (geometric nonlinearity) and formation of bearing-capacity failure surfaces (material inelasticity). The relation between monotonic behavior (static “pushover”), slow-cyclic behavior, and seismic response is explored parametrically. We show that with “light” structures uplifting is the dominant mechanism that may lead to collapse by dynamic instability (overturning), whereas “very heavy” structures mobilize soil failure mechanisms, leading to accumulation of settlement, residual rotation, and ultimately collapse.

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Journal articles on the topic 'Material and Geometrical Nonlinearity Effects'

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