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Journal articles on the topic 'Theory of shells'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Tarn, Jiann-Quo, Yung-Ming Wang, and Shi-Horng Chang. "Theory of Multilayered Anisotropic Shells Based on an Asymptotic Variational Formulation." Journal of Mechanics 14, no. 4 (1998): 173–82. http://dx.doi.org/10.1017/s1727719100000204.

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ABSTRACTA general theory for multilayered anisotropic elastic shells is developed in an asymptotic variational framework of 3-D elasticity. The generic shell continuum considered is heterogeneous through the thickness. It is shown that the classical laminated shell theory based on Love's assumption arises naturally as the first-order approximation to the 3-D theory. Higher-order corrections can be determined by solving the 2-D shell equations hierarchically. The associated edge conditions at each level of approximation are derived. Various types of shells such as shells of revolution, conical

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2

Yang, Yeong-Bin, and Jae-Hoon Kang. "Comparisons of Paraboloidal Shells and Sinusoidal-Shaped Shells in Natural Frequencies." Volume 24, No 3, September 2019 24, no. 3 (2019): 451–57. http://dx.doi.org/10.20855/ijav.2019.24.312.

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Natural frequencies and mode shapes are obtained for a sinusoidal-shaped shell of revolution by using the Ritz method from a three-dimensional (3-D) analysis instead of a mathematically two-dimensional (2-D) thin shell theory or high order thick shell theory. The present analysis uses circular cylindrical coordinates instead of 3-D shell coordinates, which have been used in traditional shell analyses. Convergence studies can analyze the first five frequencies to four-digit exactitude. Results are given for a variety of shallow and deep sinusoidal-shaped shells with different boundary condition

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3

Yang, Yeong-Bin, and Jae-Hoon Kang. "Comparisons of Paraboloidal Shells and Sinusoidal-Shaped Shells in Natural Frequencies." June 2019 24, no. 2 (2019): 451–57. http://dx.doi.org/10.20855/ijav.2019.24.31276.

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Natural frequencies and mode shapes are obtained for a sinusoidal-shaped shell of revolution by using the Ritz method from a three-dimensional (3-D) analysis instead of a mathematically two-dimensional (2-D) thin shell theory or high order thick shell theory. The present analysis uses circular cylindrical coordinates instead of 3-D shell coordinates, which have been used in traditional shell analyses. Convergence studies can analyze the first five frequencies to four-digit exactitude. Results are given for a variety of shallow and deep sinusoidal-shaped shells with different boundary condition

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4

Ovesy, Hamid Reza, and Jamshid Fazilati. "Lay-Up Effects on the Dynamic Instability of Moderately Thick Stiffened Curved Panels." Applied Mechanics and Materials 152-154 (January 2012): 1477–82. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.1477.

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The dynamic instability of cylindrical shell panels having longitudinal stiffener is studied by using the developed finite strip method (FSM). The method is formulated using the third order shear deformation shell's theory of Reddy's form and the Koiter-Sanders theory for cylindrical shells is implemented. The lay-up effects of skin as well as the stiffener are investigated.

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5

Marwah Ghazi Kareem, Saddam Khalsan Al-Raheem, sadiq emad sadiq, and Luay Sadeq Alansari. "Review of research on the vibration and buckling of functionally graded spherical shells." International Journal of Science and Research Archive 13, no. 2 (2024): 2170–86. https://doi.org/10.30574/ijsra.2024.13.2.2327.

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Spherical shells are important components in many aerospace and engineering structures. A functionally graded material (FGM) spherical shell can have its material distribution varied with the change of the radius direction, which can enhance the bearing capacity and the stability of the thin-walled shells. However, due to the special geometric characteristics of the spherical shell, the simplicity of its geometry will lead to great complexity in its vibration and buckling analysis processes. This paper mainly reviews the previous analytical and numerical research on the vibration and buckling

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6

Soldatos, K. P. "Nonlinear Analysis of Transverse Shear Deformable Laminated Composite Cylindrical Shells—Part II: Buckling of Axially Compressed Cross-Ply Circular and Oval Cylinders." Journal of Pressure Vessel Technology 114, no. 1 (1992): 110–14. http://dx.doi.org/10.1115/1.2929000.

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A linearized transverse shear deformable shell theory presented in a companion paper is confined to consideration with the buckling problem of axially compressed, cross-ply laminated noncircular cylindrical shells. Based on a solution of its governing differential equations, obtained for simply supported shells by means of Galerkin’s method, a study of the buckling problem of axially compressed circular and oval cylindrical shells, of a regular antisymmetric cross-ply laminated arrangement, is presented. Moreover, by comparing the numerical results obtained with corresponding results based on

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7

Wen, P. H., and Ferri Aliabadi. "On the Theory of Functionally Graded Moderately Thick Composite Shells." Journal of Multiscale Modelling 05, no. 03 (2013): 1350012. http://dx.doi.org/10.1142/s1756973713500121.

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In this paper, exact solutions for double curved functionally graded shells subjected to static and dynamic distributed loads are presented for the first time. Shear deformable shell theory is used and the governing equations for the laminated and functionally graded shells with respect to the middle surface are presented in the Laplace transform domain. The exact solutions of the laminated and functionally graded shells should serve as benchmark solutions for numerical methods.

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8

Li, Bing Ru, Xuan Yin Wang, Hui Liang Ge, and Yue Peng Jiang. "Study on Applicability of Sound Radiation Characteristics of Thin Finite Length Cylindrical Shells Using Wave Propagation Approach." Applied Mechanics and Materials 190-191 (July 2012): 1325–30. http://dx.doi.org/10.4028/www.scientific.net/amm.190-191.1325.

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Based on Donnell’s thin shell theory and basic equations, the wave propagation method is discussed here in detail, which is used to investigate the vibration and sound radiation characteristics of thin finite length circular cylindrical shells and ring stiffened shells under various boundary conditions. The effects of boundary conditions, mode truncation, shell’s length, thickness and rings on the acoustic radiation are explored. It is shown that the wave propagation method is more effective for the long cylindrical shell, and the mode truncation can satisfy the calculation accuracy. The concl

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9

Li, Bing Ru, Yue Peng Jiang, Xuan Yin Wang, and Hui Liang Ge. "Vibro-Acoustics Characteristics of Non-Uniform Ring Stiffened Cylindrical Shells Using Wave Propagation Approach." Advanced Materials Research 655-657 (January 2013): 562–67. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.562.

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Based on Donnell’s thin shell theory and basic equations, the wave propagation method is discussed here in detail, which is used to investigate the vibration and sound radiation characteristics of non-uniform ring stiffened cylindrical shells under various boundary conditions. The structure damp effects of cylindrical shells are investigated and the ring ribs were considered very narrow, and the rib forces are considered in radial direction. The conclusion are drawn that with the structural loss factor changing large, the whole pressure level are changed little, but the peak of resonance are s

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10

Birman, V. "Extension of Vlasov’s Semi-membrane Theory to Reinforced Composite Shells." Journal of Applied Mechanics 59, no. 2 (1992): 462–64. http://dx.doi.org/10.1115/1.2899547.

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Governing equations for the statics and dynamics of reinforced composite shells are developed based on Vlasov’s semi-membrane shell theory. These equations have closed-form solutions illustrated for buckling and free vibration problems. The buckling solution converges to the known result for unstiffened isotropic shells.

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11

Zannon, Mohammad, and Hussam Alrabaiah. "Mathematical Formulation of Laminated Composite Thick Conical Shells." Journal of Mathematics Research 8, no. 4 (2016): 166. http://dx.doi.org/10.5539/jmr.v8n4p166.

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<span lang="EN-US">The </span><span lang="EN-US">mathematical formulation</span><span lang="EN-US">of thick conical shells using third order shear deformation of thick shell theory are presented. The equations of motion are obtained using Hamilton’s principle. For present analysis, we consider shell's system transverse normal stress, rotary inertia and shear deformation.</span>

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12

Van Dung, Dao, Nguyen Thi Nga, and Pham Minh Vuong. "Nonlinear stability analysis of stiffened functionally graded material sandwich cylindrical shells with general Sigmoid law and power law in thermal environment using third-order shear deformation theory." Journal of Sandwich Structures & Materials 21, no. 3 (2017): 938–72. http://dx.doi.org/10.1177/1099636217704863.

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This paper investigates analytically nonlinear buckling and postbuckling of functionally graded sandwich circular thick cylindrical shells filled inside by Pasternak two-parameter elastic foundations under thermal loads and axial compression loads. Shells are reinforced by closely spaced functionally graded material (FGM) rings and stringers. The temperature field is taken into account. Two general Sigmoid law and general power law, with four models of stiffened FGM sandwich cylindrical shell, are proposed. Using the Reddy’s third-order shear deformation shell theory (TSDT), stress function, a

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13

Ertunç, K., Hakan Dilmaç, and Abdullah Sofiyev. "Investigation of stability behavior of clamped functionally graded cylindrical shells in elastic medium under lateral pressure." UNEC Journal of Engineering and Applied Sciences 5, no. 1 (2025): 5–15. https://doi.org/10.61640/ujeas.2025.0501.

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In this study, the stability analysis of cylindrical shells made of functionally graded materials (FGMs) in an elastic medium under the external pressure is carried out within the framework of Donnell type shell theory. First, the fundamental relations of FGM cylindrical shells are established. Then, the fundamental equations of FGM cylindrical shells on the Pasternak elastic foundation are derived based on Kirchhoff-Love theory (KLT). The fundamental equations are solved with the Galerkin procedure and analytical expression is obtained for critical lateral external pressure of FGM cylindrical

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14

Lai, Jinxing, Chunxia Guo, Junling Qiu, and Haobo Fan. "Static Analytical Approach of Moderately Thick Cylindrical Ribbed Shells Based on First-Order Shear Deformation Theory." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/274091.

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The classical shell theory (CST) without considering the shear deformation has been commonly used in the calculation of shells structures recently. However, the impact of theory of plates and shells subjected to the shear deformation on the calculation is increasingly pronounced along with the wide use of composite laminated structures. In this paper, based on first-order shear deformation theory (FSDT) of cylindrical shells, the displacement control differential equation of moderately thick cylindrical shells has been obtained, so has been the edge force at longitudinal of the shells. Meanwhi

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15

Berezin, Victor, Vyacheslav Dokuchaev, and Yury Eroshenko. "The theory of spherically symmetric thin shells in conformal gravity." International Journal of Modern Physics D 27, no. 06 (2018): 1841012. http://dx.doi.org/10.1142/s0218271818410122.

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The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy–momentum tensor of the thin shell is proportional to Diracs delta-function. We construc

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16

Taber, L. A. "Large Elastic Deformation of Shear Deformable Shells of Revolution: Theory and Analysis." Journal of Applied Mechanics 54, no. 3 (1987): 578–84. http://dx.doi.org/10.1115/1.3173072.

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Large axisymmetric deformation of pressurized shells of revolution is studied. The governing equations include the effects of transverse normal strain and transverse shear deformation for shells composed of an incompressible, hyperelastic material. Asymptotic solutions to the equations are developed which are valid for moderately large strains. Application to Mooney-Rivlin clamped spherical caps reveals that, for large enough bending and stretching, the consequences of shear deformation include: (1) bending moments can decrease at the edge after the load passes a critical point; (2) even thick

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17

Bochkarev, Sergey A., and Valery P. Matveenko. "Stability of Rotating Coaxial Cylindrical Shells Interacting with a Flowing and Rotating Fluid." International Journal of Structural Stability and Dynamics 15, no. 05 (2015): 1450071. http://dx.doi.org/10.1142/s0219455414500710.

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This paper is concerned with the numerical investigation of hydroelastic stability of stationary or rotating coaxial cylindrical shells, interacting with compressible fluid flows having the axial and tangential velocity components. The behavior of a flowing and rotating compressible fluid is considered in the framework of the potential theory. Elastic shells are described using the model of the classical shell theory. Numerical implementation was accomplished based on the semi-analytical variant of the finite element method. The paper presents the results of numerical experiments on the stabil

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18

Zhang, Chao, De Jiang Shang, and Qi Li. "Effect of Drive Location on Vibro-Acoustic Characteristics of Submerged Double Cylindrical Shells with Damping Layers." Applied Mechanics and Materials 387 (August 2013): 59–63. http://dx.doi.org/10.4028/www.scientific.net/amm.387.59.

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Based on the modal superposition method, the analytical model of vibration and sound radiation from submerged double cylindrical shells with damping layers was presented. The shells were described by the classical thin shell theory. The damping layers were described by three-dimensional viscoelastic theory. The annular plates, connecting the double shells, were analyzed with in-plane motion theory. For different drive locations of radial point force on the inner shell, the sound radiated power and the radial quadratic velocity of the model were calculated and analyzed. The results show that ma

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19

Li, Dao Kui, and Yong Jun Lei. "Free Vibration of a Cylindrical Shell with Varied Initial Stresses in Different Longitudinal Sections." Applied Mechanics and Materials 52-54 (March 2011): 717–22. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.717.

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An exact and closed-form solution is obtained for free vibration problems of homogeneous isotropic cylindrical shells, which is under arbitrary boundary conditions and with varied initial stresses in different longitudinal sections. First, the cylindrical shell is divided into multiple sub-shells according to their thicknesses and initial stresses. And the displacement functions of the sub-shell’s middle plane are expanded as trigonometric series in circumferential direction. Then, based on the simplified Donnell shell theory, a set of fundamental dynamic equations, which take initial stresses

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20

Tzou, H. S., and J. P. Zhong. "Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems." Journal of Dynamic Systems, Measurement, and Control 115, no. 3 (1993): 506–17. http://dx.doi.org/10.1115/1.2899129.

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Smart piezoelectric structures, conventional passive materials integrated with piezoelectric sensors, actuators, and control electronics, have great potentials in many engineering applications. This paper is devoted to a new theoretical development of generic piezoelectric shell distributed systems. System electromechanical equations and boundary conditions for a thick piezoelectric shell continuum with symmetrical hexagonal structure (Class C6v = 6 mm) are derived using Hamilton’s principle and linear piezoelectric theory. Further simplification leads to a set of new electromechanical system

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21

Y, Meish, and Meish V. "POSTULATION AND BUILDING OF A NUMERICAL ALGORITHM FOR SOLVING THE PROBLEMS OF THE DYNAMICS OF THE THEORY OF CONICAL SHELLS IN NONORTHOGONAL COORDINATE SYSTEM." National Transport University Bulletin 1, no. 46 (2020): 211–17. http://dx.doi.org/10.33744/2308-6645-2020-1-46-211-217.

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The paper presents the formulation and numerical algorithm for solving problems of the dynamics of the theory of conical shells in a non-orthogonal coordinate system. The object of the study are conical shells, the equations of which are represented in non-orthogonal coordinate system. Purpose of the work is to formulate and construct a numerical algorithm for solving the problems of the dynamics of conical shells in a non-orthogonal coordinate system. The methods of research include the basic principles of the theory of shells to Tymoshenko's type and numerical methods. The formulation of pro

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22

Tyurikov, E. V. "On the Construction of Mathematical Models of the Membrane Theory of Convex Shells." Advanced Engineering Research 23, no. 1 (2023): 17–25. http://dx.doi.org/10.23947/2687-1653-2023-23-1-17-25.

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Introduction. The paper considers the issues of constructing mathematical models of the momentless equilibrium stress state of elastic convex shells using methods of the complex analysis. At the same time, shells with a piecewise smooth (ribbed) lateral surface were considered for the first time. The work objective was to find classes of shells for which it is possible to build meaningful mathematical models.Materials and Methods. Using the methods of the theory of the discontinuous Riemann-Hilbert problem for generalized analytic functions, a criterion for the unconditional solvability of the

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23

Zhang, Shi, Yun Zhang, Zhigao Huang, Huamin Zhou, and Jianhui Li. "The inter-element coupling effect of triangular flat shells." Engineering Computations 32, no. 7 (2015): 1959–80. http://dx.doi.org/10.1108/ec-11-2014-0230.

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Purpose – The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary. Design/methodology/approach – In this paper, three triangular flat shells developed by combining an excellent membrane element (OPT) with three outstanding plate bending elements (DKT, RDKTM and DST-BK), respectively, are used to study this phenomenon. Benchmark tests are implemented to evaluate the performance of three selected plate elements and the formulated flat shells. Findings – The inter-element coupling effect

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24

Li, Yu Kun, Wen Hong Sun, Guan Duan, and Jun Hui Liang. "Stress Calculation for Large Storage Oil Tanks' Shells Based on the Theory of Short Cylindrical Shell." Advanced Materials Research 602-604 (December 2012): 2163–69. http://dx.doi.org/10.4028/www.scientific.net/amr.602-604.2163.

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This article adopts Krylov’s functions, getting a general solution of deflection differential equation of short cylindrical shell. Due to the general solution and continuity and smoothness conditions of shell’s deflection, detailed calculating formulas about deformation and stress of large diameter cylindrical shells with cross-section are obtained, whose solving process is realized by programming. Taking a running tank for example, the method deduced in this article calculates its deformation and stress. Compared with the FE (finite element) calculation results and the test data, this method

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25

Velikanov, P. G., and Y. P. Artyukhin. "GENERAL THEORY OF ORTHOTROPIC SHELLS. PART I." Vestnik of Samara University. Natural Science Series 28, no. 1-2 (2022): 46–54. http://dx.doi.org/10.18287/2541-7525-2022-28-1-2-46-54.

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Modern mechanical engineering sets the tasks of calculating thin-walled structures that simultaneously combine sometimes mutually exclusive properties: lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of orthotropic materials and plastics seems quite justified.The article demonstrates the complex representation method of the equations of the orthotropic shells general theory, which allowed in a complex form to significantly reduce the number of unknowns and the order of the system of differential equations. A feature of the proposed

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26

Velikanov, P. G., and Y. P. Artyukhin. "GENERAL THEORY OF ORTHOTROPIC SHELLS. PART II." Vestnik of Samara University. Natural Science Series 28, no. 3-4 (2023): 40–52. http://dx.doi.org/10.18287/2541-7525-2022-28-3-4-40-52.

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Modern mechanical engineering sets the tasks of calculating thin-walled structures that simultaneously combine sometimes mutually exclusive properties: lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of orthotropic materials and plastics seems quite justified.The article demonstrates the complex representation method of the equations of orthotropic shells general theory, which allowed in a complex form to significantly reduce the number of unknowns and the order of the system of diferential equations. A feature of the proposed techn

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27

Gubeladze, Gocha, and Paata Geradze. "A Mathematical Model of the Strain and Stress Kinetics during Welding of Thin-Walled Products." MATEC Web of Conferences 249 (2018): 02005. http://dx.doi.org/10.1051/matecconf/201824902005.

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The paper dwells on the mathematical model of the strain and stress of the elements of the thin-walled systems. A version of the sophisticated theory of shells with the use of several base surfaces has been developed at the Kutaisi Technical University [3,8]. The theory is based on a kinematic hypothesis thereby facilitating the construction of a three-dimensional field of deformation of shell by deformation of two or more surfaces. The use of several base surfaces allows not only for accounting the transverse shears and crimping, but also, with account for the shell thickness, for modeling th

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28

Lim, Teik Cheng. "Spherical Auxetic Shells." Advanced Materials Research 804 (September 2013): 146–50. http://dx.doi.org/10.4028/www.scientific.net/amr.804.146.

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Materials that exhibit negative Poissons ratio are called auxetic materials. Although such materials are quite rare, they nevertheless exist as naturally occurring materials and artificially made materials. Due to their unique material properties, auxetic materials have been intensively investigated for the past 20 years. This paper studies the effect of auxeticity on the maximum stresses in spherical shells. The results suggest that auxetic materials are not suitable for shells with built-in edge, but highly suitable for shells that are simply supported. For the latter boundary condition, it

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29

Shi, He, Wang, Ma, and Shu. "Wave Based Method for Free Vibration Analysis of Cross-Ply Composite Laminated Shallow Shells with General Boundary Conditions." Materials 12, no. 23 (2019): 3808. http://dx.doi.org/10.3390/ma12233808.

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In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulat

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Dahno, A., Yu Smirnov, A. Mashkov, and E. Ryzhenko. "DEFORMATION OF THE PACKING ELEMENT WHEN THE DIFFERENT PRESSURE IN THE BOREHOLE." Construction Materials and Products 2, no. 4 (2020): 27–38. http://dx.doi.org/10.34031/2618-7183-2019-2-4-27-38.

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a method for calculating the stress-deformed condition of the packing element shells reinforced with a system of metal tapes is proposed. The whole process of deformation of the shell under the influence of internal overpressure is conventionally divided into four stages. For each stage, the scheme of deformation of the shell is considered and the solution of the problem is given on the basis of the nonlinear theory of elasticity and the theory of soft shells. All stages of shell deformation considered in this paper are illustrated by the calculation scheme. An example of shell calculation wit

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31

Godin, Oleg A. "Sound scattering and radiation suppression by pressurized spherical shells." Journal of the Acoustical Society of America 154, no. 5 (2023): 3223–36. http://dx.doi.org/10.1121/10.0022416.

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Thin-shell models offer important insights into the complex process of sound-structure interaction but are found to be inconsistent with the rigorous thick-shell theory for fluid-loaded spherical shells. Here, linearized equations of motion of fluid-loaded, thin, spherical shells are re-derived from the first principles. The shell may be prestressed due to the difference in the static pressures in the internal and external fluids. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived of th

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Roohbakhshan, Farshad, and Roger A. Sauer. "Isogeometric nonlinear shell elements for thin laminated composites based on analytical thickness integration." Journal of Micromechanics and Molecular Physics 01, no. 03n04 (2016): 1640010. http://dx.doi.org/10.1142/s2424913016400105.

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This paper presents two different formulations for the modeling of thin laminated composite shells, which do not need any numerical integration through the shell thickness. The two proposed formulations are suitable for thin rotation-free shells based on Kirchhoff–Love kinematics. The composite shell is modeled in the framework of equivalent single layer (ESL) theory and the kinematics are adopted from classical laminated plate theory. The two formulations allow for any desired nonlinear isotropic or anisotropic material model as well as arbitrary large strains and deformations. The presented

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Kang, Jae-Hoon, and Arthur W. Leissa. "Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory." Journal of Applied Mechanics 72, no. 5 (2005): 797–800. http://dx.doi.org/10.1115/1.1989355.

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A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

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34

Cheng, Zhen-qiang, and S. Kitipornchai. "Nonlinear Theory for Composite Laminated Shells With Interfacial Damage." Journal of Applied Mechanics 65, no. 3 (1998): 711–18. http://dx.doi.org/10.1115/1.2789115.

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Interfacial damage is incorporated in the proposed nonlinear theory. for composite laminated shells. A spring-layer model is employed to characterize damaged interfaces spanning from perfect bonding to different degrees of imperfect bonding in shear. By enforcing compatibility conditions for transverse shear stresses both at interfaces and on two bounding surfaces of a laminated shell, only five unknowns are needed for modeling its behavior. The principle of virtual work is used to derive the governing equations, which are of 14th order in lines of curvature coordinates, variationally self-con

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35

Steigmann, David J. "Asymptotic theory for thin two-ply shells." Vietnam Journal of Mechanics 42, no. 3 (2020): 269–82. http://dx.doi.org/10.15625/0866-7136/15337.

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We develop an asymptotic model for the finite-deformation, small-strain response of thin laminated shells composed of two perfectly bonded laminae that exhibit reflection symmetry of the material properties with respect to an interfacial surface. No a priori hypotheses are made concerning the kinematics of deformation. The asymptotic procedure culminates in a generalization of Koiter's well-known shell theory to accommodate the laminated structure, and incorporates a rigorous limit model for pure bending.

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36

Eslami, M. R., and M. Shariyat. "Elastic, Plastic, and Creep Buckling of Imperfect Cylinders Under Mechanical and Thermal Loading." Journal of Pressure Vessel Technology 119, no. 1 (1997): 27–36. http://dx.doi.org/10.1115/1.2842263.

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Based on the concept of secant and tangent modulus, the nonlinear equilibrium and stability equations of thin cylindrical shells under axial compression, external pressure, or external fluid pressure are derived. The resulting equations are applicable to shells without length limitation as the rotations and transverse shears are included in the derivations. The reduction factors for plastic and creep buckling are then obtained. A procedure for determining secant and tangent modulus in the very general case of elastic, plastic, or creep stress in the presence of temperature gradient is proposed

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37

Astakhova, Avgustina. "Calculation of thin isotropic shells beyond the elastic limit by the method of elastic solutions." MATEC Web of Conferences 196 (2018): 01014. http://dx.doi.org/10.1051/matecconf/201819601014.

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The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tens

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38

Pang, Fuzhen, Chuang Wu, Hongbao Song, and Haichao Li. "The free vibration characteristics of isotropic coupled conical-cylindrical shells based on the precise integration transfer matrix method." Curved and Layered Structures 4, no. 1 (2017): 272–87. http://dx.doi.org/10.1515/cls-2017-0018.

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Abstract Based on the transfer matrix theory and precise integration method, the precise integration transfer matrix method (PITMM) is implemented to investigate the free vibration characteristics of isotropic coupled conicalcylindrical shells. The influence on the boundary conditions, the shell thickness and the semi-vertex conical angle on the vibration characteristics are discussed. Based on the Flügge thin shell theory and the transfer matrix method, the field transfer matrix of cylindrical and conical shells is obtained. Taking continuity conditions at the junction of the coupled conical-

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Ivanov, Vyacheslav N., and Alisa A. Shmeleva. "Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces." Structural Mechanics of Engineering Constructions and Buildings 16, no. 1 (2020): 38–44. http://dx.doi.org/10.22363/1815-5235-2020-16-1-38-44.

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The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scien

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Evans, Arthur A., Basanta Bhaduri, Gabriel Popescu, and Alex J. Levine. "Geometric localization of thermal fluctuations in red blood cells." Proceedings of the National Academy of Sciences 114, no. 11 (2017): 2865–70. http://dx.doi.org/10.1073/pnas.1613204114.

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The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, “singular lines,” leads

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Karpov, Vladimir, and Lidiya Kondratyeva. "Justification of Using Delta-Functions in the Theory of Shells Featuring Irregularities." Applied Mechanics and Materials 725-726 (January 2015): 796–801. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.796.

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The delta-functions are used in calculation of the building structures to determine irregularity places, but the delta-function proper is a limiting function featuring no geometrical interpretation. In order to justify correctness of its application, it is necessary to carry out the limiting transition based on the method of variation limiting transformations. Consideration is given to the shallow shells supported by the narrow ribs or featuring jogs of the middle surface. The places of discrete variation of shell thickness or its curvature will be set by means of singular columnar functions.

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Nwoji, C. U., D. G. Ani, O. A. Oguaghamba, and V. T. Ibeabuchi. "Static Bending of Isotropic Circular Cylindrical Shells Based on the Higher Order Shear Deformation Theory of Reddy and Liu." International Journal of Applied Mechanics and Engineering 26, no. 3 (2021): 141–62. http://dx.doi.org/10.2478/ijame-2021-0041.

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Abstract In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analy

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Hayek, Sabih I., and Jeffrey E. Boisvert. "Vibration of elliptic cylindrical shells: Higher order shell theory." Journal of the Acoustical Society of America 128, no. 3 (2010): 1063. http://dx.doi.org/10.1121/1.3466873.

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Pasternak, Hartmut, Zheng Li, Algirdas Juozapaitis, and Alfonsas Daniūnas. "Ring Stiffened Cylindrical Shell Structures: State-of-the-Art Review." Applied Sciences 12, no. 22 (2022): 11665. http://dx.doi.org/10.3390/app122211665.

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The cylindrical shell is a widely used structure in engineering practice, and its main form of failure is instability due to buckling. As a classical problem in the field of mechanics, the stability of cylindrical shells has been studied extensively. However, the large difference between the theoretically predicted results of the critical buckling load and the experimental results for the cylindrical shells subjected to uniform axial pressure has contributed to the continuous development of the shell stability theory. This paper briefly reviews the development of the shell stability theory, th

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PENG, Fan, Weili MA, Yu'e MA, Wei HUANG, and Xianfang LI. "Study on fracture of hyperelastic Kirchhoff-Love plates and shells by phase field method." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 42, no. 4 (2024): 597–605. http://dx.doi.org/10.1051/jnwpu/20244240597.

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Thin walled structures such as plates and shells are widely used in many engineering fields. To Predict its fracture behavior is of great significance for integrity design and strength evaluation of engineering structures. Numerical simulation of the fracture behavior of hyperelastic plates and shells is a challenge due to complex kinematic description, hyperelastic constitutive relationship, geometric nonlinearity and the degradation on elastic parameter caused by fracture damage. Combining Kirchhoff Love (K-L) shell theory with the fracture phase field method, and numerically discretizing th

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Kardomateas, G. A. "Buckling of Thick Orthotropic Cylindrical Shells Under External Pressure." Journal of Applied Mechanics 60, no. 1 (1993): 195–202. http://dx.doi.org/10.1115/1.2900745.

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An elasticity solution to the problem of buckling of orthotropic cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. The results show that the shell theory predictions can produce nonconservative results on the critical load of composite shells with moderately thick construction. The solution provides a means of accurately assessing the limitations of shell theories in predicting stability loss.

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Sayyad, Atteshamuddin Shamshuddin, and Yuwaraj M. Ghugal. "Assessment of refined higher order theories for the static and vibration analysis of laminated composite cylindrical shells." Journal of Mechanical Engineering and Sciences 16, no. 2 (2022): 8848–61. http://dx.doi.org/10.15282/jmes.16.2.2022.04.0700.

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In the present study, a generalized shell theory is presented and applied for the analysis of laminated composite cylindrical shells. A theoretical unification of the several refined shell theories is presented. The principle of work done is employed to derive five differential equations corresponding to five unknowns involved in the present generalized shell theory. Five differential equations are solved by an analytical procedure suggested by the Navier. The numerical results for simply supported laminated composite cylindrical shells are presented and compared with 3D elasticity solutions.

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Ren, Hong Jun, Bo Ping Wang, Xu Yuan Song, and Qing Kai Han. "Free Vibration of a CLD Combination Cylindrical Shells." Advanced Engineering Forum 2-3 (December 2011): 918–23. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.918.

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Based on elasticity plate theory and the theory of viscoelasticity, the solution of the natural frequency and dissipation factor are given under different boundary conditions. In this paper, the differential equation of the cylindrical shells is set up based on Love shell theory. Then the transfer matrix method is introduced to calculate the entirety transfer matrix and the expression of different frequency and dissipation factor. At last the natural character of CLD cylindrical shell under two different boundary conditions is researched.

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Tho Hung, Vu, Dang Thuy Dong, Nguyen Thi Phuong, et al. "Nonlinear Buckling Behavior of Spiral Corrugated Sandwich FGM Cylindrical Shells Surrounded by an Elastic Medium." Materials 13, no. 8 (2020): 1984. http://dx.doi.org/10.3390/ma13081984.

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This paper presents a semi-analytical approach for investigating the nonlinear buckling and postbuckling of spiral corrugated sandwich functionally graded (FGM) cylindrical shells under external pressure and surrounded by a two-parameter elastic foundation based on Donnell shell theory. The improved homogenization theory for the spiral corrugated FGM structure is applied and the geometrical nonlinearity in a von Karman sense is taken into account. The nonlinear equilibrium equation system can be solved by using the Galerkin method with the three-term solution form of deflection. An explicit so

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Zannon, Mohammad. "Fundamental Frequency of Laminated Composite Thick Spherical Shells." Journal of Mathematics Research 11, no. 1 (2019): 57. http://dx.doi.org/10.5539/jmr.v11n1p57.

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In this study, we apply third-order shear deformation thick shell theory to analytically derive the frequency characteristics of the free vibration of thick spherical laminated composite shells. The equations of motion are derived using Hamilton&rsquo;s principle of minimum energy and on the basis of the relationships between forces, moments, and stress displacements in the shell.  We confirm the derived equations and analytical results through the finite element technique by using the well-known software packages MATLAB and ANSYS. We consider the fundamental natural frequencie

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