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1
Radchenko, V. P., O. S. Afanaseva, and V. E. Glebov. "The effect of surface plastic hardening technology, residual stresses and boundary conditions on the buckling of a beam." PNRPU Mechanics Bulletin, no. 1 (December 15, 2020): 87–98. http://dx.doi.org/10.15593/perm.mech/2020.1.07.
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The complex influence of the surface plastic hardening technology, residual stresses, and boundary conditions on the bending of a hardened beam of EP742 alloy was performed. A phenomenological method of restoring the fields of residual stress and plastic deformations performed by its experimental verification in the particular case of ultrasonic hardening is given. The correspondence of the calculated and experimental data for the residual stresses is observed. For assess the influence of the formed residual stresses on convex cylinders, the calculation methods are used for initial strains based on using analogies between the initial (residual) plastic strains and temperature strains in an inhomogeneous temperature field. This allowed us to reduce the consideration of the problem to the problem of thermoelasticity, which was further solved by numerical methods. The effect of four types of boundary conditions for fixing the ends of the beams (rigid fastening and articulation of the ends and ribs in various combinations, cantilever) on the shape and size of the bending of the beam 10×10×100 mm after ultrasonic hardening is studied in detail. It was found that the minimum deflection is observed with a hard seal of both ends of the beam. The effect of the thickness of the beam, which varied from 2 to 10 mm, on their buckling under the same distribution of residual stresses in the hardened layer was studied, and the nonlinear nature of the increase in the deflection boom with decreasing thickness for all types of boundary conditions was established. It is shown that under all boundary conditions, the curvature along the length of the beam practically does not change, therefore it can be considered constant. The consequence of this is the preservation of the hypothesis of flat sections after the hardening procedure, which is confirmed by the calculated profile of the beam section in plane symmetry, close to a straight line. The influence of the anisotropy of surface plastic hardening on the buckling of the beam was found to be significant, which can serve as the basis for choosing the optimal hardening procedure. The performed parametric analysis of the task is presented in the form of graphical and tabular information on the results of the calculations.
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Sridharan, Srinivasan. "Imperfection Sensitivity of Stiffened Cylindrical Shells Under Interactive Buckling." Applied Mechanics Reviews 47, no. 6S (June 1, 1994): S251—S255. http://dx.doi.org/10.1115/1.3124418.
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In this paper some recent advances made in the understanding of the phenomena and computational modelling of the interaction of local and overall instabilities in stiffened cylindrical shells will be reviewed. These relate to two distinct categories of problems: (1) Axially compressed stringer-stiffened shells and (2) Ring-stiffened cylinders subjected to hydrostatic compression. The former have been analyzed with a novel methodology which employs finite elements in which the local buckling information is embedded. Comparisons of the results of the new technique with Abaqus - a well established nonlinear analysis program - reveals the validity of the underlying concepts of the new technique and efficacy of the new approach. It is shown, that provided all the key local buckling modes triggered in the interaction are considered and the modulation of local buckling amplitudes is accounted for, it is justifiable to neglect the mixed second order stresses and strains in the analysis. Imperfection-sensitivity of a stringer stiffened cylindrical shell structure is illustrated. In the case ring-stiffened cylinders subjected to hydrostatic pressure, it is shown that the amplitude modulation is the key factor in the interaction; it performs the function of capturing the contributions of several neighboring modes of the same longitudinal description as the fundamental local mode, but with differing circumferential wave numbers. An examination of the potential energy function indicates that the amplitude modulation is solely responsible for the presence of the nonvanishing cubic terms, which are dominant over the quartic terms. Once again, mixed second order fields evaluated with appropriate orthogonality conditions have little influence on the interaction and can be safely neglected. An example of an orthotropic layered shell under coincident and well separated critical stresses is presented.
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Tsai, Wan T. "Stresses and Strains of Radially Reinforced Hollow Cylinders." Journal of Engineering Mechanics 113, no. 2 (February 1987): 281–87. http://dx.doi.org/10.1061/(asce)0733-9399(1987)113:2(281).
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Chau, K. T. "Antisymmetric Bifurcations in a Compressible Pressure-Sensitive Circular Cylinder Under Axisymmetric Tension and Compression." Journal of Applied Mechanics 60, no. 2 (June 1, 1993): 282–89. http://dx.doi.org/10.1115/1.2900791.
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This paper examines antisymmetric bifurcations of geometric diffuse modes, including buckling and surface rumpling modes, for a compressible pressure-sensitive circular cylinder of finite length under axisymmetric loadings. The analysis includes the effects of nonnormality, transverse isotropy, and confining stress on the appearance of antisymmetric geometric diffuse modes and their relationship to the onset of localization. The long wavelength limit of the eigenvalue equation is found corresponding to the Euler’s buckling load; the short wavelength limit corresponds to the eigenstress for the surface rumpling mode if the cylinder is incompressible and satisfies plastic normality. If the lateral stress is nonzero, a finite solution exists for the antisymmetric long wavelength limit; for the cases that the in-plane bulk modulus becomes unbounded, this finite eigenstress equals to the plane-strain results obtained by Chau and Rudnicki (1990). The lowest possible bifurcation stresses are plotted for various constitutive parameters by combining the results of the bifurcation analyses for both the axisymmetric (Chau, 1992) and the antisymmetric modes. This eigenvalue surface also provides a condition that determines whether buckling (antisymmetric) or bulging (axisymmetric) appears first for a fixed specimen geometry under compression. For typical specimen size (length/radius ratio from 4 to 6), the numerical results suggest that the first possible bifurcation is always the antisymmetric buckling mode under compression; however, for specimen sizes with length/radius ratio approximately less than π/2, bulging mode becomes the first possible bifurcation. The hypothesis that the prepeak and antisymmetric bifurcation triggers the subsequent localization of deformation is further discussed.
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Kabir, Mohammad Zaman, and Mehdi Parvizi. "The effects of residual stresses and strains on lateral-torsional buckling behavior of cold-formed steel channel and built-up I-sections beams." International Journal of Structural Integrity 10, no. 2 (April 8, 2019): 230–43. http://dx.doi.org/10.1108/ijsi-07-2018-0044.
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Purpose The purpose of this paper is to focus on the influences of residual stresses which were induced during roll-forming sections on lateral-torsional buckling of thin-walled cold-formed steel channel and built-up I-sections beams. Built-up I section is made up of two back-to-back cold-formed channel beams. In this direction, at the primary stage, the roll-forming process of a channel section was simulated in ABAQUS environment and the accuracy of the result was verified with those existing experiments. Residual stresses and strains in both longitudinal and circumferential transverse directions were extracted and considered in the lateral-torsional buckling analysis under uniform end moments. The contribution of the current research is devoted to the numerical simulation of the rolling process in ABAQUS software enabling to restore the remaining stresses and strains for the buckling analysis in the identical software. The results showed that the residual stresses decrease considerably the lateral-torsional buckling strength as they have a major impact on short-span beams for channel sections and larger span for built-up I sections. The obtained moment capacity from the buckling analysis was compared to the predictions by American Iron and Steel Institute design code and it is found to be conservative. Design/methodology/approach This paper has explained a numerical study on the roll-forming process of a channel section and member moment capacities related to the lateral-torsional buckling of the rolled form channel and built-up I-sections beams under uniform bending about its major axis. It has also investigated the effects of residual stresses and strains on the behaviour of this buckling mode. Findings The residuals decrease the moment capacities of the channel beams and have major effect on shorter spans and also increase the local buckling strength of compression flange. But the residuals have major effect on larger spans for built-up I sections. It could be seen that the ratio of moment (with residuals and without residuals) for singly symmetric sections is more pronounced than doubly symmetric sections. So it is recommended to use doubly symmetric section of cold-formed section beams. Originality/value The incorporation of residual stresses and strains in the process of numerical simulation of rolled forming of cold-formed steel sections under end moments is the main contribution of the current work. The effect of residual stresses and strains on the lateral-torsional buckling is, for the first time, addressed in the paper.
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Dhanens, F., G. Lagae, J. Rathé, and R. Van Impe. "Stresses in and buckling of unstiffened cylinders subjected to local axial loads." Journal of Constructional Steel Research 27, no. 1-3 (January 1993): 89–106. http://dx.doi.org/10.1016/0143-974x(93)90008-g.
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Eggert, R. J. "Design Variation Simulation of Thick-walled Cylinders." Journal of Mechanical Design 117, no. 2A (June 1, 1995): 221–28. http://dx.doi.org/10.1115/1.2826126.
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Thick-walled cylinders exposed to high, static internal pressures may experience both elastic and plastic deformation. Primary design considerations include loads, geometry and material properties. However, variations in geometry and material properties due to conventional manufacturing processes, and variations of internal pressure due to actual usage patterns, propagate through the system resulting in off-design stresses and strains which may cause failure. These variations can be evaluated using probabilistic methods which are discussed in this paper. Von Mises-distortion energy yield theory is presented to predict elastic, plastic and residual stresses in thick-walled cylinders. The design variation simulation method using Monte Carlo simulation and available statistical information is used to design a pressure vessel for servo-hydraulic experiments. The use of autofrettage to induce favorable compressive stresses at the inner bore, thereby improving the margin of safety and overall reliability, is also presented.
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Cheng, Weili, and Iain Finnie. "Measurement of Residual Hoop Stresses in Cylinders Using the Compliance Method." Journal of Engineering Materials and Technology 108, no. 2 (April 1, 1986): 87–92. http://dx.doi.org/10.1115/1.3225864.
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A method is proposed for measurement of the hoop stress in an axisymmetric residual stress field in cylinders in which the axial stress is independent of the axial coordinate. The method involves measuring strains at the outside surface while an axial crack is cut progressively from the outside. Experimental results are presented for two short cylindrical rings cut from a long quenched cylinder. Good general agreement is obtained with X-ray and hole drilling measurements of residual stresses.
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Eremeev, Vadim V., and Leonid M. Zubov. "Buckling of a two-layered circular plate with a prestressed layer." Mathematics and Mechanics of Solids 22, no. 4 (November 16, 2015): 773–81. http://dx.doi.org/10.1177/1081286515612527.
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Within the framework of nonlinear elasticity we analyze instability of a uniformly compressed circular two-layered plate with an initially compressed or stretched layer. For a constitutive relation of the material we use the incompressible neo-Hookean model. We assume that the lower layer is subjected to radial tension or compression. As a result in this layer there are initial strains and stresses. The two-layered plate is subjected to a uniform lateral compression. We study the stability of the plate with the use of the static Euler method. Within the method we determine loading parameters for which the linearized boundary-value problem has non-trivial solutions. We derive the three-dimensional linearized equilibrium equations for each layer. The solutions of the latter equations are obtained with the help of the Fourier method. The equation for critical strains is derived. We present an analysis of dependence of critical stress resultants on the initial strains and stiffness parameters.
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Christoforou, A. P., and S. R. Swanson. "Strength Loss in Composite Cylinders Under Impact." Journal of Engineering Materials and Technology 110, no. 2 (April 1, 1988): 180–84. http://dx.doi.org/10.1115/1.3226028.
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The problem of strength loss in composite structures due to impact appears to be important due to the sensitivity of advanced composites to these loadings. Although a number of studies have been carried out on impact of flat composite plates, relatively little work has been done on tubular geometries such as pressure vessels despite the usage in applications. We have addressed the problem of calculating strength loss due to low velocity, lateral impact of composite cylinders. In our model we use an existing Fourier Series expansion procedure to calculate ply stresses and strains, compare these values with allowables to predict fiber breakage during the impact, and finally use fracture mechanics to predict the strength loss due to the impact. Although the model is quite simplified, the general trends of experiments appear to be represented.
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Garg, Manish, Dharmpal Deepak, and V. K. Gupta. "FE modeling of creep in linear and non-linear FGM cylinder under internal pressure." Multidiscipline Modeling in Materials and Structures 10, no. 1 (June 3, 2014): 94–105. http://dx.doi.org/10.1108/mmms-10-2012-0016.
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Purpose – The purpose of this paper is to investigate creep in an internally pressurized thick-walled, closed ends cylinder made of functionally graded composite, having linear and non-linear distribution of reinforcement, using finite element (FE) analysis. Design/methodology/approach – FE-based Abaqus software is used to investigate creep behavior of a functionally graded cylinder. The cylinder is made of composite containing linear and non-linearly varying distributions of reinforcement along the radius. The creep behavior has been described by Norton's power law. The creep stresses and strains have been estimated in linear and non-linear functionally graded materials (FGM) cylinders and compared with those estimated for a similar composite cylinder but having uniform distribution of reinforcement. Findings – The radial stress in the composite cylinder is observed to decreases over the entire radius upon imposing linear or non-linear reinforcement gradients. However, the tangential stress in the cylinder increases near the inner radius but decreases toward the outer radius, on imposing linear or non-linear reinforcement gradients. The creep strains in the FGM cylinders are significantly lower than those observed in a uniform composite cylinder. Originality/value – The creep strains in an internally pressurized functionally graded thick composite cylinder could be reduced significantly by employing non-linear distribution of reinforcement along the radial direction.
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Kollår, Låszló P. "Approximate Analysis of the Temperature Induced Stresses and Deformations of Composite Shells." Journal of Composite Materials 28, no. 5 (March 1994): 392–414. http://dx.doi.org/10.1177/002199839402800502.
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In this paper simple formulas are presented which can be used to estimate the response of composite plates and shells to hygrothermal loads. The layup of the shell can be arbitrary (i.e., it can be symmetric or unsymmetric, balanced or unbalanced). The formulas serve two purposes. First, they can be used to calculate directly the stresses, strains, and displacements caused by a temperature and a moisture gradient. Second, the formulas can be used to determine the“effective”thermal and moisture expansion coefficients which are the parameters needed in more accurate numerical (FEM) calculations. The accuracies of the approximate formulas were assessed by sample problems. In these problems the hygrothermal deformations of cylinders and cylindrical segments were calculated by the present approximate formulas and by an exact, three-dimensional analysis. The results of the exact and approximate methods were compared. These comparisons showed that the approximate formulas yield the deformations with a high degree of accuracy.
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Moayedi, H., H. Aliakbarlou, M. Jebeli, O. Noormohammadiarani, M. Habibi, H. Safarpour, and L. K. Foong. "Thermal Buckling Responses of a Graphene Reinforced Composite Micropanel Structure." International Journal of Applied Mechanics 12, no. 01 (January 2020): 2050010. http://dx.doi.org/10.1142/s1758825120500106.
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This is the first research on the thermal buckling analysis of graphene nanoplatelets reinforced composite (GPLRC) doubly curved open cylindrical micropanel in the framework of numerical-based two-dimensional generalized differential quadrature method (2D-GDQM). Additionally, the small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The stresses and strains are obtained using the high-order shear deformable theory (HOSDT). The rule of mixture is employed to obtain varying thermal expansion, and Poisson’s ratio, while module of elasticity is computed by modified Halpin–Tsai model. In addition, nonlinear temperature changes along the GPLRC micropanel’s thickness direction. Governing equations and boundary conditions of the GPLRC doubly curved open cylindrical micropanel are obtained by implementing the extended Hamilton’s principle. Besides, for the validation of the results, the results of current model are compared to the results acquired from analytical method. The results show that GPL weight function ([Formula: see text], the ratio of shell curvatures ([Formula: see text]/[Formula: see text], NSG parameters, and geometric parameters have a significant influence on the thermal buckling characteristics of the GPLRC doubly curved open cylindrical micropanel.
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Tsai, C. T., O. W. Dillon, and R. J. De Angelis. "Techniques to Predict Dislocation Generation During Growth of Silicon Ribbon." Journal of Engineering Materials and Technology 109, no. 3 (July 1, 1987): 209–15. http://dx.doi.org/10.1115/1.3225965.
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This paper describes the numerical techniques that are used to predict stresses, strains, dislocation densities, and buckling during the growth of flat plate silicon. High quality silicon ribbon would be an ideal starting material for manufacturing solar cells for electrical power generation. The techniques developed are uniquely related to the material model that is used which is a generalization of the silicon model reported by Hassen in Germany, Sumino in Japan and their co-workers. The novelty of the model is that it accounts for a changing dislocation density and through this, the plastic strain rate also changes with the dislocation density. The rate of dislocation generation depends on the stresses, temperature as well as the existing dislocation density. The numerical techniques that are discussed incorporate this novel material model in the analysis of the silicon ribbon growing process. This approach requires that the stresses and dislocation density due to a complex thermal field be determined. The details of these techniques are the main feature of this paper.
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Lee, J. H., and Y. Zhang. "A Finite-Element Work-Hardening Plasticity Model of the Uniaxial Compression and Subsequent Failure of Porous Cylinders Including Effects of Void Nucleation and Growth—Part I: Plastic Flow and Damage." Journal of Engineering Materials and Technology 116, no. 1 (January 1, 1994): 69–79. http://dx.doi.org/10.1115/1.2904257.
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Gurson’s mixed hardening plasticity model (which takes into account the progressive damage due to void nucleation and growth of an initially dense material), with strain and stress-controlled nucleations, was used in a large deformation finite element program to study the plastic flow and damage in the uniaxial compression of cylinders under sticking friction. Effects of strain hardening, nucleation models, yield surface curvature, and geometry on the distributions and evolutions of stresses, strains, mean stress, void fractions, and coalescence are studied in detail. Using Gurson’s isotropic hardening model, positive mean and axial stresses developed at the bulge of the cylinder with growth of voids at latter stages of deformation. Due low stress triaxiality (Σm/σe<0.6) at the bulge, the process is nucleation rather than growth dominated for the majority of the cases studied. At failure, the maximum void fraction at the bulge among all cases studied is 0.085 and is far less than the critical void fraction (≈0.15) for coalescence.
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Moayedi, H., M. Habibi, H. Safarpour, M. Safarpour, and L. K. Foong. "Buckling and Frequency Responses of a Graphene Nanoplatelet Reinforced Composite Microdisk." International Journal of Applied Mechanics 11, no. 10 (December 2019): 1950102. http://dx.doi.org/10.1142/s1758825119501023.
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This is the first research on the vibration and buckling analysis of a graphene nanoplatelet composite (GPLRC) microdisk in the framework of a numerical based generalized differential quadrature method (GDQM). The stresses and strains are obtained using the higher-order shear deformable theory (HOSDT). Rule of the mixture is employed to obtain varying mass density, thermal expansion, and Poisson’s ratio, while the module of elasticity is computed by modified Halpin–Tsai model. Governing equations and boundary conditions of the GPLRC microdisk are obtained by implementing Extended Hamilton’s principle. The results show that outer to inner ratios of the radius ([Formula: see text], ratios of length scale and nonlocal to thickness [Formula: see text] and [Formula: see text], and GPL weight fraction [Formula: see text] have a significant influence on the frequency and buckling characteristics of the GPLRC microdisk. Another necessary consequence is that by increasing the value of the [Formula: see text], the distribution of the displacement field extends from radial to tangent direction, especially in the lower mode numbers, this phenomenon appears much more remarkable. A useful suggestion of this research is that, for designing the GPLRC microdisk at the low value of the [Formula: see text], more attention should be paid to the [Formula: see text] and [Formula: see text], simultaneously.
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Suhir, E. "Stress Relief in Solder Joints Due to the Application of a Flex Circuit." Journal of Electronic Packaging 113, no. 3 (September 1, 1991): 240–43. http://dx.doi.org/10.1115/1.2905401.
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A stress analysis model is developed to assess the stresses in solder joints caused by thermal contraction mismatch between a low expansion flex-circuit (FC) and a high expansion rigid substrate. It is shown that application of low expansion FCs can result in significant stress relief for solder joints. This is due to the fact that the force acting on a joint cannot exceed the buckling force for the adjacent portion of the FC. It is shown that the strains in solder joints interconnecting FCs to rigid substrates can be made very small, thereby resulting in a substantially longer fatigue life of the interconnection. In the executed example these strains are about two orders of magnitude smaller, than in the case of a rigid board. The obtained results can be utilized as guidance in physical design of assemblies with FCs.
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Corum, J. M., and W. K. Sartory. "Assessment of Current High-Temperature Design Methodology Based on Structural Failure Tests." Journal of Pressure Vessel Technology 109, no. 2 (May 1, 1987): 160–68. http://dx.doi.org/10.1115/1.3264890.
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A mature design methodology, consisting of inelastic analysis methods provided in U.S. Department of Energy guidelines and failure criteria contained in ASME Code Case N-47, exists in the United States for high-temperature reactor components. The objective of this paper is to assess the adequacy of that overall methodology by comparing predicted inelastic deformations and lifetimes with observed results from structural failure tests and from an actual service failure. Comparisons are presented for three structural cases: 1) nozzle-to-spherical shell specimens, emphasizing stresses at structural discontinuities; 2) welded structures, emphasizing metallurgical discontinuities; and 3) thermally loaded cylinders and pipes, emphasizing thermal discontinuities. The comparisons between predicted and measured inelastic responses are generally reasonable; quantities are sometimes overpredicted somewhat and sometimes underpredicted. However, even seemingly small discrepancies in predicted stresses and strains can have a significant effect on life, which is thus not always as closely predicted. For a few cases, the lifetimes are substantially overpredicted, which raises questions regarding the methodology and/or the adequacy of the current design margins.
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Noor, Ahmed K., and W. Scott Burton. "Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 868–77. http://dx.doi.org/10.1115/1.2894055.
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Analytic three-dimensional elasticity solutions are presented for the free vibration and buckling of thermally stressed, multilayered, angle-ply composite plates. Sensitivity derivatives are also evaluated and used to study the sensitivity of the vibration and buckling responses to variations in the different lamination and material parameters of the plate. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but has an arbitrary symmetric variation through the thickness of the plate. A linear, Duhamel-Neumann type constitutive model is used, and the material properties are assumed to be independent of temperature. The thermal plate response is subjected to time-varying perturbation displacements, strains, and stresses. A mixed formulation is used with the fundamental unknowns consisting of the six perturbation stress components and the three perturbation displacement components of the plate. The initial thermal deformations are accounted for. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Numerical results are presented showing the effects of variations in material characteristics and fiber orientation of different layers, as well as the effects of initial thermal deformations on the vibrational and buckling responses of the plate, as well as their sensitivity derivatives.
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Lin, X. B., and R. A. Smith. "Stress intensity factors for semi-elliptical internal surface cracks in autofrettaged thick-walled cylinders." Journal of Strain Analysis for Engineering Design 32, no. 5 (July 1, 1997): 351–63. http://dx.doi.org/10.1243/0309324971513472.
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Stress intensity factors for internal semi-elliptical surface cracks in autofrettaged cylinders with and without internal pressures applied are presented. The three-dimensional finite element based displacement method with the crack tip square-root singularity of stresses and strains simulated is used to evaluate the stress intensity factors along the crack front. Both allowing and disallowing the overlapping of crack faces are considered in this investigation, the latter being simulated by considering crack surface contact through a kind of interface element introduced into the cracked area. The residual stress distribution assumed to act on the crack face is obtained according to Tresca's yield criterion with the material assumed to be elastic-perfectly plastic. Three different overstrains of autofrettage are chosen. The results show that the stress intensity factor is generally underestimated if the crack contact that has actually occurred is ignored, which may lead to a danger in the assessment of either fracture strength or fatigue life. Implications of the stress intensity factor results are also briefly discussed, particularly for the prediction of fatigue lives, and it is shown that the full autofrettage treatment might be the most beneficial for increasing the fatigue life of cracks initiated from the inner core.
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Rastgar-Agah, Mobin, Kaveh Laksari, Soroush Assari, and Kurosh Darvish. "Mechanical Instability of Aorta due to Intraluminal Pressure." International Journal of Applied Mechanics 08, no. 01 (February 2016): 1650002. http://dx.doi.org/10.1142/s1758825116500022.
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Dynamic mechanical instability in aorta due to intraluminal pressure may result in a buckling-type deformation and an increase in the pressure-induced tissue stresses and strains. The stability behavior of thoracic aorta was investigated with two boundary conditions that represented two extreme cases of in vivo constraints. The pinned–pinned boundary condition (PPBC) resulted in a decoupled system of equations while the equations for the clamped–clamped boundary condition (CCBC) were coupled. The stability regions around a physiological reference point were generated and the effects of variations in loading and geometric parameters were studied. In CCBC, the critical intraluminal pressures were higher by a factor of two to four compared to PPBC. The highest critical pressures remained below the peak aortic pressures that occur in motor vehicle accidents, which confirmed that mechanical instability can be a mechanism contributing to traumatic injury and rupture of aorta.
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Bekhadda, Ahmed, Ismail Bensaid, Abdelmadjid Cheikh, and Bachir Kerboua. "Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory." Multidiscipline Modeling in Materials and Structures 15, no. 6 (November 4, 2019): 1152–69. http://dx.doi.org/10.1108/mmms-03-2019-0057.
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Purpose The purpose of this paper is to study the static buckling and free vibration of continuously graded ceramic-metal beams by employing a refined higher-order shear deformation, which is also the primary goal of this paper. Design/methodology/approach The proposed model is able to catch both the microstructural and shear deformation impacts without employing any shear correction factors, due to the realistic distribution of transverse shear stresses. The material properties are supposed to vary across the thickness direction in a graded form and are estimated by a power-law model. The equations of motion and related boundary conditions are extracted using Hamilton’s principle and then resolved by analytical solutions for calculating the critical buckling loads and natural frequencies. Findings The obtained results are checked and compared with those of other theories that exist in the literature. At last, a parametric study is provided to exhibit the influence of different parameters such as the power-law index, beam geometrical parameters, modulus ratio and axial load on the dynamic and buckling characteristics of FG beams. Originality/value Searching in the literature and to the best of the authors’ knowledge, there are limited works that consider the coupled effect between the vibration and the axial load of FG beams based on new four-variable refined beam theory. In comparison with a beam model, the number of unknown variables resulting is only four in the general cases, as against five in the case of other shear deformation theories. The actual model represents a real distribution of transverse shear effects besides a parabolic arrangement of the transverse shear strains over the thickness of the beam, so it is needless to use of any shear correction factors.
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Bouazza, Mokhtar, and Noureddine Benseddiq. "Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings." Multidiscipline Modeling in Materials and Structures 11, no. 4 (November 9, 2015): 558–78. http://dx.doi.org/10.1108/mmms-02-2015-0008.
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Purpose – The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal loadings. The material properties of FGM are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Derivations of equations are based on novel refined theory using a new hyperbolic shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. In addition, numerical results for a variety of FG plates with simply supported edge are presented and compared with those available in the literature. Moreover, the effects of geometrical parameters of dimension the length to width aspect ratio (a/b), the plate width to thickness ratio (b/h), and material properties index (k) on the FGM buckling temperature difference are determined and discussed. Design/methodology/approach – In the current paper, the application of the refined theory proposed by Shimpi is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. It is extended to the analysis of buckling behavior of ceramic-metal FG plates subjected to the three types of thermal loadings, namely; uniform temperature rise, linear temperature change across the thickness, and nonlinear temperature change across the thickness. The material properties of the FG plates are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results, wherever possible. Additionally, the effects of geometrical parameters and material properties on the buckling temperature difference of FGM plates are determined and discussed. Findings – Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power-law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Originality/value – To the best of the authors’ knowledge, there are no research works for thermal buckling analysis of FG rectangular plates based on new four-variable refined plate theory (RPT). The novelty of this paper is extended the use of the above-mentioned RPT with the addition of a new function proposed by Shimpi for thermal buckling analysis of plates made of FG materials. Unlike any other theory, the number of unknown functions involved is only four, as against five in the case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. The plates subjected to the two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results.
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Karcher, Guido G., P. E. Monte Ward, and Gary P. Spoelstra. "Buckling of Cylindrical, Thin Wall, Trailer Truck Tanks and ASME Section XII." Journal of Pressure Vessel Technology 135, no. 4 (June 11, 2013). http://dx.doi.org/10.1115/1.4024092.
Full textAbstract:
New hazmat (hazardous material) and nonhazmat transport tanks will be constructed to the rules of the ASME Code Section XII (ASME Boiler and Pressure Vessel Code, American Society of Mechanical Engineers, 3 Park Avenue, New York, NY 10016-5990). The criteria and basis to design these tanks have been questioned and a full scale buckling test has been performed to evaluate maximum allowable over-the-road loadings and required design details. This paper summarizes the results of this testing and provides comparisons with classical Code buckling criteria, Code Case 2286-2 (ASME Code Case 2286-2, Cases of ASME Boiler and Pressure Vessel Code, Case 2286-2, “Alternative Rules for Determining Allowable Compressive Stresses for Cylinders, Cones, Spheres, and Formed Heads”) and other methods for such evaluations. The objective is to provide the ASME Section XII committee with a basis for establishing buckling design criteria and shell stiffening details for both hazmat and nonhazmat transport tanks.
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Sun, X. S., Y. Chen, V. B. C. Tan, R. K. Jaiman, and T. E. Tay. "Homogenization and Stress Analysis of Multilayered Composite Offshore Production Risers." Journal of Applied Mechanics 81, no. 3 (September 18, 2013). http://dx.doi.org/10.1115/1.4024695.
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An approach for stress analysis of multilayered composite cylinders is proposed for the analysis of new composite risers used in deep-water oil production of offshore petroleum industries. Risers essentially comprise long cylindrical sections connected end-to-end. In the formulation, only stresses and strains that are continuous through the thickness of the multilayered composite risers are taken to be equal to reported solutions for homogenous orthotropic hollow cylinders using homogenized material properties. These stress and strain solutions are then used to calculate the remaining discontinuous stresses and strains from the material properties of individual layers of materials. The homogenized elastic constants of cylindrically orthotropic composite risers are derived from force-deformation equivalence, taking into account the stress and strain distributions in each layer. Four typical loading conditions are considered in the stress analysis, namely, internal and external pressures, axial loading, bending, and torsion. Examples of homogenized elastic constants and stress analyses of composite cylindrical structures with different layups and materials are presented to demonstrate the application of the proposed method. The results compared very favorably with those from other solutions. This method provides practical benefits for the design and analysis of composite risers. Because there is no requirement to explicitly enforce interfacial continuity in this method, stress analyses of composite cylinders with many layers of different fiber angles or materials can be carried out efficiently. The homogenized elastic constants can greatly expedite the analysis of entire composite riser systems by replacing complex models of riser sections with homogenized riser sections.
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Mutikainen, Risto, and Markku Orpana. "Silicon Surface Micromachined Structures for the Stress Measurement of Thin Films." MRS Proceedings 308 (1993). http://dx.doi.org/10.1557/proc-308-153.
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ABSTRACTThe realization of structures with silicon surface micromachining requires very low stresses of the structural elements. When low tensile film strains have been difficult to measure as no double-beam type structures susceptible for buckling at low tensile strains have been in use, a new “diamond beam” structure is proposed for the tensile-to-compressive strain conversion. The device performance is analysed as a strain gauge.The micromachined structures can also be used as substrates for deposited films. The formulation is presented for double beam as substrate for deposited film compressive strain gauging. The structures were applied for strained sputter-deposited Molybdenum, and it was found that large undercut of the double beam edge must be avoided as well as the spacer film thickness must be large enough for beam buckling to be noticeable.
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Bouzid, Abdel-Hakim, Hacène Touahri, and Khaled Benfriha. "Analytical Solution of Aluminum Alloy Plates with Holes Subjected to Cold Expansion with Reverse Yielding." Journal of Pressure Vessel Technology, January 5, 2021. http://dx.doi.org/10.1115/1.4049490.
Full textAbstract:
Abstract The expansion induced by cold working is a common process that generates residual stresses. It is used when fatigue damage accumulation and life reduction of aluminum alloy perforated plates is an issue in the aeronautics industry. This process is an attractive solution to extend the fatigue lifetime of these structures. It aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plates with holes commonly used in the manufacture of airplane fuselage. Unfortunately, the life predictions require a good prediction of the residual stresses and in particular when reverse yielding takes place. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed analytical model is based on an elasto-plastic behavior, with a power law material behavior and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite-element numerical simulation is used to validate the developed analytical model by comparison of the radial, Hoop, longitudinal and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.
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Faghih, Sasan, Hamid Jahed, and Seyed Behzad Behravesh. "Variable Material Properties Approach: A Review on Twenty Years of Progress." Journal of Pressure Vessel Technology 140, no. 5 (August 2, 2018). http://dx.doi.org/10.1115/1.4039068.
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This paper provides a critical review of the advancements made in the application of the variable material properties (VMP) method over the past two decades. The VMP method was originally proposed in 1997 (Jahed and Dubey, 1997, ASME J. Pressure Vessel Technol., 119(3), pp. 264–273; Jahed et al., 1997, Int. J. Pressure Vessels Piping, 71(3), pp. 285–291) and further developed in 2001 (Parker, 2001, ASME J. Pressure Vessel Technol., 123(3), p. 271) as an elastoplastic method for the analysis of axisymmetric problems. The model was originally developed as a boundary value problem to predict the spatial distribution of stress. However, since 1997, it has been extended to include thermal effects to solve thermomechanical residual stresses; time domain to solve creep of disks and cylinders; finite deformation to solve cylinders under large strains; numerical solutions to make them more efficient; and asymmetric hardening behavior to accommodate nonslip deformation modes. These advancements, made over the past 20 years, are reviewed in this paper, and future trends and frontiers are discussed.
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Carrera, E., A. Pagani, and R. Augello. "Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics." Acta Mechanica, November 23, 2020. http://dx.doi.org/10.1007/s00707-020-02857-7.
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AbstractIn the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.
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Yuan, Zhangxian, and George A. Kardomateas. "Dynamic Stability of Sandwich Beams/Wide Plates Subjected to Axial Impulsive Loads." Journal of Applied Mechanics 88, no. 4 (January 7, 2021). http://dx.doi.org/10.1115/1.4049223.
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Abstract This paper presents an analysis for the dynamic stability of sandwich beams/wide plates subjected to axial impulsive loads. The formulation and solution of the problem is done by use of the extended high-order sandwich panel theory (EHSAPT). With the initial geometric imperfection included, the equations of motion in terms of seven generalized displacements are derived. The dynamic response of sandwich panels subjected to three different types of impulsive loads, namely, step, linear decay, and triangular impulse, is studied. Furthermore, the effects of the oscillation mode number, face/core materials, and geometries are investigated. It is observed that all measurements of the dynamic response, such as the maximum displacements, strains, and stresses, change at the same rate as the change of the impulse load magnitude and duration, for a specific impulse load profile. When the impulse load is lower than the static buckling load, the dynamic response is bounded no matter how long the load is applied. A step impulsive axial load with magnitude lower than the static buckling load can lead a sandwich panel to have a dynamic response as high as twice the static response. When the impulse load is higher than the static critical load, the dynamic response is unbounded with increasing load duration. However, it is possible that the dynamic response can be controlled at a low level if the duration of the impulse load is short enough, and thus, in this case, the load can safely exceed the static critical load.