Journal articles: 'Postbuckling'

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RAHMAN, T., S. T. IJSSELMUIDEN, M. M. ABDALLA, and E. L. JANSEN. "POSTBUCKLING ANALYSIS OF VARIABLE STIFFNESS COMPOSITE PLATES USING A FINITE ELEMENT-BASED PERTURBATION METHOD." International Journal of Structural Stability and Dynamics 11, no. 04 (August 2011): 735–53. http://dx.doi.org/10.1142/s0219455411004324.

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Modern fiber placement machines allow laminates with spatially varying stiffness properties to be manufactured. In earlier research, the authors optimized variable stiffness plates for maximum buckling load, demonstrating significant improvements in load-carrying capacity. In aerospace applications, panel structures are often permitted to enter the postbuckling regime during service. It is, therefore, not only important to understand their postbuckling behavior, but also to develop fast analysis methods that can subsequently be used in a design optimization framework. The aim of the present research is to study the postbuckling behavior of the optimized plates using a perturbation method that has been developed earlier within a general-purpose finite element environment. The perturbation approach is used to compute postbuckling coefficients, which are used to make a quick estimate of the postbuckling stiffness of the panel and to establish a reduced-order model. In the present work, the postbuckling analysis of variable stiffness plates is carried out using the reduced-order model, and the potential of the approach for incorporation within the optimization process is demonstrated.

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Han, Da Wei, An Wen Wang, Liu Wei Mao, and Gang Li. "Investigation into Dynamic Postbuckling of Thin Rectangular Plate under Elastic Compression Wave." Applied Mechanics and Materials 477-478 (December 2013): 165–69. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.165.

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The initial buckling displacements are taken as initial conditions to solve the dynamic postbuckling problem. Non-dimensional dynamic postbuckling equilibrium equations denoted by the displacements are derived and solved by use of the finite difference method. The results reveal the regulation that the dynamic postbuckling deformation develops from the initial low step mode to the subsequent higher step modes under elastic compression wave.

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WANG, C. M., Y. XIANG, and S. KITIPORNCHAI. "POSTBUCKLING OF NANO RODS/TUBES BASED ON NONLOCAL BEAM THEORY." International Journal of Applied Mechanics 01, no. 02 (June 2009): 259–66. http://dx.doi.org/10.1142/s1758825109000150.

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This paper is concerned with the postbuckling problem of cantilevered nano rods/tubes under an end concentrated load. Eringen's nonlocal beam theory is used to account for the small length scale effect. The governing equation is derived from statical and geometrical considerations and Eringen's nonlocal constitutive relation. The nonlinear differential equation is solved using the shooting method for the postbuckling load and the buckled shape. By comparing with the classical postbuckling solutions, the sensitivity of the small length scale effect on the buckling load and buckled shape may be observed. It is found that the small length scale effect decreases the postbuckling load and increases the deflection of the rod.

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Hermann, Thomas M., Dharmaraj Mamarthupatti, and James E. Locke. "Postbuckling Analysis of a Wind Turbine Blade Substructure." Journal of Solar Energy Engineering 127, no. 4 (July 12, 2005): 544–52. http://dx.doi.org/10.1115/1.2037093.

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Postbuckling analysis of composite laminates representative of wind turbine blade substructures, utilizing the commercial finite element software ANSYS, is presented in this paper. The procedure was validated against an existing postbuckling analysis. Three shell element formulations, SHELL91, SHELL99, and SHELL181, were examined. It was found that the SHELL181 element with reduced integration should be used to avoid shear locking. The validated procedure was used to examine the variation of the buckling behavior, including postbuckling, with lamination schedule of a laminate representative of a wind turbine blade shear web. This analysis was correlated with data from a static test. A 100% postbuckling reserve in a composite structure representative of a shear web was quantified through test and analysis. The buckling behavior of the shear web was improved by modifying the lamination schedule to increase the web bending stiffness. Modifications that improved the buckling load of the structure did not always equate to improvements in the postbuckling reserve.

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Arbocz, J., M. Potier-Ferry, J. Singer, V. Tvergaard, and I. Elishakoff. "Buckling and Postbuckling." Journal of Applied Mechanics 56, no. 3 (September 1, 1989): 732. http://dx.doi.org/10.1115/1.3176163.

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Li, Zhi Min. "New Results of Buckling and Postbuckling Behaviors for Fiber-Reinforced Composite Shear Deformable Anisotropic Laminated Cylindrical Shell Subjected to Torsion." Applied Mechanics and Materials 117-119 (October 2011): 89–91. http://dx.doi.org/10.4028/www.scientific.net/amm.117-119.89.

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New results of buckling and postbuckling analysis are presented for a shear deformable anisotropic laminated cylindrical shell of finite length subjected to torsion. The governing equations are based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The postbuckling equilibrium path is unstable for a moderately thick laminated cylindrical shell under torsion and the shell structure is virtually imperfection-sensitive.

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Li, Z. M., and D. Q. Yang. "Thermal Postbuckling Analysis of 3D Braided Composite Cylindrical Shells." Journal of Mechanics 26, no. 2 (June 2010): 113–22. http://dx.doi.org/10.1017/s1727719100002975.

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AbstractThermal postbuckling analysis is presented for 3D braided composite cylindrical shell of finite length subjected to a uniform temperature rise. Based on a micro-macro-mechanical model, a 3D braided composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on Reddy's higher order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling temperatures and postbuckling behaviors of 3D braided composite cylindrical shells. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction. The results show that the shell has lower buckling temperatures and postbuckling equilibrium paths when the temperature-dependent properties are taken into account. The results reveal that the fiber volume fraction, braiding angle and the shell geometric parameter have a significant effect on the thermal buckling and postbuckling behavior of braided composite cylindrical shells.

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Ansari, Reza, Mostafa Faghih Shojaei, Vahid Mohammadi, and Hessam Rouhi. "Free vibration and postbuckling of laminated composite Timoshenko beams." Science and Engineering of Composite Materials 23, no. 1 (January 1, 2016): 107–21. http://dx.doi.org/10.1515/secm-2013-0237.

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AbstractA numerical solution method was developed to investigate the postbuckling behavior and vibrations around the buckled configurations of symmetrically and unsymmetrically laminated composite Timoshenko beams subject to different boundary conditions. The Hamilton principle was employed to derive the governing equations and corresponding boundary conditions which are then discretized by introducing a set of matrix differential operators. The pseudo-arc-length continuation method was used to solve the postbuckling problem. To study the free vibration that takes place around the buckled configurations, the corresponding eigenvalue problem was solved by means of the postbuckling configuration modes obtained in the previous step. The static bifurcation diagrams for composite beams with different lay-up laminates are given, and it is shown that the lay-up configuration considerably affects the magnitude of critical buckling load and postbuckling behavior. The study of the vibrations of composite beams with different laminations around the buckled configurations indicates that the natural frequency in the prebuckling domain increases as the stiffness of a beam increases, while there is no specific relation between the lay-up lamination and natural frequency in the postbuckling domain which necessitates conducting an accurate analysis in this area.

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SHEN, HUI-SHEN, and Y. XIANG. "POSTBUCKLING OF PRESSURE-LOADED PIEZOLAMINATED CYLINDRICAL SHELLS WITH TEMPERATURE DEPENDENT PROPERTIES." International Journal of Structural Stability and Dynamics 07, no. 01 (March 2007): 1–22. http://dx.doi.org/10.1142/s0219455407002150.

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A postbuckling analysis is presented for a shear deformable laminated cylindrical shell with piezoelectric actuators subjected to lateral or hydrostatic pressure combined with electric and thermal loads. The material properties are assumed to be dependent on the temperature. The governing equations are based on higher-order shear deformation shell theory with a von Kármán-Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of pressure-loaded, perfect and imperfect, cross-ply laminated cylindrical shells with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The results reveal that the temperature rise has a significant effect on the buckling pressure and postbuckling behavior of piezolaminated cylindrical shells when the temperature-dependent properties are taken into account, but it only has a very small effect under temperature-independent case. In contrast, the control voltage has a small effect on the buckling pressure and postbuckling behavior of piezolaminated cylindrical shells.

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Zhao, K., D. Kennedy, and C. A. Featherston. "Exact strip postbuckling analysis of composite plates under compression and shear." Aeronautical Journal 123, no. 1263 (May 2019): 658–77. http://dx.doi.org/10.1017/aer.2019.27.

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ABSTRACTStiffened wing and fuselage panels often have a postbuckling reserve of strength, enabling them to carry loads far in excess of their critical buckling loads. Therefore allowing for postbuckling in design can reduce their weight, hence reducing fuel consumption and environmental impact. The present paper extends the postbuckling analysis in the exact strip software VICONOPT to more accurately reflect the skewed mode shapes arising from shear load and anisotropy. Such mode shapes are represented by a series of sinusoidal responses with different half-wavelengths which are coupled together using Lagrangian multipliers to enforce the boundary conditions. In postbuckling analysis the in-plane deflections involve responses with additional half-wavelengths which are absent from the out-of-plane deflection series. Numerical results are presented and compared with finite element analysis for validation. The present analysis gives close results compared to the finite element and finite strip methods and saves computational time significantly.

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11

Soltani, HM, and M. Kharazi. "Investigation of the incremental and deformation theories of plasticity on the elastoplastic postbuckling of plates." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 234, no. 7 (May 19, 2020): 1017–31. http://dx.doi.org/10.1177/1464420720922866.

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This article investigates the elastoplastic response of buckling and postbuckling behavior of plates under uniaxial and biaxial end-shortening considering incremental theory and deformation theory of plasticity. According to elastoplastic buckling and postbuckling behavior of plates, the finite element code considering geometrically and material nonlinearities is developed based on incremental theory and deformation theory of plasticity. The results show that boundary conditions, loading ratios, and aspect ratios of a plate have a significant effect on the discrepancy between incremental theory and deformation theory. Moreover, differences in estimating the buckling point using incremental theory and deformation theory are less than 10%, while in a number of plates at the last loading steps, postbuckling paths determined by incremental theory and deformation theory are diverted from each other. Also the difference between these two theories in the postbuckling region is more noticeable by increasing the thickness of plates.

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SINGH, S., B. P. PATEL, and Y. Nath. "POSTBUCKLING OF LAMINATED SHELLS OF REVOLUTION WITH MERIDIONAL CURVATURE UNDER THERMAL AND MECHANICAL LOADS." International Journal of Structural Stability and Dynamics 09, no. 01 (March 2009): 107–26. http://dx.doi.org/10.1142/s0219455409002916.

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A study on the influence of meridional curvature on the buckling and postbuckling behavior of cross-ply laminated shells of revolution subjected to thermal and mechanical loads is carried out using the semianalytical finite element method. The nonlinear equations are solved using the Newton–Raphson iterative technique. The adaptive displacement control method is employed to trace the equilibrium path. Examined herein are the effects of positive and negative meridional curvature, the number of layers and the number of circumferential waves on the buckling/postbuckling behavior of cross-ply laminated, simply supported shells under thermal, external pressure, torsional and axial loadings. It is found that the critical load increases with the increase in the rise-to-radius ratio of positive meridional curvature shells for the loading cases considered. The critical temperature, torsional, axial loads decrease and the critical external pressure increases with increasing magnitude of the rise-to-radius ratio of negative meridional curvature shells. The postbuckling response of shells exposed to a uniform temperature rise is of a hardening nature for both positive and negative meridional curvature cases. Shells subjected to external pressure show a softening type of initial postbuckling response for positive meridional curvature, and a hardening type of postbuckling response for negative meridional curvature. The qualitative nature of postbuckling characteristics for torsional and axial loading cases may be softening, hardening or initially softening and later hardening, depending upon the combined influence of the rise-to-radius ratio, the number of circumferential waves and the number of layers.

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13

Hui, David, and I. H. Y. Du. "Imperfection-Sensitivity of Long Antisymmetric Cross-Ply Cylindrical Panels Under Shear Loads." Journal of Applied Mechanics 54, no. 2 (June 1, 1987): 292–98. http://dx.doi.org/10.1115/1.3173010.

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This paper examines the theoretical postbuckling behavior and imperfection-sensitivity of antisymmetrically laminated open, long, cylindrical panels under shear loads. The longitudinal edges may be simply-supported or clamped. It is found that the cylindrical panels may be sensitive to the presence of geometric imperfections depending primarily on the reduced-flatness parameter and Young’s modulus ratio. The shear buckling load and the postbuckling coefficients are plotted as a function of the shell geometry, number of layers, and material parameters. The paper is the first in the literature to examine the postbuckling behavior of open laminated cylindrical panels under shear loads.

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Knight, N. F., and J. H. Starnes. "Postbuckling Behavior of Axially Compressed Graphite-Epoxy Cylindrical Panels With Circular Holes." Journal of Pressure Vessel Technology 107, no. 4 (November 1, 1985): 394–402. http://dx.doi.org/10.1115/1.3264473.

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The results of an experimental and analytical study of the effects of circular holes on the postbuckling behavior of graphite-epoxy cylindrical panels loaded in axial compression are presented. The STAGSC-1 general shell analysis computer code developed by Bo 0. Almroth and Frank A. Brogan is used to determine the buckling and postbuckling response of the panels. The loaded, curved ends of the specimens were clamped by fixtures and the unloaded, straight edges were simply supported by knife-edge restraints. The panels are loaded by uniform end shortening to several times the end shortening at buckling. The unstable equilibrium path of the postbuckling response is obtained analytically by using a method based on controlling an equilibrium-path-arc-length parameter instead of the traditional load parameter. The effects of hole diameter, panel radius, and panel thickness on postbuckling response are considered in the study. Experimental results are compared with the analytical results and the failure characteristics of the graphite-epoxy panels are described.

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15

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

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

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NGUYEN, DINH KIEN. "POSTBUCKLING BEHAVIOR OF BEAMS ON TWO-PARAMETER ELASTIC FOUNDATION." International Journal of Structural Stability and Dynamics 04, no. 01 (March 2004): 21–43. http://dx.doi.org/10.1142/s0219455404001082.

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The postbuckling behavior of beams on a two-parameter elastic foundation subjected to axial forces is investigated. Based on the strain energy expression, a two-node nonlinear beam element is formulated. The element includes the effects of shear deformation, foundation deflection in both the horizontal and vertical directions. The bracketing procedure and the iterative Newton–Raphson method with arc-length control technique are adopted to compute the critical loads and equilibrium paths of the beams with various boundary conditions. The numerical results show that the critical load and the postbuckling behavior are not only governed by the foundation stiffness, but by the foundation deflection in the horizontal direction also. The postbuckling characteristics of the beams are altered by ignoring the foundation deflection in the horizontal direction. A detail investigation is carried out to highlight the influences of the partial support by the foundation and the beam slenderness on the critical load and the postbuckling behavior.

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CUI, HAO-LEI, and HUI-SHEN SHEN. "MODELING AND SIMULATION OF BUCKLING AND POSTBUCKLING OF PLANT STEMS UNDER COMBINED LOADING CONDITIONS." International Journal of Applied Mechanics 03, no. 01 (March 2011): 119–30. http://dx.doi.org/10.1142/s1758825111000907.

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Numerical simulations for local buckling and postbuckling behavior of plant stems are presented under two combined loading cases: (1) axial compression (caused by axial grains) combined with wind pressure; and (2) bending moment (caused by eccentric axial grains) combined with wind pressure. Based on its microstructure, a hollow plant stem is modeled as a stringer stiffened multiwalled shell. The material properties of the stem are assumed to be orthotropic. The nonlinear governing equations for buckling and postbuckling of plant stems are solved through arc-length method along with Newton–Raphson technique. The numerical calculations are carried out using the finite element package ABAQUS. The results show that the postbuckling equilibrium path is unstable for plant stems subjected to axial compression or bending combined with relatively low values of wind pressure. Large reduction in buckling load and in postbuckling strength can be found even if the applied wind pressure is relatively small, which results in the easy occurrence of stem lodging.

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Nam, Vu Hoai, Nguyen Thi Phuong, and Vu Minh Duc. "Nonlinear buckling of orthogonal carbon nanotube-reinforced composite cylindrical shells under axial compression surrounded by elastic foundation in thermal environment." International Journal of Computational Materials Science and Engineering 08, no. 04 (December 2019): 1950016. http://dx.doi.org/10.1142/s2047684119500167.

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Nonlinear buckling and postbuckling of orthogonal carbon nanotube-reinforced composite (Orthogonal CNTRC) cylindrical shells subjected to axial compression in thermal environments surrounded by elastic foundation are presented in this paper. Two layers of shell are reinforced by carbon nanotube (CNT) in two orthogonal directions (longitudinal and circumferential directions). Based on Donnell’s shell theory with von Karman’s nonlinearity and the Galerkin method, the governing equations are established to obtain the critical buckling loads and postbuckling load-deflection curves. The large effects of CNT volume fraction, temperature change, elastic foundation and geometrical parameters of cylindrical shells on the buckling load and postbuckling behavior of Orthogonal CNTRC cylindrical shells are obtained.

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Kerdegarbakhsh, M., Y. Kiani, S. E. Esfahani, and M. R. Eslami. "Postbuckling of FGM rings." International Journal of Mechanical Sciences 85 (August 2014): 187–95. http://dx.doi.org/10.1016/j.ijmecsci.2014.05.021.

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Bhushan, Bharat, Gajbir Singh, and G. Venkateswara Rao. "Postbuckling of elliptical plates." Mechanics Research Communications 21, no. 1 (January 1994): 89–94. http://dx.doi.org/10.1016/0093-6413(94)90013-2.

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ABRAMOVICH, HAIM, and TANCHUM WELLER. "REPEATED BUCKLING AND POSTBUCKLING BEHAVIOR OF LAMINATED STRINGER-STIFFENED COMPOSITE PANELS WITH AND WITHOUT DAMAGE." International Journal of Structural Stability and Dynamics 10, no. 04 (October 2010): 807–25. http://dx.doi.org/10.1142/s0219455410003750.

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Eight curved blade stringer-stiffened composite panels were tested under axial compression to obtain the "first" buckling and postbuckling behavior till collapse. Except for one panel, used as a reference panel, all of the panels had stringers without dropoff layers. Four panels contained either artificial damage or both artificial and impact-induced damage. Cyclic/repeated buckling was applied well in a relatively "deep" postbuckling region. It was demonstrated that neither repeated buckling, within the number of cycles applied in the present program, nor artificial damage and impact-induced damage, which were introduced into the panels, resulted in stiffness degradation of the panels. No premature failure of any of the tested panels was observed within their expected life cycle, i.e. exposure to a few hundred cycles deep in the postbuckling region, even in the presence of either type or a combination of the damage. All of the tested panels sustained repeated postbuckling loading till they were subjected to static loading aimed at determining their collapse loads. In spite of the present design, i.e. stiffeners with no dropoff plies aimed amongst others at providing a mechanism for initiating stiffener debonding, no skin–stringer separation was encountered till collapse of the panels. It was found that composite stringer-stiffened panels can be safely and repeatedly loaded in their deep postbuckling range with no degradation in their stiffness. Damage, due to either manufacturing or impact, which usually will result in rejection of a structural element, affected neither the load-carrying capacity nor the capability to withstand repeated loading in the relatively very deep postbuckling range within the present designed life cycle of the element. It was realized that manufacturing complexities and consequently costs can be reduced by employing a simplified design configuration where the use of a dropoff ply of the stringer base has been eliminated.

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

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

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LI, ZHI-MIN, and HUI-SHEN SHEN. "POSTBUCKLING OF SHEAR-DEFORMABLE ANISOTROPIC LAMINATED CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION." International Journal of Structural Stability and Dynamics 08, no. 03 (September 2008): 389–414. http://dx.doi.org/10.1142/s0219455408002715.

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A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Kármán–Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive.

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Li, Xingjia, and Ying Luo. "Size-Dependent Postbuckling of Piezoelectric Microbeams Based on a Modified Couple Stress Theory." International Journal of Applied Mechanics 09, no. 04 (May 23, 2017): 1750053. http://dx.doi.org/10.1142/s1758825117500533.

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This paper aims to investigate the postbuckling behavior of piezoelectric microbeams (PMBs) using a modified couple stress theory (MCST) and a Euler–Bernoulli–von Kármán beam model. The critical buckling force, voltage and the deformation amplitude were calculated for the buckling of the axially compressed microbeams with a clamp–clamp boundary condition. It is found that the stiffness of microbeams considering the MCST is higher than that given by the classical model when the feature size decreases to the microscale. Moreover, the microscale size effect has a strong influence on the critical buckling loads and the amplitude of postbuckling deformation. This study brings an improved understanding of the postbuckling behavior of PMBs, and offers useful guidance for the design of piezobeam-based sensors, actuators and stretchable microelectronics.

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Juntarasaid, Chinnawut, Tawich Pulngern, and Somchai Chucheepsakul. "Postbuckling Analysis of a Nonlocal Nanorod Under Self-Weight." International Journal of Applied Mechanics 12, no. 04 (May 2020): 2050035. http://dx.doi.org/10.1142/s1758825120500350.

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This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.

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Wu, He Long, Sritawat Kitipornchai, and Jie Yang. "Thermal Buckling and Postbuckling Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Beams." Applied Mechanics and Materials 846 (July 2016): 182–87. http://dx.doi.org/10.4028/www.scientific.net/amm.846.182.

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Thermal buckling and postbuckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated in this paper based on Timoshenko beam theory within the framework of von Kármán geometric nonlinearity. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary in the beam thickness direction. The governing equations are derived by employing Hamilton’s principle then discretized by using differential quadrature (DQ) method. An iterative scheme is used to obtain the critical buckling temperature and nonlinear thermal postbuckling equilibrium path of the FG-CNTRC beam. Numerical results are presented for FG-CNTRC beams hinged or clamped at both ends, with particular focuses on the effects of the volume fraction of carbon nanotubes (CNTs), slenderness ratio, and end supports on the thermal buckling and postbuckling characteristics.

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Long, Vu Thanh, and Hoang Van Tung. "Thermal postbuckling behavior of CNT-reinforced composite sandwich plate models resting on elastic foundations with tangentially restrained edges and temperature-dependent properties." Journal of Thermoplastic Composite Materials 33, no. 10 (April 10, 2019): 1396–428. http://dx.doi.org/10.1177/0892705719828789.

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Buckling and postbuckling behaviors of sandwich plates reinforced by single-walled carbon nanotube (CNT), rested on elastic foundations and subjected to uniform temperature rise, are investigated in this article. CNT is embedded into matrix phase through uniform or functionally graded distributions. The properties of constituent materials are assumed to be temperature-dependent, and effective properties of nanocomposite are determined by extended rule of mixture. Two models of sandwich plates with face sheets and core layer reinforced by CNTs are presented. Formulations are based on the first-order shear deformation theory taking geometrical nonlinearity, initial geometrical imperfection, plate-foundation interaction, and elasticity of tangential edge constraints into consideration. Analytical solutions of deflection and stress function are assumed, and Galerkin method is applied to derive nonlinear temperature–deflection relation from which buckling temperatures and thermal postbuckling paths are obtained through an iteration algorithm. Numerical examples show the effects of CNT volume fraction, distribution patterns, in-plane edge constraint, elastic foundations, geometrical ratios, initial imperfection, and temperature dependence of properties on thermal postbuckling behavior of nanocomposite sandwich plates. The most important finding is that sandwich plate constructed from CNT-poor nanocomposite core layer and thin homogeneous face sheets with partially movable edges bring the best capacities of thermal buckling resistance and postbuckling load carrying.

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Maurini, C., Joel Pouget, and Stefano Vidoli. "Bistable Buckled Beam: Modelling and Piezoelectric Actuation." Advances in Science and Technology 54 (September 2008): 281–86. http://dx.doi.org/10.4028/www.scientific.net/ast.54.281.

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Bistable structures, such as buckled beams, are characterized by a two-well potential. Their nonlinear properties are currently exploited in actuators to produce relatively high displacements and forces with low actuation energies. We investigate the use of distributed multiparameter actuation to control the buckling and postbuckling behaviour of a three-layer piezoelectric beam pinned at either end. A two-parameter bending actuation controls the transversal motion, whilst an axial actuation modulates the tangent bending stiffness. The postbuckling behaviour is studied by reducing to a 2 dof system a nonlinear extensible elastica model. When the bending actuation is spatially symmetric, the postbuckling phenomena are characterized by a snapthrough instability. The use of a two-parameter actuation opens new transition scenarios, where it is possible to get quasi-static transitions between the two equilibria of the buckled beam, without any instability phenomenon.

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Shiau, L. C., S. Y. Kuo, and S. Y. Chang. "Postbuckling of Shape Memory Alloy Reinforced Cross-Ply and Angle-Ply Laminated Plates." Journal of Mechanics 27, no. 4 (December 2011): 559–66. http://dx.doi.org/10.1017/jmech.2011.58.

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ABSTRACTThe effect of shape memory alloy (SMA) on the postbuckling behavior of rectangular cross-ply and angle-ply plates by varying the SMA fiber spacing was investigated using the Finite Element Method. The formulation of the location-dependent linear, nonlinear stiffness matrices due to non-homogeneous material properties and the temperature-dependent recovery stress stiffness matrix were derived. Numerical results show that the increase of SMA fiber volume fraction and prestrain may generate more recovery stress, and increase the stiffness of SMA reinforced composite laminate. Therefore, the postbuckling deflections of the plate may be decreased significantly. The buckling mode that plate will buckle into is dependent on the fiber orientation of the angle-ply laminates. When the SMA fibers are concentrated in the center of the plate, the postbuckling deflections of the plate will be decreased considerably.

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30

Jayachandran, S. Arul, S. Gopalakrishnan, and R. Narayanan. "Improved Secant Matrices for the Postbuckling Analysis of Thin Composite Plates." International Journal of Structural Stability and Dynamics 03, no. 03 (September 2003): 355–75. http://dx.doi.org/10.1142/s0219455403000938.

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To study the postbuckling behavior of imperfect laminated composite plates, improved incremental or secant matrices are presented in this paper using what is called additional displacement formulation (ADF). These secant matrices are derived using the Marguerre's shell theory and they can be used in combination with any thin plate finite element. The advantage of the present formulation is that it involves no numerical approximation in forming the initial imperfection matrices as opposed to earlier secant matrices published in the literature using total displacement formulation. With the addition of shear stiffness matrix and little modification, the present incremental matrices could be extended to model postbuckling behavior of plates using the first-order shear deformation theory. The secant matrices presented in this study are shown to be very accurate in tracing the postbuckling behavior of thin isotropic and laminated composite plates with general initial imperfections.

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31

Azhari, M., A. R. Shahidi, M. M. Saadatpour, and M. A. Bradford. "Postbuckling Behavior of Triangular Plates." AIAA Journal 43, no. 3 (March 2005): 690–96. http://dx.doi.org/10.2514/1.12623.

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32

Zimmermann, Rolf, and Raimund Rolfes. "CFRP fuselage structures - postbuckling permitted." Air & Space Europe 3, no. 3-4 (May 2001): 129–31. http://dx.doi.org/10.1016/s1290-0958(01)90075-9.

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33

Alart, P., and S. Pagano. "DC Solutions of Postbuckling Problems." Journal of Global Optimization 29, no. 4 (August 2004): 353–70. http://dx.doi.org/10.1023/b:jogo.0000047908.54572.c1.

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34

Padovan, Joseph. "Solving postbuckling collapse of structures." Finite Elements in Analysis and Design 1, no. 4 (December 1985): 363–85. http://dx.doi.org/10.1016/0168-874x(85)90032-0.

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35

Byskov, Esben, Claus Dencker Christensen, and Kristian Jørgensen. "Elastic postbuckling with nonlinear constraints." International Journal of Solids and Structures 33, no. 17 (July 1996): 2417–36. http://dx.doi.org/10.1016/0020-7683(95)00166-2.

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36

Ansari, R., and R. Gholami. "Size-Dependent Buckling and Postbuckling Analyses of First-Order Shear Deformable Magneto-Electro-Thermo Elastic Nanoplates Based on the Nonlocal Elasticity Theory." International Journal of Structural Stability and Dynamics 17, no. 01 (January 2017): 1750014. http://dx.doi.org/10.1142/s0219455417500146.

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This paper presents a nonlocal nonlinear first-order shear deformable plate model for investigating the buckling and postbuckling of magneto-electro-thermo elastic (METE) nanoplates under magneto-electro-thermo-mechanical loadings. The nonlocal elasticity theory within the framework of the first-order shear deformation plate theory along with the von Kármán-type geometrical nonlinearity is used to derive the size-dependent nonlinear governing partial differential equations and associated boundary conditions, in which the effects of shear deformation, small scale parameter and thermo-electro-magneto-mechanical loadings are incorporated. The generalized differential quadrature (GDQ) method and pseudo arc-length continuation algorithm are used to determine the critical buckling loads and postbuckling equilibrium paths of the METE nanoplates with various boundary conditions. Finally, the influences of the nonlocal parameter, boundary conditions, temperature rise, external electric voltage and external magnetic potential on the critical buckling load and postbuckling response are studied.

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37

Psotný, Martin. "Aspect Ratio of Slender Web & Postbuckling Behaviour / Pomer Strán Štíhlej Steny A Pokritické Pôsobenie." Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series 12, no. 2 (December 1, 2012): 153–60. http://dx.doi.org/10.2478/v10160-012-0029-z.

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Abstract Postbuckling analysis of slender web loaded in compression is presented. The non-linear FEM equations [14] are derived from the variational principle of minimum of total potential energy [13]. To obtain the non-linear equilibrium paths, Newton-Raphson iteration algorithm [11], [12] is used. Peculiarities of the effect of the initial imperfections [7], [8] on load-deflection paths are investigated with respect to aspect ratio of the web. Special attention is focused on the postbuckling mode of the web.

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38

Shin, Dong Ku, Zafer Gu¨rdal, and O. Hayden Griffin. "Minimum Weight Design of Laminated Composite Plates for Postbuckling Performance." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S219—S231. http://dx.doi.org/10.1115/1.3121359.

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Minimum-weight design of simply-supported, symmetrically laminated, thin, rectangular, specially orthotropic laminated plates for buckling and postbuckling strength is investigated. The postbuckling analysis is based on an Marguerre-type energy method extended to generally orthotropic plates with a special consideration of the mode change in the postbuckling load regime. The failure load of laminates is calculated by the maximum strain failure criterion based on the in-plane strains. Design variables are individual layer thicknesses with specified fiber orientations and assumed to take only discrete values corresponding to multiples of the lamina thickness. The optimization with discrete valued design is achieved by introducing additional penalty terms, in the form of a sine function, to the regular pseudo-objective function of sequential unconstrained minimization technique (SUMT). The proposed optimization technique is applied to the design of rectangular laminates made up of 0, ± 45, 90 degree laminae with various aspect ratios loaded by axial compressive loads.

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Xu, Xian, Yafeng Wang, and Yaozhi Luo. "Numerical Modeling of Force-Stiffness Response of Cross-Linked Actin Networks Using Tensegrity Systems." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/182918.

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A three-dimensional tensegrity structure is used as a computational model for cross-linked actin networks. The postbuckling behavior of the members under compression is considered and the constitutive relation of the postbuckling members is modeled as a second-order polynomial. A numerical scheme incorporating the equivalent constitution of the postbuckling members is used to predict the structural response of the tensegrity model under compression loads. The numerical simulation shows that the stiffness of the tensegrity structure nonlinearly increases before member buckling and abruptly decreases to a lower level as soon as members buckle. This result qualitatively mimics the experimentally observed stiffness to compression stress response of cross-linked actin networks. In order to take member length variety into account, a large number of simulations with the length of buckling members varying in the given range are also carried out. It is found that the mean response of the simulations using different buckling member length exhibits more resemblance to the experimental observation.

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40

Tung, Hoang Van, and Pham Thanh Hieu. "Nonlinear buckling of CNT-reinforced composite toroidal shell segment surrounded by an elastic medium and subjected to uniform external pressure." Vietnam Journal of Mechanics 40, no. 3 (September 24, 2018): 285–301. http://dx.doi.org/10.15625/0866-7136/12397.

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Buckling and postbuckling behaviors of Toroidal Shell Segment (TSS) reinforced by single-walled carbon nanotubes (SWCNT), surrounded by an elastic medium and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix phase by uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Effective properties of carbon nanotube reinforced composite (CNTRC) are estimated by an extended rule of mixture through a micromechanical model. Governing equations for TSSs are based on the classical thin shell theory taking into account geometrical nonlinearity and surrounding elastic medium. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to obtain nonlinear load-deflection relation from which buckling loads and postbuckling equilibrium paths are determined. The effects of CNT volume fraction, distribution types, geometrical ratios and elastic foundation on the buckling and postbuckling behaviors of CNTRC TSSs are analyzed and discussed.

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41

Selmi, Abdellatif. "Buckling capacity of functionally graded beams: A comparative study of different shear deformation beam theories." International Journal of Computational Materials Science and Engineering 08, no. 02 (June 2019): 1950003. http://dx.doi.org/10.1142/s2047684119500039.

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This paper investigates the postbuckling response of simply supported functionally graded beams under axial loading using several beam theories; classical beam theory, CBT, Timoshenko beam theory, TBT and parabolic shear deformation beam theory, PSDBT. Hamilton’s principle is used to derive the governing equations which are solved by closed-form method. It is assumed that the Young’s modulus is varying continuously in the thickness direction according to power-law form while all other material properties are taken to be constant. The effects of the reinforcement distribution, the beam edge-to-thickness ratio and the phase contrast (ratio of the reinforcement Young’s modulus to the matrix Young’s modulus) on the postbuckling behavior and critical buckling load of functionally graded beam are studied. Results demonstrate the important contribution of the shear effect to both the buckling and postbuckling behaviors. Finally, the combinations of reinforcement distribution, beam edge-to-thickness ratio and phase contrast that correspond to the highest and the lowest buckling capacities are identified.

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Xu, S. P., M. R. Xu, and C. M. Wang. "Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/341232.

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Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.

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43

LI, YUHANG, CHI CHEN, BO FANG, JIAZHONG ZHANG, and JIZHOU SONG. "POSTBUCKLING OF PIEZOELECTRIC NANOBEAMS WITH SURFACE EFFECTS." International Journal of Applied Mechanics 04, no. 02 (June 2012): 1250018. http://dx.doi.org/10.1142/s1758825112500184.

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Surface effects, including surface elasticity, surface piezoelectricity and residual surface stress, on the postbuckling of piezoelectric nanobeams due to an electric field are investigated using an energy method in this paper. The critical buckling voltage and amplitude are obtained analytically in terms of the bulk and surface material properties and geometric parameters. The results show that surface effects play a significant role in the postbuckling of piezoelectric nanobeams. It is found that the influences of surface piezoelectricity and residual surface stress are more prominent than the surface elasticity. These results might be helpful for designing piezoelectric nanobeam-based devices.

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44

Kim, K. S., J. S. Yoo, Jae Mo An, Young Soon Jang, Yeong Moo Yi, and Gwang Rae Cho. "Postbuckling Failure Behaviours of Hat-Stiffened Composite Panels with Different Bonding Methods." Key Engineering Materials 334-335 (March 2007): 181–84. http://dx.doi.org/10.4028/www.scientific.net/kem.334-335.181.

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Postbuckling failure behaviors and strength were investigated in compression tests of the hat stiffened composite panels manufactured with different bonding methods and different stiffener section shapes. The skin-stiffener separation loads, separation failure behaviors and final collapse loads were different with respect to bonding methods and stiffener shapes. As the separation failure was initiated early and propagated larger area, collapse loads and structural performance of the panels decreased. The test results showed that the co-curing with or without adhesive film and open type stiffeners were most beneficial for the postbuckling strength.

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45

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 (April 18, 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, and Lekhnitsky’s smeared stiffeners technique, the governing equations are derived. The closed form to determine critical axial load and postbuckling load-deflection curves are obtained by the Galerkin method. The effects of the face sheet thickness to total thickness ratio, stiffener, foundation, material, and dimensional parameters on critical thermal loads, critical mechanical loads and postbuckling behavior of shells are analyzed. In addition, this paper shows that for thin shells we can use the classical shell theory to investigate stability behavior of shell, but for thicker shells the use of TSDT for analyzing nonlinear stability of shell is necessary and suitable.

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ARAICO, J. ANSÓTEGUI, I. ORTIZ DE ZARATE ALBERDI, and F. REBOLLO ARRIBAS. "POSTBUCKLING DEGRADATION FE ANALYSIS OF STIFFENED COMPOSITE PANELS." International Journal of Structural Stability and Dynamics 10, no. 04 (October 2010): 645–68. http://dx.doi.org/10.1142/s021945541000366x.

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The capability of a commercial industrial tool, ABAQUS, to simulate the critical damage mechanisms in stiffened composite panels has been evaluated. The analysis and conclusions are supported by experimental results. The focus is on skin–stringer separation during compressive loading. Results show that the advanced degradation modeling capabilities present in commercial codes today may lead to an accurate characterization of the deep postbuckling range behavior and the collapse of stiffened composite panels. Compared to current design practice, where the first indication of ply failure or the onset of damage propagation is taken as the failure load, the methods used here provide a way to exploit the reserves in composite structures. It is concluded that implementing degradation mechanisms (composite ply and adhesive interface degradation) presents a significant improvement to simulate accurately the deep postbuckling states and collapse for stiffened composite panels with adhesively bonded stringers. The nature of the final loss of load-carrying capacity for this type of structures, by composite ply and adhesive interface failure, driven by postbuckling deformation, makes this simulation approach essential.

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47

Dawe, D. J., and S. Wang. "Postbuckling Analysis of Composite Laminated Panels." AIAA Journal 38, no. 11 (November 2000): 2160–70. http://dx.doi.org/10.2514/2.880.

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48

Lee, Jaehong, Zafer Gurdal, and O. Hayden Griffin. "Postbuckling of laminated composites with delaminations." AIAA Journal 33, no. 10 (October 1995): 1963–70. http://dx.doi.org/10.2514/3.12752.

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49

Azikov, N. S., and Yu V. Gaidarzhi. "POSTBUCKLING BEHAVIOR OF SKEW COMPOSITE PLATES." Composites: Mechanics, Computations, Applications, An International Journal 3, no. 2 (2012): 161–70. http://dx.doi.org/10.1615/compmechcomputapplintj.v3.i2.50.

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50

Yitzhak, Elie, and Menahem Baruch. "Analogy for postbuckling structural resistance capability." AIAA Journal 24, no. 10 (October 1986): 1719–21. http://dx.doi.org/10.2514/3.9513.

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Journal articles on the topic 'Postbuckling'

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