Relevant bibliographies by topics / Postbuckling

Academic literature on the topic 'Postbuckling'

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Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "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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Dissertations / Theses on the topic "Postbuckling"

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Xu, Hailan. "Buckling, Postbuckling and Imperfection Sensitivity Analysis of Different Type of Cylindrical Shells by Hui's Postbuckling Method." ScholarWorks@UNO, 2013. http://scholarworks.uno.edu/td/1781.

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Hui and Chen (1986) were the first to show that the well-known Koiter’s General Theory of Elastic Stability of 1945 can be significantly improved by evaluating the postbuckling b coefficient at the actual applied load, rather than at the classical buckling load. Such improvement method was demonstrated to be (1) very simple to apply with no tedious algebra, (2) significant reduction in imperfection sensitivity and (3) although it is still asymptotically valid, there exists a significant extension of the range of validity involving larger imperfection amplitudes. Strictly speaking, Koiter’s theory of 1945 is valid only for vanishingly small imperfection amplitudes. Hence such improved method is termed Hui’s Postbuckling method. This study deals with the postbuckling and imperfection sensitivity of different kinds of cylinders, using the Hui’s postbuckling method. For unstiffened cylinder and laminate cylinder the results are compared with ABAQUS simulation results, and a parameter variation of stringer/ring stiffened cylinder is also evaluated. A significant positive shift of the postbuckling b coefficient is found which indicates that Koiter's general stability theory of 1945 has significantly overestimated the imperfection sensitivity of the structure. Also, compared with the Koiter's general stability theory, the valid region is significantly increased by using Hui's postbuckling method.
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Soncco, K., X. Jorge, and R. A. Arciniega. "Postbuckling Analysis of Functionally Graded Beams." Institute of Physics Publishing, 2019. http://hdl.handle.net/10757/625602.

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This paper studies the geometrically non-linear bending behavior of functionally graded beams subjected to buckling loads using the finite element method. The computational model is based on an improved first-order shear deformation theory for beams with five independent variables. The abstract finite element formulation is derived by means of the principle of virtual work. High-order nodal-spectral interpolation functions were utilized to approximate the field variables which minimizes the locking problem. The incremental/iterative solution technique of Newton's type is implemented to solve the nonlinear equations. The model is verified with benchmark problems available in the literature. The objective is to investigate the effect of volume fraction variation in the response of functionally graded beams made of ceramics and metals. As expected, the results show that transverse deflections vary significantly depending on the ceramic and metal combination.
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Faggiani, Andrea. "Optimisation of postbuckling stiffened composite structures." Thesis, Imperial College London, 2008. http://hdl.handle.net/10044/1/8001.

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The thesis starts off with an introductory chapter on composite materials. This includes a definition of composites, a brief history of composite materials, their use in aerostructures (primarily as stiffened structures), and also optimization of composite structures. A literature review is then presented on postbuckling stiffened structures. This includes both experimental investigations on stiffened composite panels and investigations into secondary instabilities and mode jumping as well as their numerical modelling. Next, the Finite Element (FE) modelling of posthuckling stiffened structures is discussed, relating how ABAQUS models are set up in order to trace stiffened composite panels' buckling and postbuckling responses. An experimental programme conducted on an I-stiffened panel is described, where the panel was tested in compression until collapse. The buckling and postbuckling characteristics of the panel are presented, and then an FE model is described together with its predicted numerical behaviour of the panel's buckling and postbuckling characteristics. Focus then shifts to the modelling of failure in composites, in particular delamination failure. A literature review is conducted, looking at the use of both the Virtual Crack Closure Technique (VCCT) and interface elements in delamination modelling. Two stiffener runout models, representing two specimens previously tested experimentally, are then developed to illustrate how interface elements may be used to model mixed mode delamination. The previously discussed panel is revisited, and a global-local modelling approach used to model the skin-stiffener interface. FE models of a stiffened cylindrical shell are also considered, and again the postbuckling characteristics of the shell are compared with experimental results. . The thesis then moves on to optimization of composite structures. This starts off with a literature review of existing optimization methodologies. A Genetic Algorithm (GA) is devised to increase the damage resistance of the I-stiffened panel. The global-local ABAQUS model discussed earlier is used in conjunction with the GA in order to find a revised stacking sequence of both the panel flanges and skin so as to minimize skin-stiffener debonding subject to a variety of design constraints. A second optimization is then presented, this time linked to the FE model of the stiffened cylindrical shell. The objective is to increase the collapse load of the shell, again subject to specific design constraints. The thesis concludes by summarising the importance of the work conducted. FE models were created and validated against experimental work in order to model a variety of composite stiffened structures in their buckling and postbuckling regimes. These models were able to capture the failure characteristics of these structures relating to delamination at the skin-stiffener interface, a phenomenon widely observed experimentally. Various optimizations, able to account for failure mechanisms which may occur prior to overall structural collapse, were then conducted on the analysed structures in order to obtain more damage resistant designs.
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Song, Yuzhan. "Thermo-elastoviscoplastic postbuckling behavior of shell-like structures." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/11703.

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Parsa, Kourosh. "Buckling/postbuckling of polymer composite continuum/skeletal structures." Thesis, University of Surrey, 1995. http://epubs.surrey.ac.uk/636/.

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Lee, Ho Hyung. "Postbuckling failure of composite plates with central holes." Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-10022007-145159/.

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Seresta, Omprakash. "Buckling, Flutter, and Postbuckling Optimization of Composite Structures." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/26401.

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This research work deals with the design and optimization of a large composite structure. In design of large structural systems, it is customary to divide the problem into many smaller independent/semi-independent local design problems. For example, the wing structure design problem is decomposed into several local panel design problem. The use of composite necessitates the inclusion of ply angles as design variables. These design variables are discrete in nature because of manufacturing constraint. The multilevel approach results into a nonblended solution with no continuity of laminate layups across the panels. The nonblended solution is not desirable because of two reasons. First, the structural integrity of the whole system is questionable. Second, even if there is continuity to some extent, the manufacturing process ends up being costlier. In this work, we develop a global local design methodology to design blended composite laminates across the whole structural system. The blending constraint is imposed via a guide based approach within the genetic algorithm optimization scheme. Two different blending schemes are investigated, outer and inner blending. The global local approach is implemented for a complex composite wing structure design problem, which is known to have a strong global local coupling. To reduce the computational cost, the originally proposed local one dimensional search is replaced by an intuitive local improvement operator. The local panels design problem arises in global/local wing structure design has a straight edge boundary condition. A postbuckling analysis module is developed for such panels with applied edge displacements. A parametric study of the effects of flexural and inplane stiffnesses on the design of composite laminates for optimal postbuckling performance is done. The design optimization of composite laminates for postbuckling strength is properly formulated with stacking sequence as design variables. Next, we formulate the stacking sequence design (fiber orientation angle of the layers) of laminated composite flat panels for maximum supersonic flutter speed and maximum thermal buckling capacity. The design is constrained so that the behavior of the panel in the vicinity of the flutter boundary should be limited to stable limit cycle oscillation. A parametric study is carried out to investigate the tradeoff between designs for thermal buckling and flutter. In an effort to include the postbuckling constraint into the multilevel design optimization of large composite structure, an alternative cheap methodology for predicting load paths in postbuckled structure is presented. This approach being computationally less expensive compared to full scale nonlinear analysis can be used in conjunction with an optimizer for preliminary design of large composite structure with postbuckling constraint. This approach assumes that the postbuckled stiffness of the structure, though reduced considerably, remains linear. The analytical expressions for postbuckled stiffness are given in a form that can be used with any commercially available linear finite element solver. Using the developed approximate load path prediction scheme, a global local design approach is developed to design large composite structure with blending and local postbuckling constraints. The methodology is demonstrated via a composite wing box design with blended laminates.
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Chung, Kwok Fai. "The elastic distortional and local plate buckling of slender web beam." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/7860.

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Jane, Kuo Chang. "Buckling, postbuckling deformation and vibration of a delaminated plate." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/19975.

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Cerini, Marco. "Investigation of secondary instabilities in postbuckling stiffened composite structures." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429557.

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Books on the topic "Postbuckling"

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Turvey, G. J., and I. H. Marshall, eds. Buckling and Postbuckling of Composite Plates. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4.

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Turvey, G. J. Buckling and Postbuckling of Composite Plates. Dordrecht: Springer Netherlands, 1995.

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Douglas, Coffin, ed. Handbook of thin plate buckling and postbuckling. Boca Raton, FL: Chapman & Hall/CRC, 2001.

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Simitses, G. T. A finite element program for postbuckling calculations (PSTBKL). [Washington, D.C.]: National Aeronautics and Space Administration, 1991.

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Eslami, M. Reza. Buckling and Postbuckling of Beams, Plates, and Shells. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-62368-9.

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Roman, V. G. Postbuckling behavior of thin steel cylinders under transverse shear. Edmonton, Alta., Canada: Dept. of Civil Engineering, University of Alberta, 1987.

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Somers, M. Effect of delamination location on postbuckling behavior of sandwich structures. Haifa, Israel: Technion-Israel Institute of Technology, Faculty of Aerospace Engineering, 1989.

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Stein, Manuel. Postbuckling behavior of longitudinally compressed orthotropic plates with three-dimensional flexibility. [S.l.]: [s.n.], 1986.

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Thurston, Gaylen A. Application of Newton's method to postbuckling of rings under pressure loadings. Hampton, Va: Langley Research Center, 1989.

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Somers, M. Buckling and postbuckling behavior of sandwich structures in the presence of a delamination. Haifa: Technion Israel Institute of Technology, Dept. of Aeronautical Engineering, 1989.

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Book chapters on the topic "Postbuckling"

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Buskell, N., G. A. O. Davies, and K. A. Stevens. "Postbuckling Failure of Composite Panels." In Composite Structures 3, 290–314. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-4952-2_22.

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Pignataro, M. "Stability, Bifurcation and Postbuckling Analysis." In Coupled Instabilities in Metal Structures, 29–83. Vienna: Springer Vienna, 1998. http://dx.doi.org/10.1007/978-3-7091-2510-6_2.

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Noor, A. K. "Finite element buckling and postbuckling analyses." In Buckling and Postbuckling of Composite Plates, 58–107. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_3.

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Dawe, D. J. "Finite strip buckling and postbuckling analysis." In Buckling and Postbuckling of Composite Plates, 108–53. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_4.

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Leissa, A. W. "Buckling and postbuckling theory for laminated composite plates." In Buckling and Postbuckling of Composite Plates, 3–29. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_1.

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Adali, S. "Lay-up optimization of laminated plates under buckling loads." In Buckling and Postbuckling of Composite Plates, 329–65. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_10.

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Palazotto, A. N. "Instability of composite panels." In Buckling and Postbuckling of Composite Plates, 366–89. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_11.

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Narita, Y. "Series and Ritz-type buckling analyses." In Buckling and Postbuckling of Composite Plates, 33–57. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_2.

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Bert, C. W. "Shear deformation and sandwich configuration." In Buckling and Postbuckling of Composite Plates, 157–89. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_5.

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Tauchert, T. R. "Temperature and absorbed moisture." In Buckling and Postbuckling of Composite Plates, 190–226. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-1228-4_6.

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Conference papers on the topic "Postbuckling"

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Librescu, Liviu, and Liviu Librescu. "Thermomechanical postbuckling of shells." In 38th Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-1243.

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Rahman, T., S. T. IJsselmuiden, M. M. Abdalla, and E. L. Jansen. "Postbuckling Analysis of Variable Stiffness Composite Panels Using a Finite Element Based Perturbation Method." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11663.

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In earlier research the authors optimized variable stiffness panels for maximum buckling load, using lamination parameters. The aim of the present research is to analyze those optimized panels in the postbuckling regime so that further improvement can be achieved in the future with respect to its postbuckling performance. Because the incremental-iterative nonlinear analysis in the postbuckling regime is not feasible within an optimization loop a finite element based perturbation method (Koiter type) is used to compute postbuckling coefficients, which are in turn used to make a quick estimate of the postbuckling stiffness of the panel and to establish a reduced order model. The proposed perturbation method has been implemented in a general purpose finite element code. In the present work the postbuckling analysis of variable stiffness panels carried out using the reduced order model is presented and the potential of the approach for incorporation within the optimization process is demonstrated.
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Emam, Samir A., and Ali H. Nayfeh. "Postbuckling and Free Vibrations of Composite Beams." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35007.

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An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse vibrations of a composite laminated beam accounting for the midplane stretching are presented. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single equation governing the transverse vibrations. This equation is a nonlinear fourth-order partial-integral differential equation. We find that the governing equation for the postbuckling of a symmetric or antisymmetric composite beam has the same form as that of a metallic beam. A closed-form solution for the postbuckling configurations due to a given axial load beyond the critical buckling load is obtained. We followed Nayfeh, Anderson, and Kreider and exactly solved the linear vibration problem around the first buckled configuration to obtain the fundamental natural frequencies and their corresponding mode shapes using different fiber orientations. Characteristic curves showing variations of the maximum static deflection and the fundamental natural frequency of postbuckling vibrations with the applied axial load for a variety of fiber orientations are presented. We find out that the line-up orientation of the laminate strongly affects the static buckled configuration and the fundamental natural frequency. The ratio of the axial stiffness to the bending stiffness is a crucial parameter in the analysis. This parameter can be used to help design and optimize the composite beams behavior in the postbuckling domain.
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Liu, Suihan, Nan Hu, and Rigoberto Burgueño. "Postbuckling Behavior of Axially-Compressed Strips With Discrete Rigid Constraints: A Numerical Study." In ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/smasis2015-9050.

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Axially-compressed columns, or strips, with bilateral continuous rigid constraints (CRC) are known to be able to attain multiple snap-through buckling events in their elastic postbuckling response that lead to the sudden release of strain energy from the system. This feature allows this structural prototype to be used as energy concentrators for smart applications. However, the parameters controlling the postbuckling response for such system are limited. The structural prototype discussed in this paper is that of an axially compressed strip provided with discrete rigid constraints (DRC), whereby the layout of the lateral constrains provides increased design freedom to control the strip’s postbuckling features. The study is based on numerical simulations using the finite element method. Using a previously characterized CRC strip as a baseline, two DRC design groups were considered in symmetric and asymmetric layouts for a total of 15 different arrangements. Results show that DRC strips can attain elastic postbuckling responses with distinct characteristics and that the far postbuckling response can be controlled by modifying the number and the location of the constraints. Compared to CRC strips, some DRC patterns allow attaining higher mode transitions and larger kinetic energy release after the first buckling event. The ability to design for such postbuckling response features can be potentially used for energy harvesting and other sensing and actuation applications.
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Guo, Jun, Suihan Liu, and Rigoberto Burgueño. "Tailoring the Elastic Postbuckling Response of Thin-Walled Cylindrical Shells for Applications in Mechanical Devices and Adaptive Structures." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3967.

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Postbuckling response, long considered mainly as a failure limit state is gaining increased interest for smart applications, such as energy harvesting, frequency tuning, sensing, actuation, etc. Cylindrical shells have received less attention as structural form to harness elastic instabilities due to their increased modeling complexity and high imperfection sensitivity. Yet, preliminary experimental and computational evidence indicates that the elastic postbuckling response of cylindrical shells can be controlled and potentially managed. Further, cylindrical shells offer desirable features for the design of mechanical devices and adaptive structures that other forms cannot attain without additional external constraints. This paper presents a study on tailoring the elastic postbuckling response of thin-walled cylindrical shells under compression by means of non-uniform wall stiffness distributions. The pattern of stiffness distribution was designed by discretizing the shell surface into cells and thickening selected cells with respect to a baseline uniform wall thickness. Diverse patterns were characterized in the way of how they affect the postbuckling response through numerical simulations using the finite element method. Results show that the elastic postbuckling response can be tailored into three response types: softening, sustaining, and stiffening; and that number, sequence/time and location/space of localized buckling events can be designed. This work provides new knowledge on the means to design the cylindrical shells with controlled elastic postbuckling behavior for applications in smart materials, mechanical devices, and adaptive structures.
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Salem, Talal, Pengcheng Jiao, Hamed Bolandi, and Nizar Lajnef. "Tunable Postbuckling Systems of Bi-Walled Nonuniform Beams." In ASME 2020 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/smasis2020-2227.

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Abstract Structural instability, in particular postbuckling resulted in predefined constraints, has been performing advantages in many applications given their promising mechanical characteristics. However, inadequate studies have been conducted to effectively control and tune the postbuckling behavior of bilaterally constrained nonuniform beams. This study develops postbuckling systems comprised of multiple nonuniform beams subjected to bilateral confinements. Theoretical model is developed using Euler-Bernoulli theory and small deformation assumptions to predict postbuckling response of the beam systems under quasi-static axial loading. To locate the minimum energy path of the deformed beam system, the minimization problem of total potential energies of the bi-walled beam systems is solved by Nelder-Mead algorithm. Snap-through transitions of buckled systems are shown by drops in the response curves. To validate the developed model with existing models in literature, the model was simplified to account for single uniform beam under displacement control. The proposed model is experimentally and numerically validated, and satisfactory agreements are obtained. Parametric studies are carried out to investigate the influence of varying the geometric parameters (i.e., length, thickness) of the nonuniform beams on the tunable systems. Using the presented theoretical model, the postbuckling events can be accurately controlled by the geometry properties of the nonuniform beams.
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Hu, Nan, Rigoberto Burgueño, and Nizar Lajnef. "Structural Optimization and Form-Finding of Cylindrical Shells for Targeted Elastic Postbuckling Response." In ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/smasis2014-7446.

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This paper presents a finite element based numerical study on controlling the postbuckling behavior of thin-walled cylindrical shells under axial compression. With the increasing interest of various disciplines for harnessing elastic instabilities in materials and mechanical systems, the postbuckling behavior of thin-walled cylindrical shells may have a new role to design materials and structures at multiple scales with switchable functionalities, morphogenesis, etc. In the design optimization approach presented herein, the mode shapes and their amplitudes are linearly combined to generate initial geometrical designs with predefined imperfections. A nonlinear postbuckling finite element analysis evaluates the design objective function, i.e., the desired postbuckling force-displacement path. Single and multi-objective optimization problems are formulated with design variables consisting of shape parameters that scale base eigenvalue shapes. A gradient-based algorithm and numerical sensitivity evaluations are used. Results suggest that an optimized shape for a cylindrical shell can achieve a targeted response in the elastic postbuckling regime with multiple mode transitions and energy dissipation characteristics. The optimization process and the obtained geometry can be potentially used for energy harvesting and other sensing and actuation applications.
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Anderson, M., and M. Anderson. "Design of panels having postbuckling strength." In 38th Structures, Structural Dynamics, and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-1240.

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"A strategy for postbuckling structural analysis." In 30th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1989. http://dx.doi.org/10.2514/6.1989-1318.

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GRIFIN, JR., O., J. LEE, and Z. GURDAL. "POSTBUCKLING OF LAMINATED COMPOSITES WITH DELAMINATIONS." In 34th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-1566.

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