An analytical spectral stiffness method for buckling of rectangular plates on Winkler foundation subject to general boundary conditions |
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| Institution: | 1. Key Laboratory of Traffic Safety on Track, Ministry of Education, School of Traffic and Transportation Engineering, Central South University, China;2. Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, China;3. State Key Laboratory of High Performance Complex Manufacturing, Central South University, China;1. School of Materials and Engineering, Jiangsu University of Technology, Changzhou, Jiangsu, 213001, China;2. Institute of Solid Mechanics, School of Aeronautical Science and Engineering, Beihang University, Beijing 100083, China;3. Shanghai Marine Equipment Research Institute (SMERI), Shanghai 200031, China;1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, China;2. School of Chemical Machinery and Safety, Dalian University of Technology, Dalian 116024, China;3. Studienbereich Mechanik, Technische Universität Darmstadt, Darmstadt 64289, Germany |
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| Abstract: | An analytical spectral stiffness method is proposed for the efficient and accurate buckling analysis of rectangular plates on Winkler foundation subject to general boundary conditions (BCs). The method combines the advantages of superposition method, stiffness-based method and the Wittrick–Williams algorithm. First, exact general solutions of the governing differential equation (GDE) of plate buckling considering both elastic foundation and biaxial loading is derived by using a modified Fourier series. The superposition of such general solutions satisfy the GDE exactly and BCs approximately, which guarantees the rapid convergence and high accuracy. Then, based on the exact general solution, the spectral stiffness matrix which relates the coefficients of plate generalized displacement BCs and force BCs is symbolically developed. As a result, arbitrary BCs can be prescribed straightforwardly in the stiffness-based model. As an efficient and reliable solution technique, the Wittrick–Williams algorithm with the J0 problem resolved is applied to obtain the critical buckling solutions. The accuracy and efficiency of the method are verified by comparing with other methods. Benchmark buckling solutions are provided for plates with all possible boundary conditions. Also, dependence of various factors such as foundation stiffness, load combinations and aspect ratio on the buckling behaviors are investigated. |
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