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| A new analytic solution to the buckling problem of rectangular thin plates with four corners point-supported and four edges free |
| Received:October 29, 2019 Revised:January 14, 2020 |
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| DOI：10.7511/jslx20191029001 |
| KeyWord:symplectic superposition method rectangular thin plate buckling corner-point supports |
| Author | Institution |
| 杨雨诗 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 安东琦 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 倪卓凡 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 李锐 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
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| Abstract: |
| The buckling problem of rectangular thin plates supported by corner points is an important topic in mechanics of plates and shells.However,due to the complexity of the governing equations and boundary conditions,it was difficult to obtain the analytic solutions to such problems.Although various approximate/numerical methods have been developed to solve such problems,as benchmarks,accurate analytic solutions were rarely reported in the open literature.Based on the symplectic superposition method that was proposed in recent years,the buckling problem of rectangular thin plates with four corners point-supported and four edges free is analytically solved in this paper.The problem is firstly divided into two sub-problems;then the analytic solutions of the sub-problems are derived by separation of variables and symplectic eigen expansion.The solution of the original problem is finally obtained by superposition.Since the solution procedure starts from the basic governing equation and is derived rigorously,step by step,without assuming the forms of the solutions,the presented solution method is a rational analytic method.With different aspect ratios and different in-plane load ratios,the buckling loads and typical buckling mode shapes of the rectangular thin plates with four corners point-supported and four edges free are given in the numerical examples.The correctness of the analytic solution is validated by the finite element method. |
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