用交叉梁系比拟求解正交各向异性薄板弯曲问题  

Analogic Analysis of Orthotropic Plate Bending Problems With Gridwork Systems

作　　者：袁全 袁驷[1] YUAN Quan;YUAN Si(Department of Civil Engineering,Tsinghua University,Beijing 100084,P.R.China)

机构地区：[1]清华大学土木工程系,北京100084

出　　处：《应用数学和力学》2024年第5期518-528,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51878383;51378293)。

摘　　要：采用交叉梁系结构比拟求解正交各向异性薄板结构,给出了两种结构在静力分析和自由振动分析中的相容性条件;对于满足相容性条件且仅含有简支和固支组合边界的相容问题,论证了其解答随着交叉梁系网格加密可收敛到正交各向异性板的理论解.进一步建立了所有类型内力的计算公式,并给出了采用3D结构力学求解器求解的算法实施和数值算例(包括矩形板和圆形板问题),用以验证理论分析的正确性.Orthotropic plates were analogized to gridwork systems,and the compatibility and incompatibility between these 2 structure types in static and dynamic analyses were discussed.The results show that,the grid-work results converge to the theoretical solution of plates through the grid refinement for compatible problems with simply supported and/or clamped boundaries.All the formulas for calculation of various internal forces were derived,and the algorithms required in solving the gridwork systems were proposed by means of the 3D structural mechanics solver.A wide range of numerical examples,including rectangular and circular plates,were given to verify the validity of the proposed theory and algorithms.

关 键 词：交叉梁系 正交各向异性薄板 相容性条件 3D结构力学求解器 数值计算 

分 类 号：O342[理学—固体力学]