交叉梁系比拟求解薄板弯曲问题的相容性及其计算  

Compatibility in analogy of gridworks to thin plate bending and its numerical solution

作　　者：袁驷[1,2] 袁全 Yuan Si;Yuan Quan(School of Civil Engineering,Tsinghua University,Beijing 100084,China;Key Laboratory of Civil Engineering Safety and Durability of the Ministry of Education,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学土木水利学院,北京100084 [2]清华大学土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《土木工程学报》2023年第3期1-8,共8页China Civil Engineering Journal

基　　金：国家自然科学基金(51878383,51378293)。

摘　　要：文章用交叉梁系比拟求解薄板结构,讨论两种结构在静力分析和自由振动分析中的相容性和互异性,论证含有简支和固支边组合的边界属于相容问题,其解答随着交叉梁系网格加密可收敛到薄板理论解,而含有自由边界的非相容问题则不能。文中给出了采用3D结构力学求解器求解的算法实施和数值算例,包括矩形、三角形和圆形板问题,用以验证理论分析的正确性,展示并拓展了3D求解器的出色性能。Thin plates are analogized to gridwork systems,and the compatibility and incompatibility between these two structures in static and dynamic analyses are discussed.It is proved that the plates with simply supported and/or clamped boundaries are compatible problems,for which the gridwork results converge to the theoretical solutions of plates as the grids being refined,whereas the plates with free boundaries do not have such convergence property.By employing the 3D Structural Mechanics Solver as the solution tool,the requisite algorithms and a wide range of numerical examples,including rectangular,triangular,and circular plates,are provided to verify the validity of the proposed theory and algorithms and show the great performance of the 3D Solver for such extended functions.

关 键 词：交叉梁系 薄板理论 相容性 3D结构力学求解器 数值计算 

分 类 号：TU311.4[建筑科学—结构工程]