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Apply the principles of complementary energy with mixed variables to solve the bending of the rectangular plate with simply supported on four sides under different loads

DOI：10.7511/jslx201502024

 作者 单位 E-mail 陈英杰 燕山大学 建筑工程与力学学院, 秦皇岛 066004 cyjysu@126.com 李志航 燕山大学 建筑工程与力学学院, 秦皇岛 066004 付宝连 燕山大学 建筑工程与力学学院, 秦皇岛 066004

由功的互等定理导出了弯曲矩形板混合变量的总余能,应用混合变量余能原理求解四边简支矩形板弯曲问题,给出了四边简支矩形板的混合变量余能表达式,求解了不同载荷作用下四边简支矩形板的弯曲问题,并将计算的不同载荷作用下的挠度和弯矩值与ANSYS有限元的计算值比较,给出了一种求解四边简支矩形板的新方法。

The total complementary energy with mixed variables of the bending of the rectangular plate is deduced by applying the reciprocal theorem in this article.It solves the problem of the bending of the rectangular plate with simply supported on four sides by applying the principles of complementary energy with mixed variables.And it gives the expression for complementary energy with mixed variables of the rectangular plate with simply support on four sides.Through calculating the deflection surface equation under different loads by this method and comparing the ANSYS value with deflection value, moment value under different loads.Finally the author verifies the method presented in this paper can be applied directly to the project.