弹性中厚板的摄动-变分法  

PERTURBATION-VARIATION METHODS OF ELASTIC MIDDLE-THICK PLATES

作　　者：胡成栋[1] 

机构地区：[1]吉林大学数学系

出　　处：《工程力学》1989年第1期9-17,共9页Engineering Mechanics

摘　　要：本文采用胡海昌的弹性中厚板的微分方程和边界条件。取δ=D,/(Ca^2)为小参值,应用摄动方法将广义位移势函数F的边值问题化为一系列经典理论板的弯曲问题,从而可以求得F的渐近解。应用最小势能原理求解边界效应函数f的边值问题。算例表明,应用本文方法可以求得精度较高的中厚板的广义位移近似解。The Hu Hai-Chang's differential equations of the elastic middle-thick plates and its boundary condition are applied in this paper. Taking δ=D/(Ca^2) as a small parameter, we change the boundary value problem with potential function F of generalized displacement into a series of bending problems in classical theory of plates by the perturbation method. Thus we obatin the asymptotic solution for F. The principle of minimum potential energy is created to solve the bondary value problem of the boundary effect function f. Caeulation examples show that methods in this paper have higher accuracy for the approximete solutions of generalized displacement of elastic middle-thick plates.

关 键 词：弹性中厚板 摄动-变分法 弹性板 

分 类 号：TB125[理学—工程力学]