混合边界各向异性矩形板的静力分析  

Static analysis of anisotropic rectangular plates with mixed boundary conditions

作　　者：郑荣跃[1,2] 黄炎[2] 李广利[2] 

机构地区：[1]宁波大学建筑工程与环境学院,宁波315211 [2]国防科技大学航天与材料工程学院,长沙410073

出　　处：《应用力学学报》2011年第2期163-166,215,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(50405006)

摘　　要：采用一般解析解和配点法相结合的方法,求解混合边界各向异性矩形板的弯曲问题。先由弯曲挠度的微分方程求出各种类型的齐次解和特解,然后组成一般解析解,再将板的每个边等分为很多微小的段,仅对每一微段的中点建立应满足的边界条件,由全部边界条件方程式即可求得全部积分常数。以每边一半边界为平夹、另一半边界为简支或自由的方板为例进行了计算,并与四边均为简支的方板进行了对比,表明理论简单,结果实用。The plates with differential boundary conditions are studied in this paper by the method of general analytical solution combinated with collocation point method.According to the differential equations for bending deflection of anisotropic rectangular plates,all of the homogeneous solutions and particular solutions are obtained,then a general analytical solution is composed.Each edge of the plate is divided uniformly into many small parts.Only for middle points of each small part the boundary conditions are established.From all of the equations of boundary condition,all of the integral constants are solved.As an example,a square plate with each half edge clamped and other half edge simply supported or free is calculated,.

关 键 词：各向异性矩形板 混合边界条件 一般解析解 配点法 弯曲 

分 类 号：O343.9[理学—固体力学]