正交异性板的三维渐近方程  

Three Dimensional Asymptotic Equations of Orthotropic Plates

作　　者：林逸汉[1] 陈世平[1] 王禹钦[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433

出　　处：《复旦学报（自然科学版）》2006年第2期135-140,共6页Journal of Fudan University：Natural Science

摘　　要：从正交异性薄弹性体的三维弹性方程出发,应用在板的内部区域展开为无量纲厚度参数ε的渐近级数的方法,系统地推导出由板中面位移表示的二维高阶板方程,包含了体积力和板表面力的作用效应.进一步在边界层区域将三维的边值问题分解成二维的平面应变和扭转问题.与工程的方法不同,推导过程仅基于ε→0的渐近分析,对板的变形不作任何假定.结果表明,板内域解渐近级数的首项正是熟知的K irchhoff假定或直法线假定下的板理论解.Starting from 3-D elasticity equations of a orthotropic thin elastic body, the 2-D higher order plate equations of told-plane displacements, including the effects of body and surface forces, are derived systematically by the method of asymptotic expansions in plate interior region with respect to a dimcnsionless depth parameter ε. Furthermore, the 3-D boundary value problem in boundary layer region is decomposed to 2-D plane strain and torsion problems. The derivation process is only based on the asymptotic analysis of ε→0 and makes no assumption on plate deformations distinguishing from any engineering method. It is shown that the leading terms of interior asymptotic expansions are exactly the Kirchhoff plate theory solutions.

关 键 词：渐近分析 边界层 高阶 三维 弹性板理论 正交异性 

分 类 号：O343.2[理学—固体力学]