正交异性板条的渐近分析  

Asymptotic Analysis of Orthotropic Strip Deformation

作　　者：林逸汉[1] 王禹钦[1] 陈世平[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433

出　　处：《力学季刊》2006年第1期76-83,共8页Chinese Quarterly of Mechanics

摘　　要：本文阐明由三维薄弹性体的渐近分析导出各级精度板壳理论的基本方法。将多尺度分析用于板的内部区域和边界层区域导出应力,应变和位移等物理量的不同的无量纲小厚度参数ε的渐近展开式。与工程的方法不同,推导仅基于ε→0的渐近分析,对板的变形不做任何假定。给出正交异性板的平面应变渐近展开的具体列式,仅有一些常数待定。结果表明,内域解渐近级数的首项正是熟知的Kirchhoff板理论解。本文为内域解和边界层解的渐近匹配,从而正确表述圣维南原理并用以建立各级渐近解的边界条件进而求解的研究做好了准备。The basic method of deriving higher order theories of plates and shells was illustrated by asymptotic analysis for three dimensional thin elastic body. Using the multiscale analysis in the interior and boundary layer regions of plates, the different asymptotic expansions in terms of a small non-dimensional thickness parameter ε for the variables of stress, strain and displacement were derived. Different from any engineering method, the derivation was only based on the asymptotic analysis as ε→0 without any assumption on plate deformation. The asymptotic expansions for orthotropic plates in plane strain are given up to some constant coefficients to be determined. It is shown that the leading term of interior asymptotic solutions is exactly the solution of Kirchhoff plate theory. This paper prepares for the study of asymptotic matching to formulate Saint-Venant＇s principle correctly, for the establishment of plate boundary conditions and determination of unknown constants.

关 键 词：弹性板 多尺度 渐近展开 正交异性 平面应变 

分 类 号：O34[理学—固体力学]