作　　者： ; ; ;

机构地区： 中国科学技术大学工程科学学院近代力学系

出　　处： 《应用数学和力学》 2003年第9期881-891,共11页

摘　　要： 　提出了含随厚度变化膨胀特征应变的弹性层在任意载荷作用下的一般分析步骤。该研究基于状态空间方法和一种渐近展开技巧。如果外载均匀，则展开式系数自前几项后为零，从而可得弹性层力学场量封闭形式的表达式。这一表达式仅依赖于中面的位移分量，后者由一组类似于经典板理论的二维微分方程控制。因此，获得二维方程的解便可立即给出弹性层的三维响应。作为例子，还详细分析了均匀分布载荷作用下的夹支椭圆层。 Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state_space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid_plane, which are governed by a set of two_dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two_dimensional equations immediately gives the three_dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.

关 键 词： 特征应变 弹性层 三维分析

领　　域： [理学]