三维非线性弹性壳体的维数分裂法∗

摘要

In this paper, a dimensional splitting method for three dimensional nonlinear elastic shell is established under a semi-geodesic coordinate system (S-coordinate). Then the nonlinear elastic operator can be decomposed into the sum of a membrane and bending operators in the S-coordinate system. Assume that the solution of the 3D nonlinear elastic shell can be expressed as the Taylor expansion with respect to the transverse variable, the approximation modelling with one-order and two order respectively are established. Meanwhile, we give the 2D-3C partial differential equations satisfied by the terms of zero-order, prove the existence of solution, give the related functions in the terms of first and second orders with respective to the term of zero-order without solving partial differential equations to obtain the terms of first and second orders.%本文给出了一个建立在半测地坐标系下的非线性弹性壳体的维数分裂方法，它把一个非线性弹性算子，在这个坐标系下，分裂为一个称为膜弹性算子和弯曲弹性算子之和。假设非线性弹性壳体的解可以展开为关于贯裁变量的Taylor级数，那么本文建立了关于首项的2D-3C非线性偏微分方程组，证明其解的存在性，同时给出了两个关于一阶项和二阶项对于首项的函数，从而无需求解偏微分方程即可得到一阶项和二阶项。