三维非线性弹性壳体的维数分裂法
发布时间：2018-08-02 21:33
【摘要】：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.
[Abstract]:In this paper, a dimension splitting method for nonlinear elastic shells based on semi-geodesic coordinate system is presented. It divides a nonlinear elastic operator into a sum of membrane elastic operator and bending elastic operator in this coordinate system. Assuming that the solution of a nonlinear elastic shell can be expanded into a Taylor series of intersecting variables, a 2D-3C nonlinear partial differential equation system for the first term is established, and the existence of the solution is proved. At the same time, two functions about the first order term and the second order term for the first term are given, so that the first order term and the second order term can be obtained without solving the partial differential equation.
【作者单位】： 西安交通大学数学与统计学院;燕山大学理学院;
【基金】：国家自然科学基金(91330115;11371289;11371288)~~
【分类号】：O343.5
本文编号：2160813
[Abstract]:In this paper, a dimension splitting method for nonlinear elastic shells based on semi-geodesic coordinate system is presented. It divides a nonlinear elastic operator into a sum of membrane elastic operator and bending elastic operator in this coordinate system. Assuming that the solution of a nonlinear elastic shell can be expanded into a Taylor series of intersecting variables, a 2D-3C nonlinear partial differential equation system for the first term is established, and the existence of the solution is proved. At the same time, two functions about the first order term and the second order term for the first term are given, so that the first order term and the second order term can be obtained without solving the partial differential equation.
【作者单位】： 西安交通大学数学与统计学院;燕山大学理学院;
【基金】：国家自然科学基金(91330115;11371289;11371288)~~
【分类号】：O343.5
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