NON-LINEAR ANALYSIS OF A TWISTED AXIALLY LOADED ELASTIC ROD

被引：11

作者：

ZACHMANN, DW

机构：

来源：

QUARTERLY OF APPLIED MATHEMATICS | 1979年 / 37卷 / 01期

关键词：

D O I：

10.1090/qam/530669

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A slender, inextensible elastic rod is acted upon by a twisting couple and an axial load. The position of the rod's centerline is determined by two fourth-order, coupled, nonlinear boundary value problems, each of which contains two eigenparameters. These equilibrium equations admit the trivial solution for all values of the eigenparameters, i. e. , for any axial load and any twisting couple. The linearized equilibrium equations have a countable number of eigencurves. Through using the implicit function theorem for Banach spaces it is shown that from each of the eigencurves of the linear problem there bifurcates a two-parameter sheet of nontrivial solutions of the nonlinear equilibrium equations.

引用

页码：67 / 72

页数：6