Problems of nonlinear deformation
Abstract
A method of continuing the solution is discussed with respect to a parameter for a certain class of nonlinear problems in solid mechanics. Modifications of the method are developed in order to implement a unified continuation process at regular and limit points in the set of solutions, with extensions to nonlinear boundary value problems. Algorithms are developed for solving large deflection problems of elastic arches and large axisymmetric deflection problems for shells of revolution. In particular, the algorithms are used for the analysis of large deflections of circular arches and toroidal shells. Examples of natural vibration and stability problems for parallelograms and trapezoidal membranes and panels are given.
 Publication:

IAU Symposium
 Pub Date:
 1991
 Bibcode:
 1991IAUS..........G
 Keywords:

 Continuum Mechanics;
 Deformation;
 Nonlinear Equations;
 Solid Mechanics;
 Bodies Of Revolution;
 Boundary Value Problems;
 Dynamic Structural Analysis;
 Eigenvalues;
 Nonlinear Systems;
 Perturbation Theory;
 Plate Theory;
 Shell Theory;
 Shells (Structural Forms);
 Singularity (Mathematics);
 Vector Analysis;
 Vector Spaces;
 Structural Mechanics