Numerical Solution of the Consistently Linearized Eigenproblem by Means of a Finite Difference Expression for Approximation of a Directional Derivative in MSC.MARC

Abstract

More recently, a concept of energy‐based categorization of buckling was proposed. It represents a symbiosis of mechanics of solids and spherical geometry. The fundamental mathematical background of this concept is the so‐called consistently linearized eigenproblem. The numerical solution of this eigenproblem by means of the finite element method is a key issue of the mentioned concept. This solution is obtained with the help of the commercial finite element software MSC.MARC . An iterative process, involving the programming lanuages PYTHON and FORTRAN 77 and the software MATLAB , is devised, making use of the available element library, of different types of solvers, and of further modeling tools.