Computation of Equilibrium Paths in Nonlinear Finite Element Models

Abstract

In the present paper, equilibrium paths are simulated applying the nonlinear finite element model. On the equilibrium paths, there are identified critical points which contribute to understanding and quantification of stability processes in a nonlinear system. By means of nonlinear solution, bifurcation points from which two equilibrium path branches emanate and so there is no unique tangent were identified and drawn. Mutual position of limit and bifurcation points was identified. The paper describes multidisciplinary problems of the analysis of limit states of nonlinear systems. The methods of stochastic and sensibility analyses which are frequently applied to assessment of the safety and reliability of supporting structural systems are discussed.In the present paper, equilibrium paths are simulated applying the nonlinear finite element model. On the equilibrium paths, there are identified critical points which contribute to understanding and quantification of stability processes in a nonlinear system. By means of nonlinear solution, bifurcation points from which two equilibrium path branches emanate and so there is no unique tangent were identified and drawn. Mutual position of limit and bifurcation points was identified. The paper describes multidisciplinary problems of the analysis of limit states of nonlinear systems. The methods of stochastic and sensibility analyses which are frequently applied to assessment of the safety and reliability of supporting structural systems are discussed.