Numerical calculation for limit values of control parameters in the problem about extension with torsion for special sample in the framed structure

Abstract

The numerical procedure for computation of the loads limit values was considered in this article. This loads apply to discrete gradient mechanical systems. Part of their elements can work at loss of strength stadium already. Methodic was shown for example of the problem about extension with torsion in the framed structure for special sample from nonlinear material. Properties of this material are defined by non-convex potential. This potential describe steady stats (strengthening) and non-steady (loss of strength) of the material. This calculating scheme allow don't solve nonlinear equilibrium equations with gradually increase of loads and test of the stiffness for any equilibrium for definition of loads values, which act the structure accident.

Keywords

• gradient system
• potential function
• critical point
• nonsingular critical point
• hessian matrix
• separatrix
• limit values of control parameters