Software complexes and new approaches to non-linear analysis of framed structures

Abstract

There is a great number of non-linear tasks which can be solved with the use of computer-based simulation and finite elements method (FEM). But in order to ensure high speed and accuracy of calculations it is necessary to use new mathematical models and algorithms. The analysis of the known FEM forms and approaches to numerical solution of tasks based on force method is performed in this work. Represented in the document is formulation of the finite-element stress method and algorithmization of the classical force method for calculation of framed structures based on the equation of strain compatibility – contour forces method. Statement of problems which can be more effective from the point of view of elastic-plastic deformations at numerical solution is considered. In particular, the hybrid finite-element method based on the generalized Mohr formula for determination of long bar stiffness coefficient with account of non-linear behavior. The main relationships for creation of finite-element method equation system in the form of force method are represented.