Iterative Process of AFEM and Ideal Failure Models of Structures

Abstract

This paper considers the input of ideal failure models of structures for solution of algebraic set of equations by means of iterative process when Additional Finite Element Method (AFEM) is used. AFEM is a variant of the Finite Element Method (FEM) for nonlinear analysis of structures according to the forms of collapse. From the FEM point of view, this problem is the analysis of the structure with some nonlinear properties. The author of this paper suggested and worked out AFEM, which realizes such analysis due to rational iterative process for solving of the set of equations. After fulfillment of this main operation, the problem may be considered to be determined. The end and the direction of iterative process are defined under the condition of an ideal failure model, which is the design diagram of the structure at the moment preceding the collapse. Additional design diagrams and additional finite elements (AFEs) are used for introduction of some units of methods of Limit States (Ultimate Equilibrium) and Additional Loads (Elastic Decisions). This is necessary for creation of an iterative process according to the introduced criterion of collapse. The example of such iterative process is given in the paper.