AFEM as the Variant of FEM for Analysis of N-Nonlinear Systems at Limit States

Abstract

AbstractThe aim of this paper is to present the Additional Finite Element Method (AFEM) as a special extended version of the Finite Element Method (FEM) to calculate N-nonlinear physical systems at ultimate limit states. AFEM is used to connect the numerical FEM and the constructive Limit State (Ultimate Equilibrium) Method (LSM). AFEM adds units of well-known methods of analysis to the sequence of solving problems by FEM: structural LSM and numerical Elastic Solution (Additional Load) Method (ESM). The main stiffness matrix and equations have been transformed according to the growth of load and quantity of nonlinear properties. Stiffness metrices of Additional design diagrams (ADD-s) and additional finite elements (AFE-s) are used for numerical modeling of this operation. The mathematical characteristics of these matrices correspond to the requirements of analysis for systems with several (N) nonlinear properties. As a result, the initial design diagram turns into an ideal failure model of structure (design diagram at ultimate limit state). At this moment, all (N) nonlinear properties appear and the structure is close to its limit state. The AFEM numerical algorithm increases the possibilities of FEM for analysis of N-nonlinear physical system at limit state.KeywordsFinite elementEquation setAdditional elementAdditional diagramAdditional loadFailure modelLimit state