Applied Element Method - Application to Linear Static Analysis

Abstract

The Finite element method and other numerical methods are very e ectively im- plemented in static as well as dynamic, linear and nonlinear analysis of structure. Recently, a new method has been developed called Applied Element Method (AEM). This method is more applicable for failure modelling of structure. Applied element method is used for modelling of structure subjected to large displacement and when there is possibility of separation of structural elements. FEM is helpful in predicting failure of structure but can not model separation of elements. The main advantage of applied element method is that it can track the structural collapse behaviour passing through all stages of the application of loads, like elastic stage, crack initiation and propagation in tension-weak materials, reinforcement yielding, element separation, el- ement collision (contact), and collision with the ground and with adjacent structures. The objective of present study is to understand application of AEM for linear static analysis of structure. In applied element method structure is assumed to be di- vided into number of rigid elements connected by springs. Springs represent force- displacement relationship of structural elements. So, derivation of sti ness matrix in AEM is di erent than that of FEM. The present study deals with derivation of sti ness matrix for one dimensional and two dimensional elements. The study also includes basic introduction of applied element method and funda- mental di erence between FEM and AEM. Methodology used for applied element analysis is presented. Computer program for meshing of various types of structure is prepared and is used for preparing input data for main applied element analysis pro- gram. One dimensional problems like axially loaded column subjected to point load and uniformly distributed load is studied. Two dimensional problems like cantilever beam, deep beam with and without opening, portal frame are solved using computer program developed for Applied Element Analysis. Displacement results are obtained by varying size of elements and varying number of springs used for connectivity of elements. For comparison of analysis results of AEM, nite element analysis of struc- ture is carried out using ANSYS software. From the application of AEM to various problems it is observed that it can analyse various structure with similar accuracy as nite element analysis. Further the program developed in this study can be modi ed for dynamic analysis as well as for nonlinear analysis.