The Formation Of Optimal Null Basis Vectors For The Force Method Analysis Of Finite Element Models Comprising Tetrahedron Elements Using Ant Colony Algorithm

Authors

1 Asst. Prof., Civil Eng. Dept., Faculty of Engineering, University of Isfahan

2 MSc. student, Civil Eng. Dept., Faculty of Engineering, University of Isfahan

Abstract

Most of structural mechanics problems can be solved efficiently by applying the optimization methods. In the structural analysis, a mathematical model is created from idealized structure, which consists of a set of equations with many variables and different matrices. Since the forms of these matrices are not unique, the optimal solution seeks for the most efficient format of the matrices. In this paper, an algorithm is developed for formation of optimal null bases in tetrahedron finite element models. In the proposed optimization model, the interface graph is defined to transfer the topological property of a tetrahedron element into the connectivity of a graph, and a generator is considered for each basis in order to satisfy the independency of statical bases vectors. Each sequence of generators is defined as a tour for an ant travel in ant colony optimization algorithm; therefore an efficient algorithm based on the ant colony system is presented. The optimal null bases result in highly sparse flexibility matrices and efficient force method. One significant feature of the optimal force method analysis is that the calculation is divided in to two independent part. The importance of this feature appears when solving a series of problems with fixed geometry but variable mechanical characteristics of members, such as redesign problems.

Keywords

Main Subjects

Journal of Solid and Fluid Mechanics
Volume 4, Issue 3 - Serial Number 3
September and October 2014
Pages 1-9

Files

Share

How to cite

Statistics