Swift Analysis for Size and Geometry Optimization of Structures

Abstract

In this paper an efficient method is presented to reduce the computational complexity of analysis of structures in the process of size and geometry optimization by genetic algorithms. Applying the present method, results in simultaneously swift analysis and optimal design of structures. In this method, using matrix computations, fast solution of the structures is obtained. The analysis of the structures in the optimal design via GA, includes the solution of the relationship F = KΔ in each generation of the genetic algorithm. Inverting the stiffness matrix in each generation and for each population for finding the displacements and internal forces is very time-consuming and costly. Here, using a closed-form matrix solution, compatible with the features of genetic algorithms, the amount of computations is decreased. The optimal analysis of optimal size is performed using a modified solution for structures with changed members and the optimal analysis of optimal geometry is done via a modified solution for structures with changed supports and nodes. To make the method more efficient, proper orderings are presented using the concept of Fiedler vector and partitioning matrices.