A new algorithm for size optimization of the truss structures using finite element method

Abstract

The paper presents a new algorithm for size optimization of the trusses using finite element method. The objective function was established based on weight minimization of trusses . The constraint conditions were formulated based on the conditions that the structure satisfies the strength, stiffness and compatibility requirements, and equilibrium equations. Determination of internal forces, displacements and establishment of the equations are based on finite element method. In order to solve optimization problems using finite element method, the authors proposed a new method for seeking optimal solutions. For truss weight optimization, the authors proposed a coefficient and called this coefficient as “the correlation coefficient of internal forces among trusses’s elements”. This coefficient shows the relationship between the internal forces of truss elements, which was used as the basis for re-selecting the dimensions of cross section of truss elements in iterative process. The paper introduces the calculation procedure and analysis algorithm for weight optimization of planar and space trusses. The examples for weight optimization of planar and space trusses were implemented in a subroutine written in Matlab software. The calculation results using the method proposed by the authors matched with the calculation results using other methods such as Hybridized Genetic Algorithm, Harmony search method, HyperWork, etc. However, using the method proposed by the authors gives less iterative circles.