Euler Buckling and Minimal Element Length Constraints in Sizing and Shape Optimization of Planar Trusses

Abstract

Structural optimization of trusses is a complex process and requires a realistic representation of the problem in order to achieve applicable results. In addition to using typical constraints such as minimal and maximal allowable stress and minimal displacement, in this paper dynamic constraints for Euler bucking have been used as well as minimal element length constraints for shape optimization. As shape variables can give short, impractical elements or even be in the same location, making the element length effectively 0, the minimal length constraint ensures that solutions can be produced. These constraints were used on a standard test examples with 10 and 47 bars using genetic algorithm optimization. Shape optimization results are compared to results of simultaneous sizing and shape optimization.