A hybrid optimal synthesis method for truss structures considering shape, material and sizing variables

Abstract

Abstract A generalized hybrid optimal synthesis method is developed for truss structures in which the design variables are the co‐ordinates of the panel points, cross‐sectional areas and discrete material kinds of member elements. The primary design problem is formulated in terms of the shape, material and sizing variables and approximated to a sequence of convex and separable subproblems by using mixed direct/reciprocal design variables. Each subproblem is solved by a dual method in which the continuous shape and sizing variables are optimized by a Newton‐type algorithm and the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis. Using the proposed method, discrete material kinds, shape and sizing variables can be systematically improved to obtain an optimum solution. The rigourness, reliability and efficiency of the method are demonstrated by applying it to the minimum cost design of trusses subjected to stress and displacement constraints.