Simplified direct optimization of tubular truss structures

The general problem of optimum design of trusses composed of tubular elements requires the determination of cross‐sectional dimensions for each element which satisfy a set of side constraints on those dimensions as well as Euler and local buckling constraints. A formulation is presented which eliminates the necessity to use mathematical programming methods for the determination of feasible cross‐sectional dimensions. The minimization problem is shown to be expressible in terms of area variables only, with each area subject to bounds which are functions of truss stiffness but which may be obtained by explicit analysis of the element ‘desing space’ for any design. This‘direct’ formulation is completely general and compatible with any minimization algorithm. The formulation also leads to a simple and efficient recursive procedure for producing near‐optimal fully‐constrained designs. Several examples illustrate results obtained by both the direct and recursive procedures.