A Discrete Method for Lattice Structures Optimization

The paper presents a semi-analytical approach to the discrete optimization of large space-truss structures. The optimization problem is stated as a cost (weight) minimization subject to constraints both on stresses and displacements. Some of the variables such as the cross-sectional areas of bars are chosen from a discrete set (catalogue) of available sections. The mined nonlinear programming problem is transformed to discrete nonlinear programming using the Galerkin procedure in solving the partial difference equations which describe displacements of nodes of the structure. Finally, introducing Boolean variables the problem is solved using algorithms of logical programming. Numerical results are presented for a “Unistrut” type space-truss structure.