OPTIMIZATION METHODS FOR TRUSS GEOMETRY AND TOPOLOGY DESIGN

Truss topology design for minimum external work (compliance) can be ex pressed in a number of equivalent potential or complementary energy pr oblem formulations in terms of member forces, displacements and bar ar eas. Using duality principles and non-smooth analysis we show how disp lacements only as well as stresses only formulations can be obtained a nd discuss the implications these formulations have for the constructi on and implementation of efficient algorithms for large-scale truss to pology design. The analysis covers min-max and weighted average multip le load designs with external as well as self-weight loads and extends to the topology design of reinforcement and the topology design of va riable thickness sheets and sandwich plates. On the basis of topology design as an inner problem in a hierarchical procedure, the combined g eometry and topology design of truss structures is also considered. Nu merical results and illustrative examples are presented.