TRUSS TOPOLOGY OPTIMIZATION INCLUDING BAR PROPERTIES DIFFERENT FOR TENSION AND COMPRESSION

The problem of optimum truss topology design based on the ground struc ture approach is considered. It is known that any minimum weight truss design (computed subject to equilibrium of forces and stress constrai nts with the same yield stresses for tension and compression) is - up to a scaling - the same as a minimum compliance truss design (subject to static equilibrium and a weight constraint). This relation is gener alized to the case when different properties of the bars for tension a nd for compression additionally are taken into account. This situation particularly covers the case when a structure is optimized which cons ists of rigid (heavy) elements for bars under compression, and of (fig ht) elements which are hardly/not able to carry compression (e.g. rope s). Analogously to the case when tension and compression is handled eq ually, an equivalence is established and proved which relates minimum weight trusses to minimum compliance structures. It is shown how prope rties different for tension and compression pop up in a modified globa l stiffness matrix now depending on tension and compression. A numeric al example is included which shows optimal truss designs for different scenarios, and which proves (once more) the big influence of bar prop erties (different for tension and for compression) on the optimal desi gn.