A two-level optimization method for the design of complex truss and parallel distributed implementation on a LAN is presented using parallel virtual machine (PVM) for Win 32 as message passing between PCs. The volumes of truss are minimized by decomposing the original optimization problem into a number of bar optimization problems executed concurrently and a coordinate optimization problem, subject to constraints on nodal displacements, and stresses, buckling and crippling of bars, etc. The system sensitivity analysis that derives the partial derivatives of displacements and stresses with respect to areas are also performed in parallel so as to shorten the analysis time. The convergence and the speedup performances as well as parallel computing efficiency of the method are investigated by the optimization examples of a 52-bar planar truss and a 3 126-bar three-dimensional truss. The results show that the ideal speedup is obtained in the cases of 2 PCs for the 3 126-bar space truss optimization, while no speedup is observed for the 52-bar truss. It!is concluded that (1) the parallel distributed algorithm proposed is efficient on the PC-based LAN for the coarse-grained large optimization problem; (2) to get a high speedup, the problem granularity should match with the network granularity; and (3) the larger the problem size is, the higher the parallel efficiency is.
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