Concurrent Optimization of Large Structures. I: Algorithms

Parallel algorithms are presented for optimization of structures on shared-memory multiprocessor computers. Structures subjected to multiple loading cases with limitations on nodal displacements, element stresses, and member sizes are optimized using the optimality-criteria approach in a concurrent-processing environment. Emphasis is directed toward parallelizing each computational step of the solution process. Parallel algorithms are developed to assure the best concurrent performance and speed-up within each step. A substructuring algorithm is used to achieve the best work-load balance during the solution of the generalized displacements. Concurrency is achieved through the use of the notion of cheap concurrency and the concept of threads. (A companion paper demonstrates the efficiency of the parallel algorithms through optimization of several truss and frame problems on an Encore Multimax shared-memory computer for a variable number of processors.) The algorithms are particularly suitable for optimization of large structures such as space stations.