论文信息 - A BRANCH AND BOUND ALGORITHM FOR TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURES

A BRANCH AND BOUND ALGORITHM FOR TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURES

An algorithm for the selection of a minimum weight truss, out of a set of possible candidate trusses, is presented. The trusses are subject to stress and deflection constraints. Multiple loading conditions are considered. Starling with a ground structure, a sequence of subtrusses called candidate trusses are generated and analyzed. Several criteria are used to rapidly discard non-optimal configurations. Sequential Quadratic Programming is used to solve a non-linearly constrained problem which is part of the algorithm. A technique, frequently used to keep second derivative approximations positive definite, is found to give numerical instabilities. Possible modifications to improve stability are discussed. Finally, three examples are given to demonstrate the algorithm.

Ulf Ringertz | U. Ringertz

[1] David G. Luenberger,et al. Linear and nonlinear programming , 1984 .

[2] L. Schmit,et al. Automatic minimum weight design of elastic redundant trusses under multiple static loading conditions , 1972 .

[3] M. Powell,et al. On the modification of ^{} factorizations , 1974 .

[4] C. Fleury,et al. Dual methods and approximation concepts in structural synthesis , 1980 .

[5] Lewis P. Felton,et al. Optimization of Truss Geometry , 1969 .

[6] D. Luenberger. Optimization by Vector Space Methods , 1968 .

[7] Shih-Ping Han. A globally convergent method for nonlinear programming , 1975 .

[8] Harvey J. Greenberg,et al. Automatic design of optimal structures , 1964 .

[9] A. J. Morris,et al. Foundations of Structural Optimization: A Unified Approach , 1982 .

[10] U. Ringertz. ON TOPOLOGY OPTIMIZATION OF TRUSSES , 1985 .

[11] M. J. D. Powell,et al. THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS , 1978 .

[12] Shih-Ping Han,et al. Superlinearly convergent variable metric algorithms for general nonlinear programming problems , 1976, Math. Program..

[13] D. Gabay. Reduced quasi-Newton methods with feasibility improvement for nonlinearly constrained optimization , 1982 .

[14] M. Powell,et al. On the Modification of LDL T Factorizations , 1974 .