A revised discrete Lagrangian-based search algorithm for the optimal design of skeletal structures using available sections

Issues relating to the application of the discrete Lagrangian method (DLM) to the discrete sizing optimal design of skeletal structures are addressed. The resultant structure, whether truss or rigid frame, is subjected to stress and displacement constraints under multiple load cases. The members’ sections are selected from an available set of profiles. A table that contains sectional properties for all the available profiles is used directly in structural optimization. Each profile in the table is assigned by a unique profile number, which is used as the integer design variable for each of the structural members. It is proposed that we use a revised DLM search algorithm with static weighting to design trusses and rigid frames for minimum weight. Five examples are used to demonstrate the feasibility of the method. It is shown that, for monotonic as well as nonmonotonic constraint functions, the DLM is effective and robust for the discrete sizing design of skeletal structures.

[1]  O. Hasançebi,et al.  Optimal design of planar and space structures with genetic algorithms , 2000 .

[2]  Georg Thierauf,et al.  DISCRETE OPTIMIZATION OF STRUCTURES USING AN IMPROVED PENALTY FUNCTION METHOD , 1993 .

[3]  Lawrence J. Fogel,et al.  Intelligence Through Simulated Evolution: Forty Years of Evolutionary Programming , 1999 .

[4]  Jasbir S. Arora,et al.  Methods for Discrete Variable Structural Optimization , 2000 .

[5]  Zhe Wu,et al.  Improving the performance of weighted Lagrange-multiplier methods for nonlinear constrained optimization , 1997, Proceedings Ninth IEEE International Conference on Tools with Artificial Intelligence.

[6]  J. Abel,et al.  A two-step procedure for discrete minimization of truss weight , 1995 .

[7]  A. R. Toakley,et al.  Optimum Design Using Available Sections , 1968 .

[8]  S. Chai,et al.  A relative difference quotient algorithm for discrete optimization , 1996 .

[9]  G. Jivotovski.  A gradient based heuristic algorithm and its application to discrete optimization of bar structures , 2000 .

[10]  Scott A. Burns,et al.  Recent advances in optimal structural design , 2002 .

[11]  S. Rajeev,et al.  Discrete Optimization of Structures Using Genetic Algorithms , 1992 .

[12]  Nielen Stander,et al.  Optimal discrete sizing of truss structures subject to buckling constraints , 1997 .

[13]  C. S. Krishnamoorthy,et al.  Object-Oriented Framework for Genetic Algorithms with Application to Space Truss Optimization , 2002 .

[14]  Jan A. Snyman,et al.  A regional genetic algorithm for the discrete optimal design of truss structures , 1999 .

[15]  M. P. Saka.  Optimum Design of Skeletal Structures: A Review , 2003 .

[16]  Benjamin W. Wah,et al.  A Discrete Lagrangian-Based Global-Search Method for Solving Satisfiability Problems , 1996, J. Glob. Optim..