PLASTIC LIMIT ANALYSIS, MATHEMATICAL PROGRAMMING AND GAMS

This paper outlines the use of the mathematical programming modelling language GAMS to solve plastic limit analysis problems. After a review of the close link between limit analysis and mathematical programming, two simple structures are analyzed to impart a flavour of the powerful GAMS language. These examples also serve to show that GAMS can provide a framework for expressing efficiently and transparently the algebraic structural plasticity information contained in plastic analysis models. It is suggested that such modelling languages can play a significant role in promoting the use of mathematical programming methods by engineers for solving engineering plasticity problems

[1]  Arthur M. Geoffrion,et al.  An Introduction to Structured Modeling , 1987 .

[2]  Michael A. Saunders,et al.  A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints , 1982 .

[3]  Jr. James S. Welch,et al.  PAM- a practitioner's approach to modeling , 1987 .

[4]  Li Liu,et al.  State-of-the-art in nonlinear optimization software for the microcomputer , 1989, Comput. Oper. Res..

[5]  Nguyen Dang Hung CEPAO—an automatic program for rigid-plastic and elastic-plastic analysis and optimization of frame structures , 1984 .

[6]  Robert Fourer,et al.  Modeling languages versus matrix generators for linear programming , 1983, TOMS.

[7]  Thomas L. Morin,et al.  Fixed Order Branch-and-Bound Methods for Mixed-Integer Programming: The ZOOM System , 1989, INFORMS J. Comput..

[8]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[9]  Michael A. Saunders,et al.  Large-scale linearly constrained optimization , 1978, Math. Program..

[10]  J. Meeraus A. Bisschop,et al.  ON THE DEVELOPMENT OF A GENERAL ALGEBRAIC MODELING SYSTEM IN A STRATEGIC PLANNING ENVIRONMENT , 1982 .

[11]  Leon S. Lasdon,et al.  Extending Planning Languages to Include Optimization Capabilities , 1986 .

[12]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[13]  Giulio Maier,et al.  Mathematical programming applications to structural mechanics: some introductory thoughts , 1984 .

[14]  On automatic selection of redundancies , 1979 .

[15]  M. Z. Cohn,et al.  Structural Plasticity Computer System: STRUPL , 1979 .

[16]  Leon S. Lasdon,et al.  OR Practice - The Status of Nonlinear Programming Software: An Update , 1987, Oper. Res..