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Optimal design of elastic trusses by approximate equilibrium
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approaches are essentially identical when the step-size parameter is assigned a particular value. Optimal solutions for two design examples are obtained by hybrid methods to show the potential for further development of these methods. Douty, R 'Design of steel connections by math programming'/. 5truct. Div. ASCE Vol 106 NoST5 (May 1980) pp 1135-1154 Much of the work that has been reported on the use of mathematical optimization technqiues in structural design deals with idealized models having a limited number of variables and constraints. As a result the use of mathematical optimization for direct structural design has come to be viewed in many quarters as perhaps interesting, but not very practical. This paper attempts to demonstrate that in fact, practical, competitive structural designs in all possible detail can be generated by such methods and that, as a result, it is quite possible that the bulk of structural design effort could eventually be as consignable to the computer as is now the bulk of the analysis of highly indeterminate structural systems. Fleury, C and Schmit, L A 'Primal and dual methods in structural optimization' ]. 5truct. Div. ASCE Vol 106 No ST5 (May 1980) pp 1117-1134 Application of mathematical programming methods to structural weight minimization problems is briefly reviewed in this paper. It is claimed here that a powerful approach to structural weight minimization can be achieved by constructing a sequence of linearized problems and solving them using either primal or dual algorithms. The advantages and draw backs of both primal and dual methods have been considered in the paper. Some numerical examples have also been presented to illustrate the capabilities of various primal and dual methods. Fok, E, Teferra, M and Spillers, W R A note on 'Optimization using the finite element method' ]. Civil Engng Des. Vol I No 3 (1979) pp 305-310 This note indicates how a finite-element analysis program can be modified to carry out thickness optimization for the case of a Mises material in plane stress.
52
Krisch, U and Benardout, D 'Optimal design of elastic trusses by approximate equilibrium' Comput. Methods Appl. Mechan. Eng. Vol 22 No 3 (June 1980) pp 347-359 Optimal design of elastic trusses is formulated as an approximate linear programming problem. Using the displacement methods of analysis it is shown that the system equilibrium equations represent the only nonlinear functions of the variables. The linear programming formulation is obtained by ignoring temporily the nonlinear terms in the latter equations. An iteractive procedure of solution, based on a sequence of linear programs, is proposed. The proposed procedure provides more flexibility in the solution process compared with the usual algorithms based on a sequence of linear programs and may improve the convergence to the optimum. Radford, A D and Gero, J S 'On optimization in computer aided architectural design. CompuL Rep.CR34 Department of Architectural Science, University of Sydney, NSW, Australia (1980) This report examines the role of computers in the provision of information for architectural design decision-making and compares the potential contributions of simulation, generation and optimization techniques. It argues that optimization models are particularly well suited to the provision of design information because they produce results which are prescriptive, express design options and address the problems of the stability and sensitivity of solutions to change over time. The difficulties posed by the multiple objectives which characterize architectural design problems are discussed and some solution approaches are described. The report concludes that optimization concepts offer a powerful approach to design decision-making and warrant much more research activity in the development of techniques and models for application in architecture. Rosenman, M A and Gero, J S 'Heuristic nonserial dynamic programming for large problems' Comput. Rep. CR35 Department of Architectural Science, University of Sydney, NSW, Australia (1980) Dynamic programming is an extremely powerful optimization approach used for solving problems which can be formulated to exhibit
a serial stage-state structure. However, many design problems are not serial but have highly connected interdependent structures. Existing methods for the solution of nonserial problems require the problem to possess a certain structure or limit the size of the problem due to storage and computational time requirements. The aim of this paper is to show that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics. Saka, M P 'Shape optimization of trusses' /. 5truct. Div. ASCE Vol 106 No ST5 (May 1980) pp 1155-1171 A general procedure for optimum elastic design of trusses is presented in this paper. The difference between this method and the design techniques currently practised is that it does not analyse the structure at all during the design process. The examples solved here show that the way in which the formulation of the design problem is carried out leads to obtain the optimum shape after a relatively small number of iterations. The examples also show that the method is flexible enough to cope with a variety of engineering and architectural requirements. Spillers, W R and Kountouris, G E 'Geometric optimization using simple code representation'/. Struct. Div. ASCE Vol 106 No ST5 (May 1980) pp 959-971 Efforts have been made to model formally the manual procedures used by designers in an attempt to improve computational efficiency in structural optimization. The techniques thus developed, referred to as methods of iterative structural design, is simplification through neglecting the constitutive equations. By doing so it is possible to explain the success of allowable stress design procedures through the formal methods of optimization theory and to show that in some cases these procedure lead to minimum-weight designs. The attempt here is to find some middle ground between a fullblown attempt to automate the American institute of Steel Construction (AISC) Manual and earlier attempts using constant allowable stresses which were simple but somewhat removed from reality.
Collated by Hari Murthy, University of Sydney, AustraHa
c o m p u t e r - a i d e d design
approaches are essentially identical when the step-size parameter is assigned a particular value. Optimal solutions for two design examples are obtained by hybrid methods to show the potential for further development of these methods. Douty, R 'Design of steel connections by math programming'/. 5truct. Div. ASCE Vol 106 NoST5 (May 1980) pp 1135-1154 Much of the work that has been reported on the use of mathematical optimization technqiues in structural design deals with idealized models having a limited number of variables and constraints. As a result the use of mathematical optimization for direct structural design has come to be viewed in many quarters as perhaps interesting, but not very practical. This paper attempts to demonstrate that in fact, practical, competitive structural designs in all possible detail can be generated by such methods and that, as a result, it is quite possible that the bulk of structural design effort could eventually be as consignable to the computer as is now the bulk of the analysis of highly indeterminate structural systems. Fleury, C and Schmit, L A 'Primal and dual methods in structural optimization' ]. 5truct. Div. ASCE Vol 106 No ST5 (May 1980) pp 1117-1134 Application of mathematical programming methods to structural weight minimization problems is briefly reviewed in this paper. It is claimed here that a powerful approach to structural weight minimization can be achieved by constructing a sequence of linearized problems and solving them using either primal or dual algorithms. The advantages and draw backs of both primal and dual methods have been considered in the paper. Some numerical examples have also been presented to illustrate the capabilities of various primal and dual methods. Fok, E, Teferra, M and Spillers, W R A note on 'Optimization using the finite element method' ]. Civil Engng Des. Vol I No 3 (1979) pp 305-310 This note indicates how a finite-element analysis program can be modified to carry out thickness optimization for the case of a Mises material in plane stress.
52
Krisch, U and Benardout, D 'Optimal design of elastic trusses by approximate equilibrium' Comput. Methods Appl. Mechan. Eng. Vol 22 No 3 (June 1980) pp 347-359 Optimal design of elastic trusses is formulated as an approximate linear programming problem. Using the displacement methods of analysis it is shown that the system equilibrium equations represent the only nonlinear functions of the variables. The linear programming formulation is obtained by ignoring temporily the nonlinear terms in the latter equations. An iteractive procedure of solution, based on a sequence of linear programs, is proposed. The proposed procedure provides more flexibility in the solution process compared with the usual algorithms based on a sequence of linear programs and may improve the convergence to the optimum. Radford, A D and Gero, J S 'On optimization in computer aided architectural design. CompuL Rep.CR34 Department of Architectural Science, University of Sydney, NSW, Australia (1980) This report examines the role of computers in the provision of information for architectural design decision-making and compares the potential contributions of simulation, generation and optimization techniques. It argues that optimization models are particularly well suited to the provision of design information because they produce results which are prescriptive, express design options and address the problems of the stability and sensitivity of solutions to change over time. The difficulties posed by the multiple objectives which characterize architectural design problems are discussed and some solution approaches are described. The report concludes that optimization concepts offer a powerful approach to design decision-making and warrant much more research activity in the development of techniques and models for application in architecture. Rosenman, M A and Gero, J S 'Heuristic nonserial dynamic programming for large problems' Comput. Rep. CR35 Department of Architectural Science, University of Sydney, NSW, Australia (1980) Dynamic programming is an extremely powerful optimization approach used for solving problems which can be formulated to exhibit
a serial stage-state structure. However, many design problems are not serial but have highly connected interdependent structures. Existing methods for the solution of nonserial problems require the problem to possess a certain structure or limit the size of the problem due to storage and computational time requirements. The aim of this paper is to show that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics. Saka, M P 'Shape optimization of trusses' /. 5truct. Div. ASCE Vol 106 No ST5 (May 1980) pp 1155-1171 A general procedure for optimum elastic design of trusses is presented in this paper. The difference between this method and the design techniques currently practised is that it does not analyse the structure at all during the design process. The examples solved here show that the way in which the formulation of the design problem is carried out leads to obtain the optimum shape after a relatively small number of iterations. The examples also show that the method is flexible enough to cope with a variety of engineering and architectural requirements. Spillers, W R and Kountouris, G E 'Geometric optimization using simple code representation'/. Struct. Div. ASCE Vol 106 No ST5 (May 1980) pp 959-971 Efforts have been made to model formally the manual procedures used by designers in an attempt to improve computational efficiency in structural optimization. The techniques thus developed, referred to as methods of iterative structural design, is simplification through neglecting the constitutive equations. By doing so it is possible to explain the success of allowable stress design procedures through the formal methods of optimization theory and to show that in some cases these procedure lead to minimum-weight designs. The attempt here is to find some middle ground between a fullblown attempt to automate the American institute of Steel Construction (AISC) Manual and earlier attempts using constant allowable stresses which were simple but somewhat removed from reality.
Collated by Hari Murthy, University of Sydney, AustraHa
c o m p u t e r - a i d e d design