Computational efficiency of non‐linear programming methods on a class of structural problems

Carpenter, William C.; Smith, Erling A.

doi:10.1002/nme.1620110803

Cited by 15 publications

(3 citation statements)

References 7 publications

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“…A savings of ( m -1)NOD' and (nl)NODZ has been demonstrated over two other techniques in the literature for computing gradient of 4 (References 25 and 35). It should be noted that (20) does not involve computing the gradient, dgi(b, z(b))/dh for any individual constraint function.…”

Section: Algorithm 3 Conceptual Multiplier Algorithmmentioning

confidence: 99%

A study of mathematical programming methods for structural optimization. Part I: Theory

Belegundu¹,

Arora

1985

Numerical Meth Engineering

302

100

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SUMMARYA comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

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Section: Algorithm 3 Conceptual Multiplier Algorithmmentioning

confidence: 99%

A study of mathematical programming methods for structural optimization. Part I: Theory

Belegundu¹,

Arora

1985

Numerical Meth Engineering

302

100

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show abstract

“…have been used and compared to optimize the weight of plane trusses alongside plane stress plates (Jóźwiak, 1989). In (Carpenter & Smith, 1977) the optimal designs were achieved by minimizing the average mass value for trusses using a probability-based problem, which was also converted into a nonlinear programming model. In addition, some studies have been carried out to realize more advanced designs, techniques and applications.…”

Section: Weight Optimization Of Plane Trussesmentioning

confidence: 99%

A generative design-to-BIM workflow for minimum weight plane truss design

Malgit¹,

Işıkdağ

Bekdaş

et al. 2022

rdlc

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Structural design has a significant impact on the overall cost of truss structures. In order to reduce the cost of a structure it is important to support designers' decision making starting from the early design phase. In this study, an optimization workflow is proposed, developed and implemented using well known generative design and Building Information Modeling (BIM) tools to achieve a cost-optimal design of a truss structure in the early design phase. Generative design aims to develop products that are lighter, stronger, more efficient and tailored to the specific needs of end users. Generative design tools allow users to create efficient designs via optimizing factors such as cost, weight, energy efficiency and performance. The aim of this study was to develop an optimization workflow to find and model the minimum weight / minimum cost design alternative in the early design phase using generative design, structural analysis and BIM tools in an integrated manner. The goal for the optimization was determined as finding the minimum weight (thus minimum cost) structure among the generated design alternatives. The single span steel truss was selected as the structure to be optimized, and optimization scenarios were prepared and implemented to determine the structural components of the truss with minimum weight. The results demonstrated that through integrated use of structural analysis, generative design and BIM tools minimum-weight truss design can be realized easily and practically.

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“…Because a great number of functional evaluations may be required in the solution of a typical engineering optimization problem and because functional evaluations can be computationally expensive, a great deal of early research effort involved seeking optimum solution techniques which used as few function evaluations as possible. Work by Carpenter and Smith (1977), for example, looked at the efficiency of optimization algorithms on structural engineering problems. Others, such as Schmit and Farshi (1974) and Fleury (1989), considered various formulations of the problem so as to minimize the number of functional evaluations performed.…”

Section: Introductionmentioning

confidence: 99%

A comparison of polynomial approximations and artificial neural nets as response surfaces

Carpenter

Barthélémy

1993

Structural Optimization

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Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net and the number of designs needed to train an approximation is discussed.

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Computational efficiency of non‐linear programming methods on a class of structural problems

Cited by 15 publications

References 7 publications

A study of mathematical programming methods for structural optimization. Part I: Theory

A study of mathematical programming methods for structural optimization. Part I: Theory

A generative design-to-BIM workflow for minimum weight plane truss design

A comparison of polynomial approximations and artificial neural nets as response surfaces

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