A robust optimality criteria procedure for cross-sectional optimization of frame structures with multiple frequency limits

McGee, O. G.; Phan, Khing

doi:10.1016/0045-7949(91)90001-3

Cited by 21 publications

(8 citation statements)

References 10 publications

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“…8 (see Table 1). This problem has been studied by Khan and Willmert (1981) and McGee and Phan (1991) using the optimality criterion method combined with the finite element method based on the displacement formulation.…”

Section: Member Frame (Two-story and One-bay) With Nonstructural Distmentioning

confidence: 99%

“…The moment of inertia, I is empirically related to the area, A, by the following expressions (Khan and Willmert, 1981;McGee and Phan, 1991):…”

Section: Member Frame (Two-story and One-bay) With Nonstructural Distmentioning

confidence: 99%

“…For example Saka (1984), Khan (1984), Khot (1984), Venkayya and Tischler (1983), Grandhi and Venkayya (1988), Konzelman (1986), Khan and Willmert (1981), McGee and Phan (1991), Khot and Kamat (1985), Saka and Ulker (1992), and Sedaghati and Tabarrok (2000) employed optimality criteria methods in minimization of the weight of truss and beam structures under stress, displacement, frequency or stability constraints. Modern optimality criterion algorithms would involve the case of satisfying the multiple constraints (scaling) and Karush-Kuhn-Tuker (KKT) condition (resizing) alternatively.…”

Section: Introductionmentioning

confidence: 99%

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Benchmark case studies in structural design optimization using the force method

Sedaghati

2005

International Journal of Solids and Structures

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A structural optimization algorithm is developed for truss and beam structures under stress-displacement or frequency constraints. The algorithm combines the mathematical programming based on the Sequential Quadratic Programming (SQP) technique and the finite element technique based on the Integrated Force Method. A new approach based on the single value decomposition technique has been developed to derive the compatibility matrix required in the force method. Benchmark case studies illustrate the procedure and allow the results obtained to be compared with those reported in the literature. It is shown that the computational effort required by the force method is significantly lower than that of the displacement method and in some cases such as structural optimization problems with multiple frequency constraints, the analysis procedure (force or displacement method) significantly affects the final optimum design and the structural optimization based on the force method may result in a lighter design.

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Section: Member Frame (Two-story and One-bay) With Nonstructural Distmentioning

confidence: 99%

“…The moment of inertia, I is empirically related to the area, A, by the following expressions (Khan and Willmert, 1981;McGee and Phan, 1991):…”

Section: Member Frame (Two-story and One-bay) With Nonstructural Distmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Benchmark case studies in structural design optimization using the force method

Sedaghati

2005

International Journal of Solids and Structures

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“…An active set strategy is used to handle lower and upper bounds. While fixed-point iteration algorithms can be found in the structural optimization literature [1][2][3][4][5][6][7][8], these are presented without clearly stating assumptions under which convergence may be achieved, and in fact, have been observed to not converge in certain situations without an explanation [5]. On the other hand, these algorithms have built-in bells and whistles relating to step size control and Lagrange multiplier updates that render them efficient on a wider variety of problems than targeted herein.…”

Section: Introductionmentioning

confidence: 99%

Fixed-point iteration based algorithm for a class of nonlinear programming problems

Belegundu

2017

J. Appl. Math. Comput. Mech.

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Abstract. A fixed-point algorithm is presented for a class of singly constrained nonlinear programming (NLP) problems with bounds. Setting the gradient of the Lagrangian equal to zero yields a set of optimality conditions. However, a direct solution on general problems may yield non-KKT points. Under the assumption that the gradient of the objective function is negative while the gradient of the constraint function is positive, and that the variables are positive, it is shown that the fixed-point iterations can converge to a KKT point. An active set strategy is used to handle lower and upper bounds. While fixed-point iteration algorithms can be found in the structural optimization literature, these are presented without clearly stating assumptions under which convergence may be achieved. They are also problem specific as opposed to working with general functions f, g. Here, the algorithm targets general functions which satisfy the stated assumptions. Further, within this general context, the fixed-point variable update formula is given physical significance. Unlike NLP descent methods, no line search is involved to determine step size which involves many function calls or simulations. Thus, the resulting algorithm is vastly superior for the subclass of problems considered. Moreover, the number of function evaluations remains independent of the number of variables allowing the efficient solution of problems with a large number of variables. Applications and numerical examples are presented.MSC 2010: 47N10, 49M05, 90C30, 90C06, 74P05

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“…McGee and Phan [4] proposed an efficient optimality criteria (OC) method for cross-sectional optimization of twodimensional frame structures. The iterative method involves alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing).…”

Section: Introductionmentioning

confidence: 99%