An efficient optimality criterion method for natural frequency constrained structures

Khan, Mohsin; Willmert, K. D.

doi:10.1016/0045-7949(81)90071-7

Cited by 41 publications

(14 citation statements)

References 10 publications

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“…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: 98%

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: Introductionmentioning

confidence: 98%

Benchmark case studies in structural design optimization using the force method

Sedaghati

2005

International Journal of Solids and Structures

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“…, 1979Syed el al. 1980;Khan and Willmert 1981;Khan 1984;Khot 1985;Granhdi and Venkayya 1986;Venkayya and Tischler 1983) depends on the selection of a proper step size (which is similar to a move limit in classical mathematical programming methods). Without a clear reading of the step size, the convergence to a local optimum solution is many times oscillatory.…”

Section: Introductionmentioning

confidence: 98%

On the convergence quality of minimum-weight design of large space frames under multiple dynamic constraints

McGee

Phan

1992

Structural Optimization

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Weight optimization of large space frames under dynamic constraints requires adaptable design search techniques because of the enormous number of sizing variables, the highly nonlinear frequency constraint surfaces, and the multiple points of local minima. With modern OC procedures, based on alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing), the convergence to weight minima is oftentimes oscillatory. Even though the convergence rate for OC methods is initially fast, it gradually slows near local extrema, mainly because the selection of appropriate step sizes (or move limits) in the redesign phase becomes increasingly difficult. The focus here is to create specific criteria based on past scaled designs to *'damp out" the oscillatory convergence propensity of OC recursive methods. Several OC recursive strategies, which are frequently worked to resize and to evaluate the Lagrange multipliers, are steered by the present approach to design large space frames under multiple dynamic constraints. Besides this, the design iteration histories obtained by the various recursive strategies are compared graphically. On the whole, the present OC approach achieves a smooth upper-bound convergence to weight minima, as it quickly dissolves the (sometimes violent) oscillations of scaled weights in the iteration history. Most of all, the method eliminates the need for adjustments of internal parameters during the redesign phase.

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“…Minimum weight problems under frequency constraints for truss structures were analysed by Kiusalaas and Shaw (1978), Khot (1985) and Grandhi and Venkayya (1988). Similar problems under a single frequency constraint and including only bending deformations were presented by Khan and Willmert (1981).…”

Section: Introductionmentioning

confidence: 99%

Optimality criterion for maximum fundamental frequency of free vibrations of frames including axial and bending effects

Szyszkowski

King

1993

Structural Optimization

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A b s t r a c tAn optimality criterion for maximum multiple fundamental frequency of free vibrations for structures of prescribed weights is presented. The criterion includes both axial and bending effects and can be used for analysis of truss, beam and frame structures. The error norm based on the criterion is proposed and used to verify trial designs against the optimum. The accompanying iterative procedure reduces this error norm to zero and drives a trial design to the optimum. The modality of the design at the optimum and the corresponding set of Lagrange multipliers are determined automatically.

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An efficient optimality criterion method for natural frequency constrained structures

Cited by 41 publications

References 10 publications

Benchmark case studies in structural design optimization using the force method

Benchmark case studies in structural design optimization using the force method

On the convergence quality of minimum-weight design of large space frames under multiple dynamic constraints

Optimality criterion for maximum fundamental frequency of free vibrations of frames including axial and bending effects

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