Structural optimization by methods of feasible directions

Vanderplaats, G. N.; Moses, Fred

doi:10.1016/0045-7949(73)90055-2

Cited by 208 publications

(51 citation statements)

References 4 publications

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“…The FDM was first proposed by Zoutendijk [14] and later Vanderplaats et al [15] applied the algorithm on design optimisation of space truss structures. Since then the FDM has been one of the most popular methods for finite element analysis based structural optimisation [13].…”

Section: Feasible Direction Methodsmentioning

confidence: 99%

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Optimum Shape Design of Composite Structures Using Boundary-Element Method.

Tafreshi

2005

AIAA Journal

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The boundary element method, combined with a numerical optimisation algorithm, has been employed for the shape optimisation of two-dimensional anisotropic structures. To find the optimum shape of a structure with the highest stiffness, the elastic compliance of the structure has been minimized subject to constraints upon stresses, weight and geometry.The optimum shapes of a series of anisotropic structures are obtained for maximum stiffness and minimum weight and stress, for specified loading conditions. The results are compared with the optimum shapes which were already created by the minimization of the structural weight while satisfying certain constraints upon stresses and geometry. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities of anisotropic materials. Because of the nonlinear nature of the mean compliance, weight and stresses, the numerical optimisation algorithm used is the feasible direction method, together with the golden section method for the one-dimensional search. Hermitian cubic spline functions are used to represent boundary shapes which offer considerable advantages in fitting a wide range of curves, and in the automatic remeshing process. Five example problems with anisotropic materialproperties are presented to demonstrate the applications of this general-purpose program.

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Section: Feasible Direction Methodsmentioning

confidence: 99%

“…By assuming the constraint is nonlinear and convex, a small move in this direction would violate the constraint. With these objectives, the following direction-finding problem is posed [14,15].…”

Section: Feasible Direction Methodsmentioning

confidence: 99%

Optimum Shape Design of Composite Structures Using Boundary-Element Method.

Tafreshi

2005

AIAA Journal

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“…2a and 2b. Both coefficients A and B as well as the exponent p were determined by the nonlinear optimization algorithm CONMIN [13] implemented in the software package slangTNG [5]. For the parallel system, it was found that p = 0.29 and for the series system p = 0.62.…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

Application of Asymptotic Sampling to Structural Reliability Problems

Bucher¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Monte Carlo methods are most versatile regarding applications to the reliability analysis of high-dimensional nonlinear structural systems. In addition to its versatility, the computational efficacy of Monte Carlo method is not adversely affected by the dimensionality of the problem. Crude Monte Carlo techniques, however, are very inefficient for extremely small failure probabilities such as typically required for sensitive structural systems. Therefore methods to increase the efficacy for small failure probability while keeping the adverse influence of dimensionality small are desirable.On such method is the asymptotic sampling method. Within the framework of this method, well-known asymptotic properties of the reliability index regarding the scaling of the basic variables are exploited to construct a regression model which allows to determine the reliability index for extremely small failure probabilities with high precision using a moderate number of Monte Carlo samples.The basic concepts underlying this method are explained in detail. Its applicability is demonstrated by solving the first passage problem involving several thousands of random variables. All results are cross-checked agains crude Monte Carlo results with an extremely large sample size. It is shown that the necessary number of samples can be reduced by several orders of magnitude as compared to crude Monte Carlo.

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“…A1 1 calculations were performed w i t h t h e computer program PASCO (Anderson and Stroud, 1979;and Stroud, Greene, and Anderson, 1981). PASCO , contains the computer program VIPASA ( Y i t t r i c k and Williams, 1974) f o r the buckling analysis o f s t i f f e n e d panels and the computer program CONMIN (Vanderplaats and Hoses, 1973) as the optimizer.…”

Section: W Jefferson Stroud Nasa-langley Research Centermentioning

confidence: 99%

Optimization of Composite Structures

Stroud

1983

Mechanics of Composite Materials

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Structural optimization by methods of feasible directions

Cited by 208 publications

References 4 publications

Optimum Shape Design of Composite Structures Using Boundary-Element Method.

Optimum Shape Design of Composite Structures Using Boundary-Element Method.

Application of Asymptotic Sampling to Structural Reliability Problems

Optimization of Composite Structures

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