Two-point constraint approximation in structural optimization

Haftka, R. T.; Nachlas, Joel A.; Watson, Layne T.; Rizzo, Thomas P.; Desai, Rajendra

doi:10.1016/0045-7825(87)90136-8

Cited by 79 publications

(20 citation statements)

References 8 publications

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“…The reanalysis model presented herein is intended to replace the implicit analysis equations (5). Once the displacements r are evaluated, the stresses cr can be calculated by the explicit stress-displacement relations cr=Sr (6) in which S is the stress-transformation matrix.…”

Section: The Number Of Dof Is Not Increasedmentioning

confidence: 99%

Reanalysis Models for Topology Optimization

Kirsch

1997

Topology Optimization in Structural Mechanics

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In part 1 of this paper, efficient reanalysis method for topological optimization of structures is presented. The method is based on combining the computed terms of a series expansion, used as high quality basis vectors, and coefficients of a reduced basis expression. The advantage is that the efficiency of local approximations and the improved quality of global approximations are combined to obtain an effective solution procedure.The method is based on results of a single exact analysis and it can be used with a general finite element program. It is suitable for different types of structure, such as trusses, frames, grillages, etc. Calculation of derivatives is not required, and the errors involved in the approximations can readily be evaluated.In part 2, several numerical examples illustrate the effectiveness of the solution procedure. It is shown that high quality results can be achieved with a small computational effort for various changes in the topology and the geometry of the structure.

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Section: The Number Of Dof Is Not Increasedmentioning

confidence: 99%

Reanalysis Models for Topology Optimization

Kirsch

1997

Topology Optimization in Structural Mechanics

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“…The successive approximation methods were first suggested for structural optimization by Schmit and Farshi (1974). Further development followed in the late seventies (Schmit and Miura 1976) and recently a number of review papers (Prasad 1983;Haftka et al 1987) et al (1987) distinguish between global (or multipoint) and local (single-point) approximations. Local approximations are convenient because derivatives ofresponse quantities are required anyway at a design point for the direction seeking procedure in the optimization algorithm.…”

Section: Introductionmentioning

confidence: 98%

Performance comparison of SAM and SQP methods for structural shape optimization

Barthold

Stander

Stein

1996

Structural Optimization

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This paper presents a numerical performance comparison of a modern version of the well-established sequential quadratic programming (SQP) method and the more recent spherical approximation method (SAM). The comparison is based on the application of these algorithms to examples with nonlinear objective and constraint functions, among others: weight minimization problems in structural shape optimization. The comparison shows that both the SQP and SAM-algorithms are able to converge to accurate minimum weight values. However, because of the lack of a guaranteed convergence property of the SAM method, it exhibits an inability to consistently converge to a fine tolerance. This deficiency is manifested by the appearance of small oscillations in the neighbourhood of the solution.

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“…These non-linear optimization problems usually share the common features: the objective and constraint functions are prohibitively expensive to be examined in use of finite element methods or could be impossible to be evaluated at some combinations of design variables (e.g., nodal displacements, stresses, strains). In order to improve the computational efficiency and accuracy of the solvers dedicated for such structural optimization problems, the Multipoint Approximation Method (MAM) was developed (Haftka et al 1987, Toropov 1989. The advantage of the MAM technique is presented to replace the original optimization problem with a succession of simpler mathematical programming in a scalable trust-region of design space and utilize high quality explicit approximations to reduce the total number of calls for analysis needed for the complicated optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems

Liu

Zhang

et al. 2018

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Abstract:Purpose -In real world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, it is very time-consuming in use of finite element methods. The purpose of this paper is to study the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization, and compares it with the performance of Genetic Algorithms (GA).Design/methodology/approach -In this paper, the enhanced multipoint approximation method (MAM) is utilized to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the Sequential Quadratic Programming (SQP) technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems. Findings-The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem and the superiority of the Hooke-Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.Originality/value -The authors propose three efficient hybrid algorithms: the rounding-off, the coordinate search, and the Hooke-Jeeves search assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy, and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors φ defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.

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Two-point constraint approximation in structural optimization

Cited by 79 publications

References 8 publications

Reanalysis Models for Topology Optimization

Reanalysis Models for Topology Optimization

Performance comparison of SAM and SQP methods for structural shape optimization

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems

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