An improved approximation for stress constraints in plate structures

Vanderplaats, G. N.; Thomas, Harold

doi:10.1007/bf01743168

Cited by 32 publications

(8 citation statements)

References 11 publications

(10 reference statements)

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“…Vanderplaats [12,13] has shown that, approximating the internal forces first as a linear function of the design variables, is more accurate than approximating the stress constraints directly. In this approach, the linear approximations are used to calculate the internal forces from which the stresses and hence the failure constraint(s) (e.g., von Mises stress) may be calculated.…”

Section: Successive Convex Approximation Methodsmentioning

confidence: 99%

Efficient Sizing of Structures Under Stress Constraints

Zeng¹,

Abdalla²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Optimisation algorithms used to automatically size structural members commonly involve stress constraints to avoid material failure. Therefore the cost of optimisation grows rapidly as the number of structural members is increased due to the corresponding increase in the number of constraints. In this work, an efficient method for large scale stress constrained structural sizing optimisation problems is proposed. A convex, separable, and scalable approximation for stress constraints which splits the approximation into a local fully stressed term and a global load distribution term is introduced. Predictor-corrector interior point method, an excellent option for large scale optimization problem, is chosen to solve the approximate subproblems. The core idea in this work is to achieve computational efficiency in the optimization procedure by avoiding the construction and the solution of the Schur complement system generated by the interior point method. Avoiding the Schur complement, and explicit sensitivity analysis, eliminates the high cost of solving stress constrained problems within the interior point optimisation. This is achieved using the preconditioned conjugate gradient method, and a new preconditioner is proposed specifically for stress constrained problems. The proposed method is applied to a number of beam sizing problems. Numerical results show that optimal complexity is achieved by the algorithm, the computational cost being linearly proportional to the number of sizing variables. 3436

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Section: Successive Convex Approximation Methodsmentioning

confidence: 99%

Efficient Sizing of Structures Under Stress Constraints

Zeng¹,

Abdalla²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…FEAP command consists of "TANG,,1" for linear analysis or a loop of same command for nonlinear analysis. In case one desires employing the adjoint sensitivity, then first the adjoint vector is calculated for a performance function using (6). For this purpose, a user macro is constructed to calculate sensitivity performance to response −( / D).…”

Section: Feap Implementationmentioning

confidence: 99%

“…The material has = 10×10 6 psi (69 GPa) and ] = 0.3. A numerical design is also calculated in [6] with fewer optimization iterations by exploiting improved Journal of Optimization 7 3 3.608 3.566 Tip deflection in. 0.500 0.495 approximation techniques.…”

Section: Compliance Objective and Distributed Loadmentioning

confidence: 99%

“…Thomas et al [3] indicates that early version of Altair OptiStruct is based on application of homogenization method for topology optimization [4]. GENESIS [5] focused on employing advanced approximation techniques [6,7] and sensitivity tools to provide an efficient optimization search [8]. To obtain design sensitivities in ABAQUS, Yi et al [9] application utilized response surface technique to approximate design derivatives for structural optimization of gear damper.…”

Section: Introductionmentioning

confidence: 99%

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A Structural Optimization Framework for Multidisciplinary Design

Kurdi

2015

Journal of Optimization

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This work describes the development of a structural optimization framework adept at accommodating diverse customer requirements. The purpose is to provide a framework accessible to the optimization research analyst. The framework integrates the method of moving asymptotes into the finite element analysis program (FEAP) by exploiting the direct interface capability in FEAP. Analytic sensitivities are incorporated to provide a robust and efficient optimization search. User macros are developed to interface the design algorithm and analytic sensitivity with the finite element analysis program. To test the optimization tool and sensitivity calculations, three sizing and one topology optimization problems are considered. In addition, flutter analysis of a heated panel is analyzed as an example of coupling to nonstructural discipline. In sizing optimization, the calculated semianalytic sensitivities match analytic and finite difference calculations. Differences between analytic designs and numerical ones are less than 2.0% and are attributed to discrete nature of finite elements. In the topology problem, quadratic elements are found robust at resolving checkerboard patterns.

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“…Once the optimal section properties are found, the stress is calculated based on the new properties, and a new approximation in terms of the physical properties is made. This is repeated until the stress converges (Vanderplaats and Thomas 1993;Vanderplaats and Kodiyalam 1990).…”

Section: Introductionmentioning

confidence: 99%

A compliance approximation method applied to variable stiffness composite optimisation

Peeters

Zeng

Abdalla

2018

Struct Multidisc Optim

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A way to approximate the compliance of composites for optimisation is described. A two-level approximation scheme is proposed inspired by traditional approximation concepts such as force approximations and convex linearisation. In level one, an approximation in terms of the reciprocal in-plane stiffness matrix is made. In level two, either the lamination parameters, or the nodal fibre angle distribution are used as design variables. A quadratic approximation is used to build the approximations in terms of the fibre angles. The method of conservative, convex separable approximations is used for the optimisation. Conservativeness is guaranteed by adding a convex damping function to the approximations. Two numerical examples, one optimisng the compliance of a plate clamped on the left, loaded downwards on the bottom right, another one optimising the compliance of a plate loaded with a shear force and a moment show the computational efficiency of the proposed optimisation algorithm.

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An improved approximation for stress constraints in plate structures

Cited by 32 publications

References 11 publications

Efficient Sizing of Structures Under Stress Constraints

Efficient Sizing of Structures Under Stress Constraints

A Structural Optimization Framework for Multidisciplinary Design

A compliance approximation method applied to variable stiffness composite optimisation

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