The Integrated Approach of FEM-SLP for Solving Problems of Optimal Design

Pedersen, Pauli

doi:10.1007/978-94-009-8603-9_30

Cited by 17 publications

(7 citation statements)

References 12 publications

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“…This led to the Sequential Linear Programming (SLP) method and the wide use of the linear Taylor series approximations. Applications can be found in the paper by Zienkiewicz and Campbell (1973) who optimize the shape of dams and in the paper by Pedersen (1981) who finds the optimum design of space trusses, for example. Another reason for the popularity of local approximations is that, as discussed later, some global approxhnations become very expensive computationally when the dimensionality of the design space becomes large.…”

Section: I Local Function Approximationsmentioning

confidence: 97%

Approximation concepts for optimum structural design — a review

Barthélémy

Haftka

1993

Structural Optimization

485

177

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This paper reviews the basic approximation concepts used in structural optimization. It also discusses some of the most recent developments in that area since the introduction of approximation concepts in the nfid-seventies. The paper distinguishes between local, medium-range and global approximations; it covers function approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It appears also that some new methodologies emerge which could greatly benefit from the introduction of new computer architectures.

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Section: I Local Function Approximationsmentioning

confidence: 97%

Approximation concepts for optimum structural design — a review

Barthélémy

Haftka

1993

Structural Optimization

485

177

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“…The above minimization problem was solved by nonlinear mathematical programming techniques, namely sequential linear programming (SLP) with move-limits (Pedersen 1981), sequential quadratic programming (SQP) (Powell 1977) and sequential convex programming (SCP) (Fleury and Braibant 1986), which are available in the general purpose structural optimization package ADS (Vanderplaats 1987). It was found that among the three strategies, SLP and SCP terminated with fewer functional evaluations but more gradient calculations than SQP.…”

Section: Coy Q-cyy D=mentioning

confidence: 99%

Optimization — a tool in advanced materials technology

Thomsen

Wang

Karihaloo

1994

Structural Optimization

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technology AbstractThis paper demonstrates the use of simple optimization techniques in the production of two advanced materials -a fibre-reinforced composite laminate and a transformation toughened ceramic --having enhanced mechanical properties. Both example materials are based on a brittle matrix prone to cracking at very low applied stresses. The optimization process aims at altering the microstructure so that the materials have enhanced resistance to crack propagation without any undesirable side effects.

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“…The above minimization problem was solved by nonlinear mathematical pro gramming techniques, namely sequential linear programming (SLP) with movelimits (Pedersen 1981), sequential quadratic programming (SQP) (Powell 1977) and sequential convex programming (SCP) (Fleury &;Braibant 1986) which are available in the general purpose structural optimization package ADS (Vanderplaats 1987). The number of functional and gradient evaluations for the above problem and an alternative formulation to be considered below, are given in ta ble 2.…”

Section: Optimization Problem and Solutionmentioning

confidence: 99%

Cracked composite laminates least prone to delamination

Wang

Karihaloo

1994

Proc. R. Soc. Lond. A

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In [( ± θ ) n 2 /(90°) n 1 /( ǂ θ ) n 2 ] fibre-reinforced composites, the outer (± θ ) n 2 sublaminates are known to act as crack arrestors, i. e. to reduce the stress intensity factors at the tips of a crack in the central (90°) n 1 layer in all three modes of loading. The degree of reduction depends on the stiffness of the plies, the ply angle θ and the thickness of the outer sublaminates. However, although the stress intensity factor decreases, the crack-induced largest interfacial principal tensile stress increases. The situation is particularly severe under transverse mode II loading, inevitably resulting in interfacial delamination. The aim of this paper is to choose the design variables of the laminate, namely the ply angle θ , relative ply stiffness and thickness, in such a way as to minimize the stress intensity factor at a crack tip in the (90°) n 1 layer without exceeding the interfacial bond strength. A constraint is also placed on the minimum flexural stiffness of the laminate. An alternative optimization problem in which the largest interfacial principal tensile stress is minimized subject to a limit on the stress intensity factor is also formulated and solved. The above optimization problem is solved in two stages. First, an analysis of the non-homogeneous, anisotropic medium containing a flaw is performed within the bounds of the classical lamination theory and fracture mechanics. This allows development of mathematical expressions relating the stress intensity factor in the central (90°) n 1 layer and the interfacial tensile stress to the sublaminate thickness and stiffness and the ply angle θ . These expressions are highly complicated, precluding a completely analytical approach to the calculation of design sensitivities. In the next stage the optimization problem is reduced to a nonlinear mathematical programming one, whose solution is attempted by several techniques. The sensitivities with respect to the design variables required in these techniques are calculated by a mixed analytical/numerical approach.

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The Integrated Approach of FEM-SLP for Solving Problems of Optimal Design

Cited by 17 publications

References 12 publications

Approximation concepts for optimum structural design — a review

Approximation concepts for optimum structural design — a review

Optimization — a tool in advanced materials technology

Cracked composite laminates least prone to delamination

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