Journal ArticleDOI
Shape optimisation by the boundary element method: a comparison between mathematical programming and normal movement approaches
J. Parvizian,Roger T. Fenner +1 more
TLDR
Solving the optimisation problem of stress concentration for a perforated plate which has an analytical solution, shows that the presented mathematical programming method results in almost the same as the analytical solution.Abstract:
The aim of this work is to find the best boundary shape of a structural component under certain loading, to have minimum weight, or uniformly distributed equivalent stresses. Two shape optimisation algorithms are developed. One of them is a mathematical programming method, and considers nodal coordinates on the design boundary directly as the design variables, while the other one is rather an optimality criterion approach, based on normal movement of the design boundary. Solving the optimisation problem of stress concentration for a perforated plate which has an analytical solution, shows that the presented mathematical programming method results in almost the same as the analytical solution. Nevertheless, increasing the number of design variables to find more smooth shapes in mathematical methods can cause severe programming problems. Comparing the result of this method with that of the optimality criterion indicates that the latter is much easier to apply without any limit on the number of design variables. To calculate stresses at every iteration, the boundary element method (BEM) is used. Therefore both algorithms benefit from a simple mesh generation based on equal length elements, which provides the possibility of solving multiply-connected domains or geometrically complicated mechanical components. Both methods are used to find the optimum shape of a circular plate under radial loading with four design holes. Finally, the problem of the best topology and shape of circular disks is solved by the optimality criterion approach. Also it is proposed that ‘a fully stressed design algorithm which starts from the best topology design, has the best shape for weight optimisation.read more
Citations
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Journal ArticleDOI
Topology optimization using the finite cell method
TL;DR: Very attractive properties of the proposed method can be observed: Due to the high order approach the stress field in the optimized structure is approximated very accurately, no checkerboarding is observed, the iteratively found boundary of the structure is very smooth and the observed number of iterations is in general very small.
Journal ArticleDOI
Optimization of 2D boundary element models using β-splines and genetic algorithms
TL;DR: Two numerical examples are presented and discussed in detail, showing that the proposed combined technique is able to optimize the shape of the domains with minimum computational effort.
Journal ArticleDOI
Shape optimization using the boundary element method and a SAND interior point algorithm for constrained optimization
TL;DR: In this paper, the shape optimization problem is dealt with using the boundary element method (BEM) to define a simultaneous analysis and design formulation (SAND) that is solved using an interior point algorithm.
Journal ArticleDOI
A 3D boundary element optimization approach based on genetic algorithms and surface modeling
TL;DR: The paper summarizes the genetic optimization process, using genetic algorithms and β-spline-surface modeling for the optimization of boundary element models to optimize the shape of domains requiring a minimum of computational effort.
Journal ArticleDOI
Metamodel-assisted distributed genetic algorithms applied to structural shape optimization problems †
TL;DR: A general optimization tool based on distributed real genetic algorithms assisted by metamodel evaluation and applied to structural shape optimization problems of general boundary-element models (BEMs) is developed.
References
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Book
Theory of elasticity
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Book
Numerical Optimization Techniques for Engineering Design: With Applications
TL;DR: This book contains the edited version of lectures and selected papers presented at the NATO ADVANCED STUDY INSTITUTE on computer aided optimal design: Structural and Mechanical Systems, held in Tr6ia, Portugal, 29th June to 11th July 1986.
Journal ArticleDOI
Structural shape optimization — a survey
TL;DR: A survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two-and three-dimensional bodies is given in this paper, where the authors focus on the special problems of shape optimization which are due to a finite element model which must change during the optimization process.
Book
Finite Element Approximation for Optimal Shape Design: Theory and Applications
TL;DR: Algorithms for FEM on the differentation of stiffness and mass matrices and force vectors subgradient method for convex linearly constrained optimization description of the sequential quadratic programming (SQP) algorithm on theDifferentiability of a projection on a convex set in Hilbert space.