Journal Article10.1080/03601218308907451
An Efficient Technique in Shape Optimization
M. Week,P. Stelnke +1 more
- 01 Jan 1983
- Vol. 11, Iss: 4, pp 433-449
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TL;DR: In this paper, a shape optimization method is presented for smoothing stress peaks that are caused by notch effects on unloaded edges of holes in plates or shell structures with linear-elastic, homogeneous, isotropic material under external forces.
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Abstract: A shape optimization method is presented for smoothing stress peaks that are caused by notch effects on unloaded edges of holes in plates or shell structures with linear-elastic, homogeneous, isotropic material under external forces. The optimization problem is first formulated as a functional whose integrand contains the difference between the stresses at the hole edge and the optimal stress. This mechanical problem is approximated by a sequence of purely geometric, substitute functionals. The substitute functional is discretized by means of splines and formulated as a nonlinear constrained optimization problem which is solved with a quasi-Newton method. The efficiency of the method is demonstrated on the basis of examples.
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Citations
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.
604
Shape optimization of structures: a literature survey
TL;DR: Several steps in the shape optimization process, such as model description, selection of the objective function and shape variables, representation of boundary shape, finite element mesh generation and refinement, sensitivity analysis and solution methods, are reviewed in detail as discussed by the authors.
305
Structural shape optimization - A survey
Raphael T. Haftka,Ramana V. Grandhi +1 more
- 01 Jan 1985
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.
100
A review of structural shape optimization
TL;DR: A general review of structural shape optimization can be found in this article, with emphasis on the recent developments in this field and the difficulties in expanding from two-to-three-dimensional shape optimization.
92
A geometry-based parameterization method for shape design of elastic solids
Kuang-Hua Chang,Kyung K. Choi +1 more
TL;DR: In this article, a shape design parameterization method that is built on the geometric modeler PATRAN is presented, where a number of geometric entities that represent structural design boundaries are parameterized, and a design parameter linking process can be performed to create geometric features from geometric entities.
74
References
Optimization of shape to minimize stress concentration
TL;DR: In this paper, the problem of minimizing stress concentrations in machinery components is formulated as one of unconstrained minimization by incorporating all "side" constraints on design variables by use of penalty functions.
166
On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases
TL;DR: In this paper, the shape of a plate in plane stress is determined, such that the maximum elastic stress corresponding to given loads is minimized, and optimization is carried out by solving a sequence of linearized minimum-maximum problems using linear programming.
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