Showing papers on "Shape optimization published in 1985"
TL;DR: A finite element mesh generation capability which requires only boundary information is used to generate the mesh, and a solution-based adaptive mesh refinement scheme is usedto provide a more accurate estimate of the true solution.
Abstract: Earlier work on shape optimization indicated that a simple problem description format was crucial to effective use of the program. As a result, a geometric problem description format which uses only boundary information was developed. A finite element mesh generation capability which requires only boundary information is used to generate the mesh, and a solution-based adaptive mesh refinement scheme is used to provide a more accurate estimate of the true solution. During the optimization process, periodic refinements are performed to generate estimates of the refined stresses based on unrefined solutions. Nonlinearities in the constraints led to some convergence difficulties; however, minimum mass designs typically were obtained in 30-40 finite element solutions.
230 citations
TL;DR: In this article, a finite element analysis code is adapted to the purposes of the method and numerical examples are performed and comparisons made with sensitivity analysis based on forward finite differences, where the authors use a finite number of master nodes to characterize the surfaces of a set of isoparametric finite elements and the adoption of their coordinates as design variables of the shape optimization.
107 citations
1 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.
Abstract: This paper is a survey of structural shape optimization with an emphasis on techniques dealing with shape optimization of the boundaries of two and three dimensional bodies. Attention is focused on the special problems of structural shape optimization which are due to a finite element model which must change during the optimization process. These problems include the requirement for sophisticated automated mesh generation techniques and careful choice of design variables. They also include special problems in obtaining sufficiently accurate sensitivity derivatives.
100 citations
TL;DR: This work has now been extended to handle structures created from an assembly of segments that may be rotated into any plane as well as to contain the nonplanar surface curvature within any segment.
Abstract: The basic features of a previously described shape optimization capability included a general geometric problem description format and adaptive finite element analysis. The finite element mesh for each design step was created from the boundary information only and refined using finite element solution results. At that time, only structures in a single plane could be treated. This work has now been extended to handle structures created from an assembly of segments that may be rotated into any plane as well as to contain the nonplanar surface curvature within any segment. In order to handle these more general problems, it was necessary to introduce a more efficient mesh generation scheme. Several design examples are presented to demonstrate each of the features.
52 citations
32 citations
TL;DR: In this article, the problem of optimal shaping of a free and loaded boundary has been formulated in terms of the boundary element method, where a maximal stiffness criterion together with the limitation of volume of a body has been used.
29 citations
25 citations
1 Jan 1985
18 citations
TL;DR: In this paper, a unified shape optimum design scheme combining the material derivative and boundary parametrization is presented to find the optimal cross-sectional shapes of elastic hollow bars, based on bending stiffness, the torsional rigidity, or the weight of the bar.
Abstract: In this paper a unified shape optimum design scheme, combining the material derivative and boundary parametrization is presented to find the optimal cross-sectional shapes of elastic hollow bars. Performance criteria can be the bending stiffness, the torsional rigidity, or the weight of the bar. The existence of a keyway (an example of geometric irregularity) can be considered as well. Material property can be either isotropic or anisotropic. Various numerical examples have been provided to show the validity of the presented approach.
12 citations
1 Jan 1985
TL;DR: In this article, a shape optimization method for elastic beams with segmentwise constant height is proposed, where the ends of the beam are simply supported, clamped or free, and the deflection is expanded into a Fourier series by eigenfunctions.
TL;DR: It is shown that cost-efficient methods for structural sizing may be advantageously extended to shape optimal design problems and a new general optimization algorithm is presented that combines mixed approximations and dual methods.