Evolutionary Structural Shape Optimization Based on Adaptive FEM and Boundary Representation of B-Spline

This paper presents a structural shape optimization algorithm based on the evolutionary structural optimization (ESO) method in conjunction with element error estimate and adaptive FEM. B-splines are used to describe the boundary of the design domain; the shape of these B-splines is governed by a set of master nodes which can be taken as the design variables. The optimal shape of the design boundary with constant stress is achieved iteratively by the movement and update of the position of the master nodes based on nodal stress leveling. The result quality, in terms of accuracy and efficiency, is tested and discussed with an analytical solution.

Download Full-text

Structural Shape Optimization Wth Error Control

20th Design Automation Conference: Volume 2 — Robust Design Applications; Decomposition and Design Optimization; Optimization Tools and Applications ◽

10.1115/detc1994-0112 ◽

1994 ◽

Author(s):

Pierre Duysinx ◽

WeiHong Zhang ◽

HaiGuang Zhong ◽

Pierre Beckers ◽

Claude Fleury

Keyword(s):

Shape Optimization ◽

Computer Aided Design ◽

Adaptive Mesh Refinement ◽

Error Control ◽

Optimization Procedure ◽

Adaptive Mesh ◽

Structural Shape ◽

Structural Shape Optimization ◽

Design Variables ◽

Recent Developments

Abstract A robust and automatic shape optimization procedure is presented in this paper, which incorporates recent developments in the field of computer-aided design (CAD) of mechanical structures, such as geometric modelling, automatic selection of independent design variables, sensitivity analysis using reliable mesh perturbation schemes, error estimation and adaptive mesh refinement. A numerical example is given to show the efficiency of the procedure.

Download Full-text

Structural shape optimization for the torsion problem using direct integration and B-splines

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(93)90179-2 ◽

1993 ◽

Vol 107 (1-2) ◽

pp. 251-268 ◽

Cited By ~ 14

Author(s):

Uwe Schramm ◽

Walter D. Pilkey

Keyword(s):

Shape Optimization ◽

Direct Integration ◽

Torsion Problem ◽

Structural Shape ◽

B Splines ◽

Structural Shape Optimization

Download Full-text

An Algorithm for Automated Design Variable Selection in Structural Shape Optimization With Intrinsically Defined Geometry

Volume 1: 21st Design Automation Conference ◽

10.1115/detc1995-0053 ◽

1995 ◽

Author(s):

James M. Widmann ◽

Sheri D. Sheppard

Keyword(s):

Shape Optimization ◽

Optimization Problems ◽

Analysis Model ◽

Structural Shape ◽

Structural Shape Optimization ◽

Design Variables ◽

Sufficient Set ◽

Compatibility Constraint ◽

Selection Of

Abstract A major difficulty encountered in the shape optimization of structural components is the selection of an adequate set of shape design variables. The quality of the solution and the value of the optimal objective function depend on the chosen set of design variables. This paper presents an algorithm for the automated selection of intrinsically defined design variables to solve two-dimensional structural shape optimization problems. The algorithm arrives at a sufficient set of design variables by solving a series of optimization problems. Using the results of intermediate solutions, the algorithm adaptively refines the set of design variables until the solution converges. The algorithm specifies the addition and deletion of design variables and makes use of a model compatibility constraint to determine whether the analysis model must be updated. Two examples are presented which illustrate the effectiveness of the algorithm.

Download Full-text

Intrinsic Geometry for Shape Optimal Design With Analysis Model Compatibility

20th Design Automation Conference: Volume 2 — Robust Design Applications; Decomposition and Design Optimization; Optimization Tools and Applications ◽

10.1115/detc1994-0137 ◽

1994 ◽

Author(s):

James M. Widmann ◽

Sheri D. Sheppard

Keyword(s):

Shape Optimization ◽

Geometric Modeling ◽

Explicit Knowledge ◽

Optimization Problems ◽

Structural Response ◽

Analysis Model ◽

Intrinsic Geometry ◽

Structural Shape ◽

Structural Shape Optimization ◽

Design Variables

Abstract This paper presents a comparison of geometric modeling techniques and their applicability to structural shape optimization. A method of shape definition based on intrinsic geometric quantities is then outlined. Explicit knowledge of curvature and arc length allow for a quantitative assessment of the compatibility of analysis model with the design model when using finite elements to determine structural response quantities. The compatibility condition is formalized by controlling finite element idealization error and is incorporated into the shape optimization model as simple bounds on the curvature design variables. Several examples of shape optimization problems are solved using sequential quadratic programming which proves to be an effective tool for maintaining the geometric equality constraints that arise from intrinsically defined curves.

Download Full-text