Interactive shape optimization of continuum structures

The monomial method is an alternative to Newton’s method for solving systems of nonlinear algebraic equations. It possesses several properties not shared by Newton’s method that enhance performance, yet does not require substantial computational effort beyond that required for Newton’s method. Previous work has demonstrated that the monomial method treats problems in structural design very effectively. This paper combines the monomial method with the method of generalized geometric programming to treat the problem of structural shape optimization of continuum structures modeled by finite elements.

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Application of the Monomial Method to Shape Optimization

19th Design Automation Conference: Volume 1 — Mechanical System Dynamics; Concurrent and Robust Design; Design for Assembly and Manufacture; Genetic Algorithms in Design and Structural Optimization ◽

10.1115/detc1993-0365 ◽

1993 ◽

Author(s):

Scott A. Burns

Keyword(s):

Shape Optimization ◽

Newton’S Method ◽

Structural Design ◽

Newton's Method ◽

Computational Effort ◽

Algebraic Equations ◽

Structural Shape ◽

Continuum Structures ◽

Structural Shape Optimization ◽

Nonlinear Algebraic Equations

Abstract The monomial method is an alternative to Newton’s method for solving systems of nonlinear algebraic equations. It possesses several properties not shared by Newton’s method that enhance performance, yet does not require substantial computational effort beyond that required for Newton’s method. Previous work has demonstrated that the monomial method treats problems in structural design very effectively. This paper combines the monomial method with the method of generalized geometric programming to treat the problem of structural shape optimization of continuum structures modeled by finite elements.

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Shape optimization of three-dimensional continuum structures via force approximation techniques

AIAA Journal ◽

10.2514/3.10253 ◽

1989 ◽

Vol 27 (9) ◽

pp. 1256-1263 ◽

Cited By ~ 27

Author(s):

Srinivas Kodiyalam ◽

Garret N. Vanderplaats

Keyword(s):

Shape Optimization ◽

Three Dimensional ◽

Continuum Structures ◽

Approximation Techniques

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Sensitivity Analysis With the Shape Optimization Program

16th Design Automation Conference: Volume 2 — Optimal Design and Mechanical Systems Analysis ◽

10.1115/detc1990-0076 ◽

1990 ◽

Author(s):

Erdal Atrek

Keyword(s):

Sensitivity Analysis ◽

Finite Element ◽

Shape Optimization ◽

Computer Program ◽

Continuum Structures ◽

Numerical Examples ◽

Optimization Program

Abstract SHAPE is an industry oriented commercial finite element based computer program for the shape optimization of continuum structures. It employs sensitivity analysis extensively during optimization. A new option allows the user to create, access, and plot sensitivity information for any prescribed design that can be processed by SHAPE. This feature of the program is described herein, and is illustrated by means of numerical examples.

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