Application of the Monomial Method to Shape Optimization

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.

Application of the Monomial Method to Shape Optimization

1994 ◽  
Vol 116 (4) ◽  
pp. 1013-1018 ◽  
Author(s):  
S. 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

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.

On a newton-type method under weak conditions with dynamics

2020 ◽  
pp. 2150145
Author(s):  
Manoj Kumar Singh ◽  
Arvind K. Singh
Keyword(s):  
Iterative Methods ◽  
Newton’S Method ◽  
Newton's Method ◽  
Second Order ◽  
Numerical Results ◽  
Order Derivative ◽  
Algebraic Equations ◽  
Type Method ◽  
Nonlinear Algebraic Equations ◽  
Fractal Patterns

In this paper, we present new cubically convergent Newton-type iterative methods with dynamics for solving nonlinear algebraic equations under weak conditions. The proposed methods are free from second-order derivative and work well when [Formula: see text]. Numerical results show that the proposed method performs better when Newton’s method fails or diverges and competes well with same order existing method. Fractal patterns of different methods also support the numerical results and explain the compactness regarding the convergence, divergence, and stability of the methods to different roots.

Structural Shape Optimization Wth Error Control

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.

Structural Shape Optimization with MSC/NASTRAN

1990 ◽  
Author(s):  
SRINIVAS KODIYALAM ◽  
GARRET VANDERPLAATS ◽  
HIROKAZU MIURA ◽  
GOPAL NAGENDRA ◽  
DAVID WALLERSTEIN
Keyword(s):  
Shape Optimization ◽  
Structural Shape ◽  
Structural Shape Optimization
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