Sensitivity Analysis With the Shape Optimization Program

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.

Predicting the Benefits of Topology Optimization

2015 ◽  
Author(s):  
Shiguang Deng ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Shape Optimization ◽  
Systematic Method ◽  
Topological Sensitivity ◽  
Numerical Examples ◽  
Initial Design

Topology optimization is a systematic method of generating designs that maximize specific objectives. While it offers significant benefits over traditional shape optimization, topology optimization can be computationally demanding and laborious. Even a simple 3D compliance optimization can take several hours. Further, the optimized topology must typically be manually interpreted and translated into a CAD-friendly and manufacturing friendly design. This poses a predicament: given an initial design, should one optimize its topology? In this paper, we propose a simple metric for predicting the benefits of topology optimization. The metric is derived by exploiting the concept of topological sensitivity, and is computed via a finite element swapping method. The efficacy of the metric is illustrated through numerical examples.

scholarly journals Elasto - plastic analysis of anisotropic hardening materials by finite element method

1985 ◽  
Vol 7 (1) ◽  
pp. 8-13
Author(s):  
Tran Duong Hien
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Yield Criterion ◽  
Element Model ◽  
Isotropic Hardening ◽  
Anisotropic Hardening ◽  
Numerical Examples ◽  
Plastic Analysis ◽  
Hill's Yield Criterion

An elasto- plastic analysis for general three dimes10nal problems using a finite element model is presented. The analysis is based on Hill's yield criterion which included anisotropic materials displaying kinematic - isotropic hardening. The validity and practical applicability of the algorithm are illustrated by a number of numerical examples, calculated by a computer program written in fortran.

scholarly journals Two Algorithms for a Class of Elliptic Problems in Shape Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Tian ◽  
Dai Xiaoxia ◽  
Zhang Chengwei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Shape Optimization ◽  
Variational Problem ◽  
Optimization Problem ◽  
Elliptic Boundary ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Elliptic Boundary Value

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.

Numerical Considerations in Structural Component Shape Optimization

1985 ◽  
Vol 107 (3) ◽  
pp. 334-339 ◽  
Author(s):  
R. J. Yang ◽  
K. K. Choi ◽  
E. J. Haug
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Shape Optimization ◽  
Structural Component ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Test Problems ◽  
Material Derivative ◽  
Boundary Shape ◽  
Component Shape

A unified design sensitivity analysis theory and a linearization method of optimization are employed for structural component shape optimization. A material derivative method for shape design sensitivity analysis, using the variational formulation of the equations of elasticity and the finite element method for numerical analysis, is used to calculate derivatives of stress and other structural response measures with respect to boundary shape. Alternate methods of boundary shape parameterization are investigated, through solution of two test problems that have been treated previously by other methods: a fillet and a torque arm. Numerical experiments with these examples and a variety of finite element models show that component shape optimization requires careful selection of boundary parameterization, finite element model, and finite element grid refinement techniques.

Sensitivity Analysis in Shape Optimization Design for Pressure Vessel

1992 ◽  
Vol 114 (4) ◽  
pp. 428-432 ◽  
Author(s):  
L. Younsheng ◽  
L. Ji
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Shape Optimization ◽  
Pressure Vessel ◽  
Optimization Design ◽  
Element Model ◽  
Element Analysis ◽  
Design Variables ◽  
The Finite Element Analysis ◽  
Derivatives Of

In this paper, sensitivity analysis for a finite element model during shape optimization design for a pressure vessel is discussed. The derivation is emphatically carried out for the derivatives of stiffness matrix and various load ranks with respect to design variables. Because the information resulting from the finite element analysis is fully utilized in this method, the programs are greatly simplified so that it becomes possible to carry out the shape optimization with comparatively more versatility. The conclusion is illustrated by an example.

Finite Element Formulation for the Vibration Analysis of Couple-Stress Continuum

2013 ◽  
Vol 367 ◽  
pp. 156-160
Author(s):  
Wen Zheng Su
Keyword(s):  
Finite Element ◽  
Vibration Analysis ◽  
Couple Stress ◽  
Finite Element Formulation ◽  
Initial Moment ◽  
Element Formulation ◽  
Continuum Structures ◽  
Numerical Examples ◽  
Bubble Function ◽  
Lagrange Element

This paper proposed a finite element formulation to analysis the vibration of couple-stress continuum. A four-node discrete couple-stress element relaxed the requirement of C1 continuity is developed. This element is modified by a bubble function, based on the classical four-ode Lagrange element. The element includes the internal bending constants and the internal initial moment of rotation. Numerical examples show that the present FE scheme is accurate for the eigenvalue analysis of couple-stress continuum structures, especially for the low order frequency analysis.

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