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.

Design Sensitivity Analysis for the Meshfree Shell Structure

2001 ◽  
Author(s):  
Kyung K. Choi ◽  
Nam H. Kim ◽  
Mark E. Botkin
Keyword(s):  
Sensitivity Analysis ◽  
Shell Structure ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Analysis Method ◽  
Sensitivity Equation ◽  
Material Derivative ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Shell Formulation

Abstract A unified design sensitivity analysis method for a meshfree shell structure with respect to sizing, shape, and configuration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. The design variable is selected from the CAD parameters, and a consistent design velocity field is then computed by perturbing the surface geometric matrix. The material derivative concept is used to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and efficiency of the proposed design sensitivity analysis method compared to the analytical solution and the finite difference solution.

Development of a Design Sensitivity Analysis Technique for Explicit Finite Element Software With Applications in Crashworthiness

2000 ◽  
Author(s):  
Douglas W. Stillman
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Time Integration ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Element Analysis ◽  
Automotive Safety ◽  
Explicit Finite Element ◽  
Finite Element Software ◽  
Analysis Technique

Abstract Design Sensitivity Analysis (DSA) is a widely used technique in many areas of finite element analysis, but one that hasn’t yet become available for industrial problems in crashworthiness and automotive safety. In the following effort, an implementation of DSA in the automotive safety simulation program, Radioss, is described. Radioss is a non-linear structures program using an explicit time integration method. A full set of DSA equations are developed and integrated into Radioss so that the design sensitivities can be computed directly and accurately as a result of a single crashworthiness simulation. Some validation results are included. The resulting methodology promises to be an extremely useful tool for engineers involved in the design of safety and crashworthiness of automobiles.

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