Numerical Considerations in Structural Component Shape Optimization

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.