Shape sensitivity analysis of sequential structural–acoustic problems using FEM and BEM
Abstract A shape design sensitivity formulation for structural–acoustic problems using sequential finite element and boundary element methods is presented. Frequency-response analysis is used to obtain the dynamic behavior of the structure, while boundary element analysis is used to solve for the pressure response of the acoustic domain. It is shown that the adjoint method, which takes the reverse direction to response analysis, provides a very efficient way of sensitivity calculation. In addition, it has been shown that the adjoint equation for the shape design problem is the same as that of the sizing design problem. The only difference is the numerical integration that evaluates the sensitivity coefficient. The combination of the semi-analytical method for the structure and the analytical differentiation method for the acoustic cavity yields a very practical approach for the shape design sensitivity formulation. The accuracy of the sensitivity information is compared with the analytical sensitivity as well as the sensitivity calculated using the finite difference method.
Structural sensitivity analysis and optimization
Structural Design and Analysis.- to Structural Design.- Variational Methods of Structural Systems.- Variational Equations and Finite Element Methods.- Design Sensitivity Analysis of Linear Structural Systems.- Discrete Design Sensitivity Analysis.- Continuum Sizing Design Sensitivity Analysis.- Continuum Shape Design Sensitivity Analysis.- Configuration Design Sensitivity Analysis.
Automatic shape optimization of three-dimensional shell structures with large shape changes
Abstract A finite element-based shape optimization program has been developed for three-dimensional shell structures which allows for large shape changes. The new shape optimization program has been achieved by linking together adaptive mesh generation, substructuring, and linear and nonlinear optimization techniques to a commercial finite element analysis program (MSC/NASTRAN). The program has the capability of optimizing shapes by allowing multiple edges to move. A new procedure was developed to determine the best edge to move at each iteration of the shape optimization. The position of this edge is then determined using nonlinear optimization techniques. This process is incrementally continued until the edges are at their minimum positions, or the change in objective function is less than a tolerance value. This program is presently being applied to weight minimization.