Sensitivity Analysis, Optimization and Inverse Problems
This chapter is devoted to the application of the boundary element method (BEM) to sensitivity analysis, optimization and inverse problems of solid mechanics. A few approaches of sensitivity analysis based on the boundary element formulation are presented
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(BEM) to sensitivity analysis, optimization and inverse problems of solid mechanics. A few approaches of sensitivity analysis based on the boundary element formulation are presented. The influence of the geometry change in extemal or irrtemal boundaries on displacements, stresses and natural frequencies and various kinds of functionals is presented. Applications of sensitivity analysis information and BEM to optimization for different optimality criteria and to defect identification are considered. Evolutionary computations based on boundary element models of structures are applied for various problems of topology and shape optimization. The optimization of elastic and thermoelastic structures and elastoplastic and cracked solids under static and dynamic Ioads is considered. Solutions of a class of inverse problems for identification of voids and cracks and searching optimal boundary conditions are presented. Several numerical examples and tests are included.
1 Introduction The boundary element method (BEM) is well established in research circles as a numerical technique which enables the solution of analysis problems. In such problems one should determine a distribution of statical and dynamical fields of displacements and stresses induced by specified boundary conditions and body forces when the shape of the body and material properties are given. The shape determination of structural components plays an essential role in mechanical designing and the problern of shape sensitivity analysis and the optimal design is much more complicated than the typical conventional analysis. For such problems the shape of structural components is treated as a design variable and boundaries are changing during the design process. Finding the best direction of shape change to minimize or maximize a measure of a merit of the structure becomes a very important prob lern. The determination of the effect of shape change of a structural component is the problern of shape design sensitivity analysis. The value of shape design sensitivity information is greater than conventional analysis with no trend information. To optimize or modity the shape of the structural component, shape design sensitivity analysis for each performance functional is needed. D. Beskos et al. (eds.), Boundary Element Advances in Solid Mechanics © Springer-Verlag Wien 2003
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In the shape optimal design one should deterrnine the shape of the structural component in such a way that an objective functional ought to reach an extremurn and constraints have to be satisfied. It appears that BEM is an exceptionally natural and convenient nurnerical technique in shape sensitivity analysis and the optimal design. Substantialliterature has been developed on BEM sensitivity analysis and the optimal design. W e can mention here Barone and Yang (1989), Burczynski (1993a), Burczynski (1993b), Burczynski and Fedelinski (1990), Burczynski et al. (1995), (1997), Kane and Saigal (1988) and Kane et al. (1992). Inverse problems deal with the deterrnination of the p
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