三次元音響問題における直接微分法に基づく形状感度解析法の定式化(機械力学,計測,自動制御)

概要

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A set of new boundary integral equations relating the sensitivity coefficients of sound pressure and its normal derivative is presented for three-dimensional acoustic problems based on the direct differentiation method. A linear combination of the derived boundary integral equations is used to avoid divergent, erroneous numerical results around the fictitious eigenfrequencies which are observed for exterior acoustic fields. The boundary integral equations have strongly-singular and hypersingular boundary integrals, and are evaluated as principal values and finite-parts for trianglular constant element discretization. The present formulation is more efficiently used for the fast multipole boundary element method than the conventional one which is based on the regularization, because multipole expansion formulas and other translation formulas have to be implemented also for the fundamental solution of the Laplace's equation for the conventional formulation. The effectiveness of the method based on the present formulation is demonstrated through a numerical test example for an exterior acoustic field.
2010-11-25