Home / Journals / CMES / Vol.78, No.2, 2011
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  • Open Access

    ARTICLE

    Acoustic Design Shape and Topology Sensitivity Formulations Based on Adjoint Method and BEM

    T. Matsumoto1, T. Yamada1, T. Takahashi1, C.J. Zheng2, S. Harada1
    CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 77-94, 2011, DOI:10.3970/cmes.2011.078.077
    Abstract Shape design and topology sensitivity formulations for acoustic problems based on adjoint method and the boundary element method are presented and are applied to shape sensitivity analysis and topology optimization of acoustic field. The objective function is assumed to consist only of boundary integrals and quantities defined at certain number of discrete points. The adjoint field is defined so that the sensitivity of the objective function does not include the unknown sensitivity coefficients of the sound pressures and particle velocities on the boundary and in the domain. Since the final sensitivity expression does not have the sensitivity coefficients of the… More >

  • Open Access

    ARTICLE

    Higher-Order Green's Function Derivatives and BEM Evaluation of Stresses at Interior Points in a 3D Generally Anisotropic Solid

    Y.C. Shiah1, C. L. Tan2
    CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095
    Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to… More >

  • Open Access

    ARTICLE

    Generalized Westergaard Stress Functions as Fundamental Solutions

    N.A. Dumont1, E.Y. Mamani1
    CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 109-150, 2011, DOI:10.3970/cmes.2011.078.109
    Abstract A particular implementation of the hybrid boundary element method is presented for the two-dimensional analysis of potential and elasticity problems, which, although general in concept, is suited for fracture mechanics applications. Generalized Westergaard stress functions, as proposed by Tada, Ernst and Paris in 1993, are used as the problem's fundamental solution. The proposed formulation leads to displacement-based concepts that resemble those presented by Crouch and Starfield, although in a variational framework that leads to matrix equations with clear mechanical meanings. Problems of general topology, such as in the case of unbounded and multiply-connected domains, may be modeled. The formulation, which… More >

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