On The Determination of Approximate Frequency-Dependent Mass Matrices in The Hybrid Boundary Element Method
Previous works have demonstrated that the concepts introduced by Pian in the finite element method may be generalized in terms of boundary integrals, resulting in a variationally consistent formulation [1, 2]. As a matter of further generalization, De Oliveira  developed some basic formulations of the hybrid boundary element method (HBEM) for time dependent problems. He also demonstrated that too simple formulations, as arrived at from the static fundamental solution, in which the dynamic equilibrium is not explicitly ensured, yield bad numerical results related to high vibration frequencies. Such inaccuracies are also observed in the conventional boundary element formulation (BEM), in case of the double reciprocity with no internal points -and even in the finite element method (FEM), if one eliminates the internal degrees of freedom by means of a static condensation [4, 5].
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