Acoustic displacement tetrahedra developed using the IET rules

Acoustoelastic pure-displacement elements based on Biot’s poromechanics theory

“…It must have the same nodal fluid degrees of freedom as the original matrix. The one developed in [7] is used in this paper. The displacement-based acoustic fluid proposed by Hamdi et al [3] is also a serious candidate.…”

“…The coefficient is not determined in Hamdi's paper. The element developed by Correa et al [7] presents a closed form for this factor and, because it satisfies the Individual Element Test of Bergan and Hanssen [9], a different factor for each element can be used without affecting convergence. The following form for the stiffness matrix is proposed:…”

“…The matrix KJJ S ' C is the one for computing the unit changes in the volume of the fluid and the matrix K rot is the one in charge of computing energy under a fluid rotation. In [7] a is obtained using dynamic fluid behaviour considerations. No changes are needed for the out-ofdiagonal sub-matrix.…”

“…In [7], the following closed form was obtained for the stabilization factor: 21 F (38) where h, in metres, is a measure of the element size. When h ranges from 1 m to 1 cm, a ranges from 25 to 210,000.…”

“…Raviart-Thomas expansions produce irrotational fields, but they have the problem that degrees of freedom are placed at the midsides or at the centre-face of finite elements, making it difficult to interface them with standard elements [6]. The other solution was introduced in [7], where, by the use of the Parameterized Variational Principies [8] and the Individual Element Test [9], a weakly irrotational constraint is introduced in the original formulation. It also required the introduction of an additional parameter, but an energy balance allowed the authors to compute it in closed form as a function of element size.…”