Narrow Results

We apply here a class of substructuring method to improve the performance of linear tetrahedral element used in finite element analysis (FEA). The method is novel and relied on the construction of mesh inside a tetrahedron volume which behaves as an assembly of substructures. The corresponding stiffness matrix of the mesh is assembled using a static condensation procedure which is used further to obtain strain energy from a set of particular displacement vectors. This energy is the key to obtain a so-called energy ratio that will modify the stiffness matrix of a linear tetrahedral element. In the numerical tests, we show that the method can improve the performance of the tetrahedral element to approximate displacement and stress fields from the analytical solutions for cantilever and stress concentration problems, respectively.

The Helmholtz equation is a reliable model for acoustics in inviscid fluids. Real fluids, however, experience viscous and thermal dissipation that impact the sound propagation dynamics. The viscothermal losses primarily arise in the boundary region between the fluid and solid, the acoustic boundary layers. To preserve model accuracy for structures housing acoustic cavities of comparable size to the boundary layer thickness, meticulous consideration of these losses is essential. Recent research efforts aim to integrate viscothermal effects into acoustic boundary element methods (BEM). While the reduced discretization of BEM is advantageous over finite element methods, it results in fully populated system matrices whose conditioning deteriorates when extended with additional degrees of freedom to account for viscothermal dissipation. Solving such a linear system of equations becomes prohibitively expensive for large-scale applications, as only direct solvers can be used. This work proposes a revised formulation for the viscothermal BEM employing the Schur complement and a change of basis for the boundary coupling. We demonstrate that static condensation significantly improves the conditioning of the coupled problem. When paired with an iterative solution scheme, the approach lowers the algorithmic complexity and thus reduces the computational costs in terms of runtime and storage requirements. The results demonstrate the favorable performance of the new method, indicating its usability for applications of practical relevance in thermoviscous acoustics.