Wave packet enriched finite elements for thermo-electro-elastic wave propagation problems with discontinuous wavefronts

Abstract

In this article, we study the numerical properties of the recently developed local (element-domain) harmonic basis function enriched finite element (FE) for wave propagation problems. The study includes the effect of the enrichment harmonics on the conditioning of system matrices and how the diagonal scaling mass lumping technique influences the possible ill-conditioning and the solution accuracy. Subsequently, a wave packet enriched thermoelectromechanical FE formulation is presented for axisymmetric and planar wave propagation problems in piezoelastic media. The conventional Lagrange interpolations for the displacement, temperature, and electric potential fields are enriched with the element-domain sinusoidal functions which satisfy the partition of unity condition. The extended Hamilton’s principle and constitutive relations of the Lord–Shulman and Green–Lindsay generalized piezothermoelasticity are employed to derive the coupled system of equations of motion which is solved using Newmark-$\beta$ direct time integration scheme. The performance of the proposed elements is assessed and wave characteristics are studied for the problems of thermoelastic shock waves in an elastic annular disk and thermoelectric shock waves in a piezoelectric hollow cylinder. The element shows significant improvement in the computational efficiency and accuracy over the conventional FE for these problems involving sharp discontinuities in the fields at the wavefronts.

Keywords:

• Enriched finite element
• impact
• piezoelectric material
• piezothermoelasticity
• thermal shock
• wave packet enrichment
• wave propagation

Additional information

Funding

S. Kapuria is thankful to the Science & Engineering Research Board, Government of India, for supporting this work through Sir J. C. Bose National Fellowship (Grant No. JCB/2018/000025).