Trefftz functions and application to 3D elasticity

When solving complex boundary value problems, the primary advantage of the Trefftz method is that Trefftz functions a priori satisfy the governing differential equations. For the treatment of three-dimensional isotropic elasticity problems, it is proposed that the bi-harmonic solutions in Boussinesq's method can be expressed as half-space Fourier series to bypass the difficulties of integration. A total of 29 Trefftz terms for each component of the displacement vectors are derived from the general solutions of the elasticity system. Numerical assessments on the proposed formulations are performed through two examples (a cubic and a cylindrical body). Results are compared with those from the method of fundamental solutions (MFS) and the commercial finite element method (FEM) software STRAND 7, suggesting that Trefftz functions can provide pseudo-stability, faster convergence and reduced error margins.