INTENT Project contributes a new time-stepping solution for transient elastodynamic simulations

Engineering Analysis with Boundary Elements has published a new open-access paper by Sandra Silva Pinto and Ionuţ Dragoş Moldovan, entitled “An efficient time-stepping solution for transient elastodynamic problems using hybrid-Trefftz finite elements”.

The paper presents a new hybrid-Trefftz finite element formulation for transient elastodynamic problems, combining classical time-stepping algorithms with a Trefftz-based Dual Reciprocity Method. This allows transient analyses to be performed over arbitrary time durations, while preserving the main advantages of hybrid-Trefftz formulations: implicit satisfaction of the governing equations in the domain and a boundary-only solving system.

A central contribution of the work is the construction of the particular solution using regular Trefftz-type trial functions associated with artificial frequencies. This avoids the complex and potentially singular expressions typically found in conventional Dual Reciprocity formulations for elastodynamics.

The formulation was implemented in the open-source FreeHyTE platform and validated through benchmark problems involving shock-wave propagation in bounded and semi-unbounded elastic media. The results show very good agreement with previously published wavelet-based solutions, while reducing spurious high-frequency noise and improving computational efficiency.

Reference: Pinto, S.S. and Moldovan, I.D. (2026). “An efficient time-stepping solution for transient elastodynamic problems using hybrid-Trefftz finite elements”. Engineering Analysis with Boundary Elements, 190, 106845. DOI: 10.1016/j.enganabound.2026.106845.