1. A hybrid-Trefftz finite element platform for solid and porous elastodynamics
- Author
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Natalia Climent, Elena Daniela Bendea, António Gomes Correia, Ildi Cismasiu, Ionut Moldovan, and Universidade do Minho
- Subjects
Differential equation ,Computer science ,Traction (engineering) ,Transient problem ,Harmonic (mathematics) ,02 engineering and technology ,01 natural sciences ,0203 mechanical engineering ,Engenharia e Tecnologia::Engenharia Civil ,Boundary value problem ,0101 mathematics ,Hybrid-trefftz finite element ,Science & Technology ,Basis (linear algebra) ,Applied Mathematics ,Mathematical analysis ,General Engineering ,Porous medium ,Finite element method ,010101 applied mathematics ,Computational Mathematics ,020303 mechanical engineering & transports ,Engenharia Civil [Engenharia e Tecnologia] ,Elastodynamics ,Transient (oscillation) ,Analysis ,Unbounded medium - Abstract
"Available online 28 December 2020", Hybrid-Trefftz finite elements are well suited for modeling the response of materials under highly transient loading. Their approximation bases are built using functions that satisfy exactly the differential equations governing the problem. This option embeds relevant physical information into the approximation basis and removes the well-known sensitivity of the conventional finite elements to high solution gradients and short wavelength excitations. Despite such advantages, no public software using hybrid-Trefftz finite elements to model wave propagation through solid and porous media exists to date. This paper covers the formulation and implementation of hybrid-Trefftz finite elements for single-phase, biphasic and triphasic media, subjected to dynamic loads. The formulation is cast in a unified framework, valid for the three types of materials alike, and independent of the nature (harmonic, periodic or transient) of the applied load. Displacement, traction, elastic and absorbing boundary conditions are accommodated. The implementation is made in three novel, open-source and user-friendly computational modules which are freely distributed online., This work was partly funded by Fundação para a Ciência e a Tecnologia (MCTES) through national funds (PIDDAC) under the R&D Units “Institute for Sustainability and Innovation in Structural Engineering (ISISE)” and “Civil Engineering Research and Innovation for Sustainability (CERIS)”, references UIDB/04029/2020 and UIDB/04625/2020, respectively, and through research project CEN-DynaGEO, reference PTDC/EAM-GTC/29923/2017.
- Published
- 2021