A hybrid-Trefftz finite element platform for solid and porous elastodynamics

Moldovan, Ionuţ Dragoş; Climent, N.; Bendea, Elena Daniela; Cismaşiu, Ildi; Correia, A. Gomes

doi:10.1016/j.enganabound.2020.12.014

Cited by 12 publications

(17 citation statements)

References 24 publications

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“…All derivations and solutions obtained in this section are valid for all spectral problems. Substituting definition (28) into Equations ( 15) and ( 16), a dependent stress approximation is,…”

Section: Hybrid-trefftz Displacement Modelmentioning

confidence: 99%

“…where ÛT and ẐT are the transposed conjugates of bases U and Z. Finally, integrating by parts Equation (33), enforcing the Trefftz condition (30) and substituting approximations (28) and (29), the problem is reduced to solving the algebraic system 24,25…”

Section: Hybrid-trefftz Displacement Modelmentioning

confidence: 99%

“…The time basis is constructed using Daubechies wavelets, 36 the same as implemented in the corresponding 2D FreeHyTE module. 28 In previous works, exponential 25 and polynomial bases 26 were also implemented. However, the exponential basis is not adequate for highly transient problems and polynomial bases are not powerful enough to work in a single time step.…”

Section: Numerical Testingmentioning

confidence: 99%

“…The 2D simulations are carried out with the 2D FreeHyTE biphasic transient platform. 28 Finally, a simulation of a 3D bender element test is performed and presented in Section 3.3.…”

Section: Numerical Testingmentioning

confidence: 99%

“…For poroelastodynamic problems, hybrid-Trefftz finite elements have been developed for two-dimensional saturated and unsaturated media [24][25][26] and implemented in the 2D FreeHyTE platform. [27][28][29] In this article, the authors present a new hybrid-Trefftz finite elements formulation for three dimensional saturated porous media. Free-field spherical solutions of the governing equations are found and included in the domain approximation basis of the hybrid-Trefftz element.…”

Section: Introductionmentioning

confidence: 99%

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Three‐dimensional hybrid‐Trefftz displacement elements for poroelastodynamic problems in saturated media

Climent

Moldovan

Freitas

2022

Numerical Meth Engineering

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The hybrid‐Trefftz displacement element formulation for poroelastodyamics in three‐dimensional saturated media is presented in this article. The governing equations are integrated in time using a wavelet decomposition which expands the time‐dependent problem into several spectral problems. Displacements are discretized in each finite element and tractions are approximated on each essential element boundary (displacement model). The displacement approximation functions satisfy the governing equations of the media (Trefftz constraint) and are not linked to the nodes. Trefftz bases are derived solving the governing equations and are composed of four types of modes: two compression waves and two shear waves. The weak enforcement of the Navier equation and boundary conditions yields a solving system where the unknown are the weights of the approximation bases. Numerical tests have been carried out to assess the convergence of the models. The results of the simulations are satisfactory: the numerical tests converge to known analytical solutions and the simulation of a propagation of a vertical shock wave is consistent to the one obtained with a 2D plane simulation under the same conditions. The results of a bender element test simulation in three dimensions are also presented.

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Section: Hybrid-trefftz Displacement Modelmentioning

confidence: 99%

Section: Hybrid-trefftz Displacement Modelmentioning

confidence: 99%

Section: Numerical Testingmentioning

confidence: 99%

“…The 2D simulations are carried out with the 2D FreeHyTE biphasic transient platform. 28 Finally, a simulation of a 3D bender element test is performed and presented in Section 3.3.…”

Section: Numerical Testingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three‐dimensional hybrid‐Trefftz displacement elements for poroelastodynamic problems in saturated media

Climent

Moldovan

Freitas

2022

Numerical Meth Engineering

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An adaptive order finite element method for poroelastic materials described through the Biot equations

Jonckheere

Bériot

Dazel

et al. 2022

Numerical Meth Engineering

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Poroelastic materials are essential to engineers to improve the sound and vibration properties of a product. The most common mathematical model that describes the vibro-acoustics of these materials is the Biot theory, which considers the fully coupled behavior of a homogenized solid phase, based on the structural skeleton, and a homogenized fluid phase, describing the inter-penetrating fluid. This article focuses on an adaptive higher order finite element implementation to solve poroelastic models. Owing to the presence of several wave solutions, namely, two compressional wave types and one shear wave type, it is difficult to define clear meshing guidelines a priori for poroelastic material modeling and trial and error is required to ensure reliable results. Multiple scales may be present, and local resonance phenomena may significantly modify the resolution requirements in certain frequency bands. In order to remedy this, and to be able to deliver a (nearly) mesh-independent solution, a physics based adaptivity mechanism is developed which determines the distribution of (directional) element orders at each frequency prior to the calculation, to reach a user-defined target error. The resulting approach is verified for different element topologies and is further applied to relevant applications of poroelastic materials in vibro-acoustics.

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FreeHyTE: A Hybrid-Trefftz Finite Element Platform for Poroelastodynamic Problems

Climent

Moldovan

Correia

2021

Lecture Notes in Civil Engineering

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A hybrid-Trefftz finite element platform for solid and porous elastodynamics

Cited by 12 publications

References 24 publications

Three‐dimensional hybrid‐Trefftz displacement elements for poroelastodynamic problems in saturated media

Three‐dimensional hybrid‐Trefftz displacement elements for poroelastodynamic problems in saturated media

An adaptive order finite element method for poroelastic materials described through the Biot equations

FreeHyTE: A Hybrid-Trefftz Finite Element Platform for Poroelastodynamic Problems

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