FreeHyTE: a hybrid-Trefftz finite element platform

Moldovan, Ionuţ Dragoş; Cismaşiu, Ildi

doi:10.1016/j.advengsoft.2018.03.014

Cited by 15 publications

(11 citation statements)

References 22 publications

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“…The spectral problems defined by Equations ( 14) to (20) and (27) are expressed in space variables only and are formally similar to those reported in References 24 and 28 for elastodynamic problems in two-dimensional media. The time-dependent fields are computed using approximations (8) to (10) once the space fields are calculated.…”

Section: Integration In Timementioning

confidence: 55%

“…The hybrid formulation of the displacement model is derived by enforcing weakly Equation (27) in the domain element with the Trefftz bases U as weighting functions, and Equations ( 17), (19), and (20) on the essential boundaries with the boundary traction basis Z as weighting functions…”

Section: Hybrid-trefftz Displacement Modelmentioning

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%

“…Freitas et al 23 formulated hybrid‐Trefftz stress elements for elastostatic problems in three‐dimensional media. For poroelastodynamic problems, hybrid‐Trefftz finite elements have been developed for two‐dimensional saturated and unsaturated media 24‐26 and implemented in the 2D FreeHyTE platform 27‐29 …”

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: Integration In Timementioning

confidence: 55%

Section: Hybrid-trefftz Displacement Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Climent

Moldovan

Freitas

2022

Numerical Meth Engineering

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“…As a benefit, good numerical accuracy can be expected and the challenging shear locking problem can be easily eliminated. Since its inception, the hybrid-Trefftz finite element method has become increasingly popular and been applied to solve various solid mechanics problems [31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

A novel displacement-based Trefftz plate element with high distortion tolerance for orthotropic thick plates

Shang

Zhou

2019

Engineering Analysis with Boundary Elements

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In this work, a simple but robust 4-node displacement-based Trefftz plate element is proposed for efficiently analysis of orthotropic plate structures. This is achieved via two steps. First, the element's deflection and rotation fields are directly formulated at the base of the Trefftz functions of the orthotropic Mindlin-Reissner plate. Second, to ensure the convergence property and further enhance the element performance, the generalized conforming theory is employed to satisfy the requirement for interelement compatibility in weak sense. The resulting displacement-based element belongs to the nonconforming models on coarse meshes and gradually converges into a conforming one with the mesh refinement. Numerical benchmarks reveal that the new element can produce high precision results for both displacement and stress resultant. Moreover, it is free of shear locking and has good tolerances to mesh distortions.

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