Automatic Adaptive 3-D Finite Element Refinement Using Different-Order Tetrahedral Elements

Lee, C. K.; Lo, S.H.

doi:10.1002/(sici)1097-0207(19970630)40:12<2195::aid-nme153>3.0.co;2-3

Cited by 23 publications

(14 citation statements)

References 13 publications

(4 reference statements)

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“…An intermediate possibility for the use of solid elements was proposed by Lee and Xu [39,1] for applications in offshore structures where both thin and thick plates coexist. Performing a cost study for quadratic and cubic approximations, the authors deduced that quadratic elements were a good compromise between computational cost and accuracy [15,16]. Moreover, they showed that it was more efficient to refine the computational mesh first in the plane of the plate then in the thickness.…”

Section: The Extended Finite Element Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets

Legrain

Geuzaine

Remacle

et al. 2013

Finite Elements in Analysis and Design

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International audienceAn efficient approach is proposed in order to predict the mechanical response of complex industrial parts. As these structures are usually composed of massive and thin parts, different models have to be mixed together (plate, shells, solid). The transition between these different kinematic assumptions can be problematic and non-linear models cannot be employed depending on the plate model that is considered. Moreover, Finite Element analysis in the case of large and complex assemblies implies tedious meshing steps. The idealization and simplification of these structures into a mix of 2D and 3D Finite Elements usually takes therefore significantly more time than the analysis itself. The objective of the present contribution is to explore a calculation process that enables a simple automation of the meshing steps. Even though potentially computationally more expensive, the meshing automation may lead to drastic time reduction for the CAD to mesh process and a much tighter link between CAD and calculated assembly. Finally, easier and faster design explorations would be allowed. This strategy relies on the use of a non-conforming quadratic approximation that is defined on a sufficiently fine mesh. The eXtended Finite Element Method is used in order to alleviate meshing issues. The mesh and Level-Set function are built from the CAD input, by means of an automated approach. The strategy is verified against analytical solutions and real aerospace substructures

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Section: The Extended Finite Element Methodsmentioning

confidence: 99%

“…This method has to be tolerant with damaged CAD files and accurate. The accuracy is obtained thanks to the use of quadratic elements that have been reported to represent a good compromise between accuracy and computational cost for modelling thin structures with solid elements [15,16].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets

Legrain

Geuzaine

Remacle

et al. 2013

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

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“…For high accuracy FE solutions over complicated domains of curved boundary, however, we could also use quadratic solid elements such as 10-node and 20-node tetrahedral elements, 20-node and 27-node hexahedral elements, etc. [36,37]. Such methods are demonstrably useful for simulating a variety of complex science and engineering systems.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Models of Elastic Earthquake Deformation

Tung¹,

Masterlark²,

Lo³

2018

Earthquakes - Forecast, Prognosis and Earthquake Resistant Construction

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The Earth's surface deforms in response to earthquake fault dislocations at depth. Deformation models are constructed to interpret the corresponding ground movements recorded by geodetic data such GPS and InSAR, and ultimately characterize the seismic ruptures. Conventional analytical and latest numerical solutions serve similar purpose but with different technical constraints. The former cannot simulate the heterogeneous rock properties and structural complexity, while the latter directly tackles these challenges but requires more computational resources. As demonstrated in the 2015 M7.8 Gorkha, Nepal earthquake and the 2016 M6.2 Amatrice, Italy earthquake, we develop state-of-art finite element models (FEMs) to efficiently accommodate both the material and tectonic complexity of a seismic deformational system in a seamless model environment. The FEM predictions are significantly more accurate than the analytical models embedded in a homogeneous half-space at the 95% confidence level. The primary goal of this chapter is describe a systematic approach to design, construct, execute and calibrate FEMs of elastic earthquake deformation. As constrained by coseismic displacements, FEM-based inverse analyses are employed to resolve linear and nonlinear fault-slip parameters. With such numerical techniques and modeling framework, researchers can explicitly investigate the spatial distribution of seismic fault slip and probe other in-depth rheological processes.

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“…Tetrahedral elements are favored in the meshing of 3D complex objects . Ten‐node tetrahedral element is a common type of tetrahedron used in computing with meshes of tetrahedra, because the linear four‐node tetrahedra badly lock and provide very poor accuracy with coarse meshes.…”

Section: Introductionmentioning

confidence: 99%

Mean‐strain 10‐node tetrahedron with energy‐sampling stabilization for nonlinear deformation

Pakravan

Krysl

2017

Numerical Meth Engineering

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Summary A mean‐strain 10‐node tetrahedral element is developed for the solution of geometrically nonlinear solid mechanics problems using the concept of energy‐sampling stabilization. A uniform‐strain tetrahedron for applications to linear elasticity was recently described. The formulation as extended here is able to solve large‐strain hyperelasticity. The present 10‐node tetrahedron is composed of several four‐node linear tetrahedral elements, four tetrahedra in the corners, and four tetrahedra that tile the central octahedron in three possible sets of four‐node tetrahedra, corresponding to three different choices for the internal diagonal. We formulate a mean‐strain element with stabilization energy evaluated on the four corner tetrahedra, which is shown to guarantee consistency and stability. The stabilization energy is expressed through a stored‐energy function, and contact with input parameters in the small‐strain regime is made. The neo‐Hookean model is used to formulate the stabilization energy. As for small‐strain elasticity, the stabilization parameters are determined by actual material properties and geometry of a tetrahedra without any user input. The numerical tests demonstrate that the present element performs well for solid, shell, and nearly incompressible structures. Copyright © 2016 John Wiley & Sons, Ltd.

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Automatic Adaptive 3-D Finite Element Refinement Using Different-Order Tetrahedral Elements

Cited by 23 publications

References 13 publications

Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets

Numerical simulation of CAD thin structures using the eXtended Finite Element Method and Level Sets

Finite Element Models of Elastic Earthquake Deformation

Mean‐strain 10‐node tetrahedron with energy‐sampling stabilization for nonlinear deformation

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