A discontinuous stabilized mortar method for general 3D elastic problems

Hauret, Patrice; Tallec, Patrick Le

doi:10.1016/j.cma.2007.06.014

Cited by 33 publications

(30 citation statements)

References 34 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, the mortar method can be seen as a variational multi-scale finite element method [41,51,59,87,140].…”

Section: The Mortar Finite Element Methodsmentioning

confidence: 99%

“…Additional references dealing with mortar methods can be found in [9,16,47,49,51,59,108,171]. The reader may also refer to [41,51,59,87,140] for specific applications to linear isotropic elasticity and elliptic problems.…”

Section: Domain Decompositionmentioning

confidence: 99%

“…Relaxing the constraint on the boundaries of the interfaces and employing Lagrange multipliers is a standard framework in which the method is understood at the present time, for example as in Pencheva [133] and Belgacem [13]. One of the key aspects of the method consists of defining appropriate spaces of Lagrange multipliers for enforcing the gluing constraint [87]. Additional references dealing with mortar methods can be found in [9,16,47,49,51,59,108,171].…”

Section: Domain Decompositionmentioning

confidence: 99%

See 2 more Smart Citations

Domain Decomposition Methods in Geomechanics

Florez

Wheeler

Rodríguez

2013

SPE Reservoir Simulation Symposium

View full text Add to dashboard Cite

Dedicated to the memory of my beloved mother Emma Guzman and mysister Aura E. Florez-Guzman. AcknowledgmentsI would like to express my sincere appreciation for my advisor, Professor Mary F. Wheeler. She practically brought me from Venezuela for giving me the opportunity to attend graduate school at US. This ultimately opened new avenues to insert myself successfully in a country with a different language and culture. I will always appreciate this opportunity. She introduced me to topics such as mixed finite elements, discontinuous Galerkin schemes, domain decomposition and mortar methods. I am also thankful for her financial support, enthusiasm, and persistence on pursuing cutting-edge research.

show abstract

“…Indeed, the mortar method can be seen as a variational multi-scale finite element method [41,51,59,87,140].…”

Section: The Mortar Finite Element Methodsmentioning

confidence: 99%

Section: Domain Decompositionmentioning

confidence: 99%

Section: Domain Decompositionmentioning

confidence: 99%

See 1 more Smart Citation

Domain Decomposition Methods in Geomechanics

Florez

Wheeler

Rodríguez

2013

SPE Reservoir Simulation Symposium

View full text Add to dashboard Cite

show abstract

“…In (4.6) and (4.7), the most robust choice is to take for V h , respectively, the continuous first-order and secondorder finite element spaces augmented with suitable face bubbles on Γ, leading to an inf-sup constant β h in (4.3) independent of h in both 2D/1D and 3D/2D settings; see [2,17]. In 2D/1D whenever at least one of the endpoints of Γ is free, it is also possible to take (4.7); then, the discrete inf-sup condition (4.3) still holds, but the constant β h is of order h. The choice (4.8) has been introduced in [25] and differs from the two previous choices in the fact that Λ h = M h .…”

Section: The Discrete Settingmentioning

confidence: 99%

A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

Doyen¹,

Ern²,

Piperno³

2010

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract.We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian. The finite element spaces for the bulk displacement and the Lagrange multiplier must satisfy a discrete inf-sup condition, while discontinuous finite element spaces spanned by nodal basis functions are considered for the unilateral contact variable so as to use collocation methods. Two iterative algorithms are presented and analyzed, namely an Uzawa-type method within a decompositioncoordination approach and a nonsmooth Newton's method. Finally, numerical results illustrating the theoretical analysis are presented.Mathematics Subject Classification. 65N30, 65K10, 74S05, 74M15, 74R99.

show abstract

“…Thus, these techniques provide a very flexible and computationally attractive setting to handle numerically coupled multi-physics problems. Mortar methods have been applied successfully in many engineering applications, such as, e.g., contact problems [4][5][6][7], dynamic and static structural analysis [8][9][10], flow problems [11][12][13] and coupled problems in acoustics [14,15]. Further, the mortar method is used to simulate eigenvalue problems in [16,17].…”

Section: Introductionmentioning

confidence: 99%

A new mortar formulation for modeling elastomer bedded structures with modal-analysis in 3D

Horger

Kollmannsberger

Frischmann

et al. 2014

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

Background: It is a well-known fact that cross-laminated timber structures are sensitive to rumbling noises. These transmissions are best captured by a fully three-dimensional mathematical model. Since the discretization of such models with hexahedral elements in a conforming manner is highly complex, we chose the mortar method to reduce the algorithmic complexity for the mesh generation. Moreover we consider high-order finite elements in order to deal with the high aspect ratios in three-dimensionally resolved, cross-laminated walls and slabs. The geometric models and material specification was derived from a building information model. Methods: This paper derives a new mortar formulation designed to replace an explicitely discretized elastomer with a new coupling condition. To this end, tailored Robin conditions are applied at the interface as coupling conditions instead of the more standard continuity constraints. Having demonstrated the suitability of the mortar method for high order finite elements, we proceed with the derivation of the dimensional reduced model with the new coupling condition and to show its stability by numerical experiments. We then test the performance of the new formulation on benchmark examples and demonstrate the engineering relevance for practical applications. Results: The newly derived mortar formulation performs well. We tested the new formulation on fully three-dimensional examples of engineering relevance discretized by high-order finite elements up to degrees of p = 10 and found the reproduction of both eigenvalues and eigenmodes to be accurate. Moreover, the mortar method allows for a significant reduction in the algorithmic complexity of mesh generation while simultaneously reducing the overall computational effort. Conclusion: The newly derived modified mortar method for replacing an elastomer layer is not only an academically interesting variant but is capable of solving problems of practical importance in modal-analysis of cross-laminated timber structures.

show abstract

A discontinuous stabilized mortar method for general 3D elastic problems

Cited by 33 publications

References 34 publications

Domain Decomposition Methods in Geomechanics

Domain Decomposition Methods in Geomechanics

A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

A new mortar formulation for modeling elastomer bedded structures with modal-analysis in 3D

Contact Info

Product

Resources

About