scholarly journals A Comparison of Dual Lagrange Multiplier Spaces for Mortar Finite Element Discretizations

2002 ◽  
Vol 36 (6) ◽  
pp. 995-1012 ◽  
Author(s):  
Barbara I. Wohlmuth
Keyword(s):  
Finite Element ◽  
Lagrange Multiplier ◽  
Finite Element Discretizations ◽  
Element Discretizations

scholarly journals A quasi-symmetric formulation for contact between deformable bodies

2008 ◽  
pp. 907-918
Author(s):  
Lionel Fourment
Keyword(s):  
Finite Element ◽  
Lagrange Multiplier ◽  
Numerical Results ◽  
Test Cases ◽  
Contact Conditions ◽  
Finite Element Software ◽  
Finite Element Discretizations ◽  
Deformable Bodies ◽  
Symmetric Formulation ◽  
Element Discretizations

In the frame of contact issues between 3D deformable bodies with non-matching finite element discretizations of possibly very different mesh sizes, a quasi-symmetric formulation is proposed to obtain satisfactory results whichever body is selected as master or slave. This approach is not based on usual mortar elements in order to avoid the creation of an additional integration surface. It draws its inspiration from a symmetric treatment of the contact conditions, where the formulation is made compatible by replacing the Lagrange multiplier of the master body by the projection of the slave one. Numerical results are obtained within the FORGE3® finite element software. Numerous 3D test cases numerically show that this approach actually solves the main issues of contact between deformable bodies, in a rather simple way.

FINITE ELEMENT METHODS FOR NONLINEAR ACOUSTICS IN FLUIDS

2007 ◽  
Vol 15 (03) ◽  
pp. 353-375 ◽  
Author(s):  
TIMOTHY WALSH ◽  
MONICA TORRES
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Acoustics ◽  
Time Step ◽  
Partial Differential ◽  
Time Step Size ◽  
Finite Element Discretizations ◽  
Acoustic Fluid ◽  
Element Discretizations

In this paper, weak formulations and finite element discretizations of the governing partial differential equations of three-dimensional nonlinear acoustics in absorbing fluids are presented. The fluid equations are considered in an Eulerian framework, rather than a displacement framework, since in the latter case the corresponding finite element formulations suffer from spurious modes and numerical instabilities. When taken with the governing partial differential equations of a solid body and the continuity conditions, a coupled formulation is derived. The change in solid/fluid interface conditions when going from a linear acoustic fluid to a nonlinear acoustic fluid is demonstrated. Finite element discretizations of the coupled problem are then derived, and verification examples are presented that demonstrate the correctness of the implementations. We demonstrate that the time step size necessary to resolve the wave decreases as steepening occurs. Finally, simulation results are presented on a resonating acoustic cavity, and a coupled elastic/acoustic system consisting of a fluid-filled spherical tank.

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