Frictional unilateral contact for hemitropic solids in micropolar elasticity and boundary element approximation

2016 ◽  
Author(s):  
Joachim Gwinner
Keyword(s):  
Boundary Element ◽  
Unilateral Contact ◽  
Element Approximation ◽  
Micropolar Elasticity

scholarly journals Two-level preconditioning for $$h$$-version boundary element approximation of hypersingular operator with GenEO

2020 ◽  
Vol 146 (3) ◽  
pp. 597-628
Author(s):  
Pierre Marchand ◽  
Xavier Claeys ◽  
Pierre Jolivet ◽  
Frédéric Nataf ◽  
Pierre-Henri Tournier
Keyword(s):  
Boundary Element ◽  
Element Approximation

scholarly journals A FEM-Green Approach for Magnetic Field Problems with Open Boundaries

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1662
Author(s):  
Jacques Lobry
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Galerkin Approximation ◽  
Outer Region ◽  
Open Boundary ◽  
Element Approximation ◽  
Green Approach ◽  
Element Method

A new finite element method/boundary element method (FEM/BEM) scheme is proposed for the solution of the 2D magnetic static and quasi-static problems with unbounded domains. The novelty is an original approach in the treatment of the outer region. The related domain integral is eliminated at the discrete level by using the finite element approximation of the fundamental solutions (Green’s functions) at every node of the related mesh. This “FEM-Green” approach replaces the standard boundary element method. It is simpler to implement because no integration on the boundary of the domain is required. Then, the method leads to a substantially reduced computational burden. Moreover, the coupling with finite elements is more natural since it is based on the same Galerkin approximation. Some examples with open boundary and nonlinear materials are presented and compared with the standard finite element method.

Unilaterally Supported Plates on Elastic Foundations by the Boundary Element Method

1992 ◽  
Vol 59 (3) ◽  
pp. 580-586 ◽  
Author(s):  
E. J. Sapountzakis ◽  
J. T. Katsikadelis
Keyword(s):  
Boundary Element Method ◽  
Integral Representation ◽  
Contact Problem ◽  
Boundary Element ◽  
Biharmonic Equation ◽  
Solution Procedure ◽  
Unilateral Contact ◽  
Thin Elastic Plate ◽  
Element Solution ◽  
Subgrade Reaction

A boundary element solution is developed for the unilateral contact problem of a thin elastic plate resting on elastic homogeneous or nonhomogeneous subgrade. The reaction of the subgrade may depend linearly, or nonlinearly, on the deflection of the plate. The contact between the plate and the subgrade is unbonded. The subgrade surface is not necessarily plane, and miscontact between plate and subgrade due to initial gaps is also encountered. The solution procedure is based on the integral representation of the deflection for the biharmonic equation in which the unknown subgrade reaction is treated as loading term. The effectiveness of the proposed method is illustrated by several examples.

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