scholarly journals Non-symmetric isogeometric FEM-BEM couplings

2021 ◽  
Vol 47 (5) ◽  
Author(s):  
Mehdi Elasmi ◽  
Christoph Erath ◽  
Stefan Kurz
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
A Priori ◽  
Galerkin Approximation ◽  
Coupled System ◽  
Material Behavior ◽  
Thin Domains ◽  
Lipschitz Continuous ◽  
Element Method

AbstractWe present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting of two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly non-linear materials. The Boundary Element Method is applied in unbounded or thin domains where the material behavior is linear. The isogeometric framework allows to combine different design and analysis tools: first, we consider the same type of NURBS parameterizations for an exact geometry representation and second, we use the numerical analysis for the Galerkin approximation. Moreover, it facilitates to perform h- and p-refinements. For the sake of analysis, we consider the framework of strongly monotone and Lipschitz continuous operators to ensure well-posedness of the coupled system. Furthermore, we provide a priori error estimates. We additionally show an improved convergence behavior for the errors in functionals of the solution that may double the rate under certain assumptions. Numerical examples conclude the work which illustrate the theoretical results.

scholarly journals Inelastic Analysis of Transverse Deflection of Plates by the Boundary Element Method

1980 ◽  
Vol 47 (2) ◽  
pp. 291-296 ◽  
Author(s):  
M. Morjaria ◽  
S. Mukherjee
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Model Material ◽  
Material Behavior ◽  
State Variables ◽  
Simply Supported ◽  
Inelastic Analysis ◽  
Transverse Deflection ◽  
Element Method

A numerical scheme for time-dependent inelastic analysis of transverse deflection of plates of arbitrary shape by the boundary element method is presented in this paper. The governing differential equation is the inhomogeneous biharmonic equation for the rate of small transverse deflection. This complicated boundary-value problem for an arbitrarily shaped plate is solved by using a novel combination of the boundary element method and finite-element methodology. The number of unknowns, however, depends upon the boundary discretization and is therefore less than in a finite-element model. A combined creep-plasticity constitutive theory with state variables is used to model material behavior. The computer code developed can solve problems for an arbitrarily shaped plate with clamped or simply supported boundary conditions and an arbitrary loading history. Some illustrative numerical results for clamped and simply supported rectangular and triangular plates, under various loading histories, are presented and discussed.

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.

Application of the Boundary Element Method and Modal Analysis to Tire Acoustics Problems

1993 ◽  
Vol 21 (2) ◽  
pp. 66-90 ◽  
Author(s):  
Y. Nakajima ◽  
Y. Inoue ◽  
H. Ogawa
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Radiation ◽  
Traffic Noise ◽  
Noise Prediction ◽  
Prediction System ◽  
Tire Noise ◽  
Acoustic Contribution ◽  
Element Method

Abstract Road traffic noise needs to be reduced, because traffic volume is increasing every year. The noise generated from a tire is becoming one of the dominant sources in the total traffic noise because the engine noise is constantly being reduced by the vehicle manufacturers. Although the acoustic intensity measurement technology has been enhanced by the recent developments in digital measurement techniques, repetitive measurements are necessary to find effective ways for noise control. Hence, a simulation method to predict generated noise is required to replace the time-consuming experiments. The boundary element method (BEM) is applied to predict the acoustic radiation caused by the vibration of a tire sidewall and a tire noise prediction system is developed. The BEM requires the geometry and the modal characteristics of a tire which are provided by an experiment or the finite element method (FEM). Since the finite element procedure is applied to the prediction of modal characteristics in a tire noise prediction system, the acoustic pressure can be predicted without any measurements. Furthermore, the acoustic contribution analysis obtained from the post-processing of the predicted results is very helpful to know where and how the design change affects the acoustic radiation. The predictability of this system is verified by measurements and the acoustic contribution analysis is applied to tire noise control.

Postbuckling Analysis of Plates Under Combined Loads by a Mixed Finite Element and Boundary Element Method

1993 ◽  
Vol 115 (3) ◽  
pp. 262-267 ◽  
Author(s):  
J. Q. Ye
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Mixed Boundary ◽  
Mixed Finite Element ◽  
Plane Deformation ◽  
Thin Plates ◽  
Combined Loads ◽  
Element Method

The postbuckling behavior of thin plates under combined loads is studied in this paper by using a mixed boundary element and finite element method. The transverse and the in-plane deformation of the plates are analyzed by the boundary element method and the finite element method, respectively. Spline functions were used as the interpolation functions and shape functions in the solution of both methods. A quadratic rectangular spline element is adopted in the finite element procedure. Numerical results are given for typical problems to show the effectiveness of the proposed approach. The possibilities to extend the method developed in this paper to more complicated postbuckling problems are discussed in the concluding section.

Combined finite element-boundary element method modelling of elastic multi-asperity contacts

2009 ◽  
Vol 223 (5) ◽  
pp. 767-776 ◽  
Author(s):  
S Ilincic ◽  
G Vorlaufer ◽  
P A Fotiu ◽  
A Vernes ◽  
F Franek
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Hertzian Contact ◽  
Multilayer Systems ◽  
Influence Coefficients ◽  
Asperity Contacts ◽  
First Time ◽  
Element Algorithm ◽  
Element Method

A novel formulation of elastic multi-asperity contacts based on the boundary element method (BEM) is presented for the first time, in which the influence coefficients are numerically calculated using a finite element method (FEM). The main advantage of computing the influence coefficients in this manner is that it makes it also possible to consider an arbitrary load direction and multilayer systems of different mechanical properties in each layer. Furthermore, any form of anisotropy can be modelled too, where Green's functions either become very complicated or are not available at all. The rest of the contact analysis is then performed applying a custom-developed boundary element algorithm. The scheme was tested by considering the frictionless contact between a flat surface and a sphere. The obtained results are in good agreement with the analytical solution known for a Hertzian contact. Applied to either a frictionless or a frictional contact between real surfaces of different samples, our FEM-BEM method has shown that the composite roughness of surfaces in contact uniquely determines the contact pressure distribution.

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