Three-Dimensional Boundary Element Method and Finite Element Method Simulations Applied to Stray Current Interference Problems. A Unique Coupling Mechanism That Takes the Best of Both Methods

CORROSION ◽  
2007 ◽  
Vol 63 (6) ◽  
pp. 561-576 ◽  
Author(s):  
L. Bortels ◽  
A. Dorochenko ◽  
B. Van den Bossche ◽  
G. Weyns ◽  
J. Deconinck
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Coupling Mechanism ◽  
Stray Current ◽  
Dimensional Boundary ◽  
Interference Problems ◽  
Element Method

scholarly journals The implementation of the boundary element method to the Helmholtz equation of acoustics

2021 ◽  
pp. 13-19
Author(s):  
Sergey Sivak ◽  
Mihail Royak ◽  
Ilya Stupakov ◽  
Aleksandr Aleksashin ◽  
Ekaterina Voznjuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Numerical Methods ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Element Method

Introduction: To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.

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.

Simulation of Axisymmetric Forming Processes, With Friction, Coupling Finite Elements and Boundary Elements

2006 ◽  
Author(s):  
Dominique Bigot ◽  
Hocine Kebir ◽  
Jean-Marc Roelandt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Finite Elements ◽  
Boundary Element ◽  
Symmetric Part ◽  
Forming Process ◽  
Optimal Shapes ◽  
Numerical Software ◽  
Element Method

Nowadays, the simulation of forming processes is rather well integrated in the industrial numerical codes. However, to take into account the possible modifications of the tool during cycle of working, we develop dedicated numerical software. This one more particularly will allow the identification of the fatigue criteria of the tool. With the view to conceiving the optimal shapes of tool allowing increasing their lifespan while ensuring a quality required of the part thus manufactured. This latter uses coupling with friction finite element method — for modelling the axi-symmetric part — and boundary element method — for modelling the tool. For the validation, we modeled forming process.

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