scholarly journals An Explicit Boundary Integral Representation of the Solution of the Two-Dimensional Heat Equation and Its Discretization

2000 ◽  
Vol 12 (1) ◽  
pp. 63-83 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
V.L. Makarov
Keyword(s):  
Integral Representation ◽  
Heat Equation ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Boundary Integral Representation

Alternative Boundary-Integral Representations of Ship Waves

2002 ◽  
Author(s):  
Francis Noblesse ◽  
Chi Yang ◽  
Dane Hendrix ◽  
Rainald Lo¨hner
Keyword(s):  
Integral Representation ◽  
Fundamental Problem ◽  
Boundary Integral ◽  
Ship Hull ◽  
Integral Representations ◽  
Singular Boundary ◽  
Ship Waves ◽  
Classical Boundary ◽  
The Green Function ◽  
Boundary Integral Representation

The fundamental problem of determining the free-surface potential flow that corresponds to a given flow at a ship hull surface is reconsidered. Stokes’ theorem is used to transform the dipole distribution over the ship hull surface in the classical boundary-integral representation of the velocity potential. This Stokes’ transformation yields a weakly-singular boundary-integral representation that defines the potential in terms of the Green function G and related functions that are no more singular than G. Accordingly, the velocity representation only involves functions that are no more singular than ∇G.

Novel Boundary Integral Equations for Two-Dimensional Isotropic Elasticity: An Application to Evaluation of the In-Boundary Stress

2003 ◽  
Vol 70 (6) ◽  
pp. 817-824 ◽  
Author(s):  
V. Manticˇ ◽  
F. J. Calzado ◽  
F. Pari´s
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Anisotropic Elasticity ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Tangential Derivative ◽  
Boundary Stress ◽  
Isotropic Elasticity ◽  
Boundary Integral Representation

A new nonsingular system of boundary integral equations (BIEs) of the second kind for two-dimensional isotropic elasticity is deduced following a recently introduced procedure by Wu (J. Appl. Mech., 67, pp. 618–621, 2000) originally applied for anisotropic elasticity. The physical interpretation of the new integral kernels appearing in these BIEs is studied. An advantageous application of one of these BIEs as a boundary integral representation (BIR) of tangential derivative of boundary displacements on smooth parts of the boundary, and subsequently as a BIR of the in-boundary stress, is presented and analyzed in numerical examples. An equivalent BIR obtained by an integration by parts of the integral including tangential derivative of displacements in the former BIR is presented and analyzed as well. The resulting integral is only apparently hypersingular, being in fact a regular integral on smooth parts of the boundary.

scholarly journals BEM Solutions of Frequency Domain Gradient Elastodynamic 3-D Porblems

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
D. Polyzos ◽  
K. G. Tsepoura ◽  
D. E. Beskos
Keyword(s):  
Integral Representation ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Normal Derivative ◽  
Solution Procedure ◽  
Boundary Integral ◽  
Material Behavior ◽  
Linear Elastic ◽  
Microstructural Effects ◽  
Boundary Integral Representation

A boundary element methodology is presented for the frequency domain elastodynamic analysis of three-dimensional solids characterized by a linear elastic material behavior coupled with microstructural effects taken into account with the aid of the simple gradient elastic theory of Aifantis. A variational statement is established to determine all possible classical and non-classical (due to gradient terms) boundary conditions of the general boundary value problem. The gradient frequency domain elastodynamic fundamental solution is explicitly derived and used to construct the boundary integral representation of the solution with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well posed problem. All the kernels in the integral equations are explicitly provided. Surface quadratic quadrilateral boundary elements are employed and the discretization is restricted only to the boundary. The solution procedure is described in detail. A numerical example serves to illustrate the method and demonstrate its accuracy. The present version of the method does not provide explicit expressions for the computation of interior stresses.

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