Boundary Elements

Boundary Elements

Introduction. Boundary Elements and Finite Elements. Historical development of the BEM. Preliminary Mathematical Concepts. The Gauss-Green theorem. The divergence theorem of Gauss. Green’s second identity. The Dirac delta function. The BEM for Potential Problems in Two Dimensions. Fundamental solution. The direct BEM for the Laplace and the Poisson equation. Transformation of the domain integrals to boundary integrals. The Dual reciprocity method. The BEM for potential problems in anisotropic bodies. Numerical Implementation of the ΒΕΜ. The BEM with constant boundary elements. Programming of the method in FORTRAN. Multiply connected domains. The method of subregions. Boundary Element Technology. Linear elements. Higher order elements. Applications. Torsion of non-circular bars. Deflection of elastic membranes. Heat transfer problems. Fluid flow problems. The BEM for the plate problem. The Rayleigh-Green identity for the biharmonic operator. Fundamental solution. Integral representation of the solution. The boundary integral equations. Two-Dimensional Elastostatic Problems. Equations of plane elasticity. Betti’s reciprocal identity. Fundamental solution of the Navier equations. Integral representation of the solution

Topics

Introduction. Boundary elements and field methods. Historical development of BEM. The direct BEM for the Laplace and Poisson equations. Numerical implementation of BEM. The Dual Reciprocity Method. Multiple cohesion area. The method of sub-areas. Applications. BEM for non-homogeneous bodies.

Who Should Attend

  • Recommended for students who have basic knowledge of Differential Equations, Solid Mechanics, Mechanics of Deformable Body – Material Strength, Computer Programming.

Course Benefits

  • The trainees will be able to understand the boundary element Method and its PC programming.
  • Calculation using the relevant codes Real Application Boundary elements

Course Instructor: Prof. John Katsikadelis

 

 

 

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