Boundary Element Form
OverviewIntroduction. Boundary Elements and Finite Elements. Historical development of the BEM. Preliminary Mathematical Concepts. The GaussGreen 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 noncircular bars. Deflection of elastic membranes. Heat transfer problems. Fluid flow problems. The BEM for the plate problem. The RayleighGreen identity for the biharmonic operator. Fundamental solution. Integral representation of the solution. The boundary integral equations. TwoDimensional Elastostatic Problems. Equations of plane elasticity. Betti’s reciprocal identity. Fundamental solution of the Navier equations. Integral representation of the solution Topics ntroduction. 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 subareas. Applications. BEM for nonhomogeneous bodies. Course Instructor: Prof. John Katsikadelis

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