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# Finite Element Method in Geotechnical Engineering

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Finite Element Method in Geotechnical Engineering FINITE ELEMENT METHOD IN GEOTECHNICAL ENGINEERING Computational Geotechnics Course Computational Geotechnics 1 Finite Element Method in Geotechnical Engineering Contents Steps in the FE Method Introduction to FEM for Deformation Analysis Discretization of a Continuum Elements Strains Stresses Constitutive Relations Hooke s Law Formulation of Stiffness Matrix Solution of Equations Course Computational Geotechnics 2 Finite Element Method in Geotechnical Engineering Steps in the FE Method 1 Establishment of stiffness relations for each element Material properties and equilibrium conditions for each element are used in this establishment 2 Enforcement of compatibility i e the elements are connected 3 Enforcement of equilibrium conditions for the whole structure in the present case for the nodal points 4 By means of 2 And 3 the system of equations is constructed for the whole structure This step is called assembling 5 In order to solve the system of equations for the whole structure the boundary conditions are enforced 6 Solution of the system of equations Course Computational Geotechnics 3 Finite Element Method in Geotechnical Engineering Introduction to FEM for Deformation Analysis Finite Element Method General method to solve boundary value problems in an approximate and discretized way Often but not only used for deformation and stress analysis Division of geometry into finite element mesh Pre assumed interpolation of main quantities displacements over elements based on values in points nodes Formation of stiffness matrix K and force vector r Global solution of main quantities in nodes d d D KD R r R k K Course Computational Geotechnics 4 Finite Element Method in Geotechnical Engineering Discretization of a Continuum 2D modeling 2D cross section is divided into element Several element types are possible triangles and quadrilaterals Course Computational Geotechnics 5 Finite Element Method in Geotechnical Engineering

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