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چكيده انگليسي :

Elasto plastic Analysis with Boundary Element Method Ali Reza Fathi alirezafathi62@gmail com Date of Submission 8 22 2010 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr M Moradi Email moradi@cc iut ac ir Abstract This thesis is devoted to application of boundary element method to elasto plastic analysis Boundary element method is described for elastic problems in two and three dimensions and it is followed by extension of theories and method application to elasto plastic problems Following description of mathematical principles and basic theories of elasticity Betti s reciprocal work theory and Somoigliana identity are presented to form the boundary integral equation Formulation of internal points displacement and stresses along with those for boundary nodes Traction recovery method is employed to extract the boundary stresses Description of discretization method in boundary element method and different kind of integrals encountered in boundary element method are presented Techniques to deal with every kind of integrals are discussed Regular integrals are evaluated through Gauss quadrature method Weakly singular integrals in two dimensions are evaluated by a semi analytical method while weakly singular integrals in three dimensions are evaluated employing element subdivision technique and identities of degenerate cells and elements Rigid body motion technique is employed to circumvent evaluation of strongly singular integrals Rate independent theory of plasticity is employed in which Von Mises yields function and Illyushin s flow theory are employed for plastic analysis Isotropic Kinematic and a mixture of them are incorporated in hardening models The constitutive equation and all required relations necessary for upcoming chapters and for programming a code are presented Presenting the required relations in plasticity boundary integral equation in elasto plastic deformation state is developed Like the procedure taken for elastic problems now displacement and stress relations for interbnal and boundary nodes are presented The technique employed to evaluate strongly singular integrals on the domain of the problem is to turn the mentioned integrals into nonsingular boundary integrals The technique and mathematical representation of it are presented too Discretization of the elasto plastic equations in BEM is discussed BEM elasto plastic equations discretization compels domain discretization Domain discretization and various kinds of integrals encountered are discussed Once again element subdivision technique is described this time for cells that discretize the problem domain in order to evaluate weakly singular integrals on the domain Mathematical representation of the technique used to evaluate strongly singular integrals on the domain is presented next Then it is discussed how the boundary element equations are arranged to form a matrix equation Stress return theory and Newton Raphson iterative scheme for solution of the nonlinear matrix equations are described Finally an algorithm for solution of elasto plastic problems is presented which is implemented through a Fortran code Finally some sample problems are solved using the mentioned code to demonstrate boundary element application to elasto plastic problems For the first example a thick cylinder under internal pressure is solved Results obtained through present code are compared with previous BEM codes analytic solution and Finite Element solution results Perforated plate under extension is the second problem considered Results of the present code are compared with finite element method and experimental results A cube under uniaxial extension is the second example considered Results obtained by the present code are in good agreement with the results from other alternative methods and codes Keywords Boundary element method BEM ealsto plastic analysis linear nonlinear

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