Issues of continuum mechanics and basic tensor analysis. Introduction to nonlinear analysis. Incremental equations of motion, Green Lagrange strain tensor. Cauchy stress tensor, Piola Kirchhoff stresses, Incremental total and updated Lagrangian formulations. Principle of Virtual work in a non-linear setting. Linearization of non-linear equations of motion and incremental - iterative solution methods. Newton-Raphson algorithm. Path following techniques. Arc-Length. Geometric Non linearity. Finite element method for geometric non – linear problems: Truss and Cable elements, Plane Strain and plane stress elements, Three-dimensional solid elements, Structural elements: beam and general shell elements. Material nonlinearity. Problem statement. Elastoplastic problem in one dimension. Isotropic and Kinematic Hardening. J2 Plasticity. Deviatoric stress. Deviatoric strain. Yield surface. Von Mises & Tresca Yield criteria. Drucker’s postulate. Maximum dissipation principle. Associated and non-associated flow rules. Perfect plasticity. Radial return algorithm. Algorithms for isotropic, kinematic and combined hardening. Algorithmic tangent operator. Finite element method for materially nonlinear problems. Implementation using MSOLVE and Commercial Software.
- Teacher: Βησσαρίων Παπαδόπουλος
- Teacher: Κωνσταντίνος Σπηλιόπουλος