Problems from heat conduction and solid mechanics are addressed. The key topics include relationships between strong, weak, and variational statements of BVPs, weighted residual methods with an emphasis on the Galerkin method, specialization of Galerkin approximations of weak statements and Ritz approximations of variational statements to obtain finite element formulations, specific element formulations, convergence properties, solutions of linear systems of equations, and time-dependent problems. 560.731 Theoretical Methods in Computational Mechanics Basic mathematical tools required for research in computational mechanics. Emphasis is on numerical linear algebra and approximation theory. Specific topics include properties of linear models and procedures for their analysis, variational principles, numerical eigenvalue problem, projections in finite dimensional spaces, least-squares problem, and iterative algorithms.
Applications emphasize finite elements, dynamic systems, and signal analysis.
Topics include weak statements, analysis of convergence properties, solution of nonlinear systems of equations, and temporal integration methods. Plastic, viscoelastic, viscoplastic, thermodynamic, and micromechanical modeling of inelastic behavior. Review of existing constitutive models, with special focus on theories to describe liquefaction behavior of sands and effect of initial and induced anisotropy. Integration of rate equations for solving boundary value problems. 560.743 Limit Analysis in Geotechnical Engineering Theorems of limit analysis.