Course title: Numerical Methods in Nonlinear Structural Analyses

Study: graduate program in Mechanical Engineering

Course director: Prof. Dr. Jurica Soric
Hours/Semester: 50
Semester: optional
 
Course syllabus:
Basic equations in geometrically nonlinear theories, total Lagrangian formulations. Basic equations of small strain plasticity. Finite element formulations: incremental principle of virtual work, linearized finite element equation. Numerical procedures for solution of nonlinear problems: Newton-Raphson and arch-length iterative methods, line-search computational technique. Constitutive equations in elastoplasticity: three-dimensional problems, plane stress problems, formulation for Reissner-Mindlin shell kinematics. Von-Mises yield criterion, elastic-ideal plastic material behavior, linear hardening responses. Principle of maximum plastic dissipation. Nonlinear hardening responses. Nonisothermal constitutive models. Formulations of cyclic plasticity. Explicit computational strategies for integration of constitutive equations. Implicit integration procedures, closest-point projection algorithm. Consistent linearisation and elastoplastic tangent modulus. Finite strain elastoplasticity. Lagrangian and Eulerian formulations. Conjugate stress and strain measures. Rigid body motions and objectivity. Intermediate configuration theory and multiplicative finite elastoplasticity. Computational strategies for integration large strain constitutive equations. Finite element formulations in elastoplasticity. Elastoplastic analyses of shell structures.
Bibliography:

1.Crisfield, M.A., Non-linear Finite Element Analysis of Solids and Structures, Volume 1, John Wiley, New York 1991.

2.Crisfield, M.A., Non-linear Finite Element Analysis of Solids and Structures, Volume 2, John Wiley, New York 1997

3. Chen, W-F., Saleeb, A.F., Constitutive Equations for Engineering Materials,Volume 1: Elasticity and Modeling, Elsevier, Amsterdam 1994.

4.Chen, W-F., Constitutive Equations for Engineering Materials, Volume 2: Plasticity and Modeling, Elsevier, Amsterdam 1994.

5. Khan, A.S., Huang, S., Continuum Theory of Plasticity, John Wiley, New York 1995.

6.Lemaitre, J., Chaboche, J-L., Mechanics of solid materials, Cambridge University Press, Cambridge 1990

7.Bathe, K-J., Finite Element Procedures, Prentice Hall, New Jersey 1996.