AE701A - Nonlinear Finite Element Method

Overview of nonlinear problems in structural analysis geometric and material nonlinearities, non linear forces and boundary conditions; nature of force deflection curves, critical points. Single degree of freedom system with geometric non linearity Incremental solution, iterative solution using direct and Newton Raphson approaches; combined incremental and iterative solution with full or modified Newton Raphson or initial stress method. One dimensional continuum problem: Axial bar under compression, various strain measures, weak and variational formulations based on Green strain measure. I D Finite element formulation: Total and Updated Lagrangian approaches: derivation of stiffness and tangent stiffness matrices, limit point and bifurcation; traversal of critical points. Two dimensional problems: Strain measures in two and three dimensions, stress measures (Cauchy and Piola Kirchhoff), objectivity, Updated Lagrangian formulation stress increments. 2D Incremental formulation with updates, derivation of stiffness and tangent stiffness matrices. Advanced Solution Procedures: Line search, arc length quasi Newton and Secant methods. Nonlinear Dynamics: Direct Integration techniques: explicit and implicit solution techniques. Stability of time integration schemes. New marks scheme. The method; energy conserving and automatic time stepping methods.