Nonlinear behaviour of solids and structures: geometric and material nonlinearities; problems involving contact; nonlinear dynamics; mathematical idealisation of nonlinear problems; nonlinear continuum mechanics; solution strategies for nonlinear problems, finite element software, experimental verification. Finite element (FE) equations in nonlinear analysis: weak and strong forms; general FE equations; incremental form of FE equations; total and updated Lagrange framework. FE solution strategies: linearization of FE equations, incremental-iterative methods; convergence criteria; tangent stiffness matrices. FE solution of geometrically nonlinear problems: stability problems, Riks algorithm, FE solution of problems involving material nonlinearities: continuum quantities and approaches; principle of objectivity; displacement-pressure formulations; implicit and explicit integration; consistent tangent stiffness matrices; radial return algorithm. FE solution of contact problems: frictionless problems; finite element equations; penalty and Lagrange multipliers approaches; frictional problems. Computer implementation of nonlinear FE algorithms: commercial packages; user-subroutines.

1. Evaluate finite element matrices for various element types under large deformation conditions (finite strain and finite rotations) in the total and updated Lagrangian frameworks (homework for credit and final exam) 2. Predict force-deflection curves for structural finite elements experiencing geometrically nonlinear conditions using incremental-iterative methods (homework for credit and final exam) 3. Calculate the true stress-strain behaviour of continuum finite elements assuming the nonlinear elastic constitutive behaviour (homework for credit and final exam) 4. Derive general finite element equations under given contact constraints using the penalty and Lagrange multipliers approaches (homework for credit and final exam) 5. Write a code in Matlab for calculation of stress-strain curves for a given finite element and prescribed type of an elastoplastic material behaviour (homework for credit) 6. Perform a finite element analysis (with ABAQUS) of a given nonlinear engineering problem involving large deformations and contact constraints (lab-work for credit)

7. Co-operate with other members of small groups (lab) 8. Appreciate mathematical idealisations involved in modelling of nonlinear problems of solids and structures, and accept the necessity for experimental verification of results of nonlinear finite element calculations (homework for credit)

N/A