
NON LINEAR SOLID AND STRUCTURAL MECHANICS
Prerequisites:

Structural Dynamics 
Examination methods:

Practical applications 
Course unit contents:

Theory: Mathematical preliminaries: vector and tensor algebra, linearization and directional derivative, tensor analysis. Finite rotations: the vector and tensor representation of rotations in 3D space, quaternion representation. Formulation of a beam undergoing finite deformation: kinematic, balance laws and constitutive relationships. Formulation of shell undergoing finite displacements, rotations and deformations: kinematic and balance laws. Numerical methods for solving nonlinear equations: NewtonRaphson, Orthogonal Residual and ArcLength. Introduction to non linear dynamic analysis: Newmark algorithm and energyconserving methods. Classes of problems and solutions: problems of solid and structures undergoing with finite displacements and rotations, problems involving beams in finite deformations, problems dealing with shells in finite deformations.
Exercises: Introduction to MatLab Scilab Ansys code; analyses using nonlinear truss elements; analyses with nonlinear beam elements; analyses with nonlinear brick element; implementation of elastoplastic constitutive laws; implementation of different solution techniques; non linear dynamic analyses. 

