In linear analysis, the behaviour of the structure is assumed to be completely reversible, i.e. the body returns to its original un-deformed state upon the removal of the applied loads, and solutions for various load cases can be superimposed. In many engineering applications, however, the behaviour of the structure may depend on the load history or result in large deformations beyond the elastic limit. For such nonlinear problems, the solutions from several load cases cannot be superimposed. Examples of nonlinear applications include elastoplasticity of metals, creep behaviour, buckling and metal forming.

Before attempting the solution of nonlinear problems, accurate and reliable material data must be adequately defined, often requiring the utilisation of experimental data. The application of the Finite Element Method (FEM) to nonlinear problems usually requires the use of small load increments and/or an iterative procedure. Iterations are usually performed to ensure that the solution is convergent, i.e. the error in approximating the equilibrium state is acceptably small.

Contents

Part 1: General Introduction to Non-Linear FE Analysis
Part 2: Time-Independent Material Non-linearity (Plasticity)
Part 3: Time-Dependent Material Non-linearity (Creep)
Part 4: Geometric Non-linearity
Part 5: Boundary Non-linearity (Contact)