Most problems in engineering are of nonlinear nature. The nonlinearities are caused basically due to the nonlinear material behavior, contact conditions and instability of structures. The principles of the nonlinear Finite-Element-Method (FEM) will be introduced for treating such problems. The finite element program ABAQUS is introduced to investigate real engineering problems.

The course teaches the basics of nonlinear optimization and concepts of machine learning. An introduction to the finite element method allows an extension of the application area to real engineering problems such as structural optimization and modeling of material behavior on different length scales.

Introduction to Dimensioning of components and machine parts. Basic structural theories are introduced and a short introduction to finite elements is given. Further, elements from fracture mechanics, plasticity and stability of structures are presented.

Introduction to MATLAB; vectors and matrices; graphics in MATLAB; calculus, differential equations; programming with MATLAB; data analysis and statistics; interpolation and polynomials. Excercises with solutions: using MATLAB commands, technical applications.

The course "Introduction to FEM programs" familiarizes the students with performing of simple structural analyses with the finite-element method.