This course is designed to enable the students to solve linear as well as non-linear time variant engineering problems by well suited numerical methods. In particular, students should be placed in a position to develop, implement and investigate novel methods of computational dynamics. Furthermore, the educated application of these methods to practical engineering problems should be a key competence of the students.
Methods of computational dynamics are taught in two parts dealing with linear and non-linear dynamics. Starting in the first part with the Hamilton principle of elastodynamics, numerical methods for the solution of linear structural dynamics and linear elastodynamics are within the focus of the course. In particular, the spatial discretization by the finite element method is briefly reviewed and the generation and solution of the eigenvalue problem of dynamics and the time domain solution by numerical integration methods are taught. Out of the broad range of time integration schemes the central difference method, the generalized Newmark method as well as discontinuous and continuous Galerkin methods are discussed with respect of the numerical properties and supplemented by adequate error measures and adaptive time stepping schemes.
A similar structure of the lecture is used for computational non-linear dynamics. Special attention is taken to energy stable and higher order accurate integration methods.
The lectures are supported by exercises which encourage the understanding of the underlying theory.
The solution of illustrative examples by numerical methods presented in the lecture are additionally studied by in homeworks. The homework consists of reproductive and creative parts. In the reproductive part the understanding of methods taught in lectures is engrossed. The individual development of a software package including simple finite elements (truss elements), eigenvalue analysis and several error controlled time integration schemes represents the creative part of the homework.
Prof. Dr.-Ing. Detlef Kuhl
Certification of credits: