Mechanik und Mechatronik
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MODELLING, SIMULATION AND ANALYSIS OF MECHATRONICAL SYSTEMS

The Research Group Mechanics of Solids is working in the fields of modelling of mechatronical systems, insofar as they constitute themselves as solid material bodies, the computer-based simulation of the resulting mathematical models, and the analysis of the later with methods of Mathematical Physics.

Nonlinear stability and control

The stability of solutions and the control of nonlinear systems and their sensitivity with respect to disturbances and uncertainties is one of the main research areas we are active in. Nonlinear stability theory, dynamical systems, optimal control, and structural stability and control are just a few topics of interest to us. In particular, we study mechatronical systems in the post-critical regime, in order to enable their stabilisation and control not only in the linear regime, but over a broad range of operation. In addition to stabilisation, we are also interested in the active destabilisation with possible applications to bumping and switching devices and energy harvesting.

Smart structures

In addition to nonlinear systems, the research group’s interests are concerned with inelastic processes in solids. This includes classical inelasticity such as plasticity and thermo-elasticity, but also comprises sources of inelastic processes, which appear due to a multi-field coupling in smart structures. Smart structures are typically put into practice by means of embodied active materials in load bearing structures; e.g. piezoelectric materials or electro-active polymers are some prominent examples. This enables structurally integrated sensing and actuation as well as the development of novel innovative concepts for monitoring and controlling vibrations, instabilities, and damage. With our research, we support bringing new intelligent monitoring and control systems into the real world.

Computational mechanics

The Research Group uses commercially available software packages for symbolic and numerical computations and in-house numerical methods for problem-oriented solutions of mathematical models. E.g. we develop nonlinear Finite Elements for the efficient simulation of slender and thin-walled rods as well as for thin plates and shells. The Finite Elements are used in industrial co-operations as well as for basic research. In particular, we are focussing on implementations for axially moving structures and smart structures.

Practical applications

Practical applications of our scientific results can be found in many fields involving nonlinear structural mechanics such as the optimal control of tethered satellites, the buckling and post-buckling behaviour of thin plates and shells, the early detection of damage in thin-walled structures, and the efficient simulation of axially moving structures like belt drives and metal sheets in hot roll milling.