Niels Leergaard Pedersen

Topology optimization of laminated plates with prestress

Abstract Laminated plates with different prestress in the layers are topology optimized. The objectives are to minimize the deflection due to the prestress or to minimize ordinary compliance. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the structural stiffness. The calculations of sensitivities are complicated not only by the prestress but also because we are dealing with laminates. The topology optimization problem is solved using a new penalization scheme as an alternative to the SIMP (power law) approach. In the examples we are optimizing a practical micro-electro-mechanical systems (MEMS) application involving a backplate used in a microphone for hearing aids. In this MEMS application the prestress level is very high.

Design Optimization of Conveyor Systems

In this paper an approach to the design of conveyor systems and particular the design of tracks suited for luggage handling systems in airports is presented. The considered system consists of a closed track with a closed loop of carts carrying the luggage for different flight destinations. The track is a 3 dimensional structure assembled of both straight and arc segments as well as level changes of different kinds. The loop of carts is considered as a multibody system including joint flexibility and the stationary track as a guiding frame. While the track forms a continuous line the closed loop of carts approximates the same geometry in a piecewise linear discretized form. Due to geometric effects caused by the use of straight and arc segments the required length of the discretized line varies in order to remain closed when the system is in service. Since the length variation is one of the principal factors in the resulting load spectrum for the carts in the system the aim of the presented work is to reduce this length variation and thereby reduce the fatigue load on the carts.

Shape, position and orientational design of holes for plates with optimized eigenfrequencies

A hole with a given size is placed in the interior of a plate with an arbitrary external boundary. To avoid stress concentrations the shape of the hole must be smooth (continuous curvature). The objectives of the optimization are the eigenfrequencies of the plate with the hole. The optimization is performed in relation to maximizing the first eigenfrequency or maximizing the gap between the first and second eigenfrequency. An inverse problem is also shown, i.e., find the shape and position of a hole in the plate that result in a specified eigenfrequency. To obtain a smooth boundary of the hole we use an analytical description of the hole. A rather general parameterization with only seven design parameters is applied, including the possibility of going from an ellipse to a square or even to a triangle. Optimal designs are obtained iteratively using mathematical programming, each of the redesigns is based on finite element analysis and sensitivity analysis. Mindlin plate theory is the basis for the FE-analysis and the semi-analytical sensitivity analysis includes only the elements on the boundary of the hole.