Structural Analysis and Optimization of Adaptive Structures by use of the Finite Element Method.

Abstract

New finite elements which allow for the analysis and optimization of adaptive structures are presented. In the first part of this paper two finite elements accounting for integrated piezo-electric devices are formulated: a shell element for the analysis of shallow shell structures with piezo-electric polymers bonded to the surfaces and a truss element with an integrated piezo-electric ceramic. Test cases are presented to illustrate the potential of the finite elements. The shell element is used to compute the vibration excitation of a thin plate as well as the vibration control of a cantilever beam. The truss element is applied to the problem of optimal actuator placement in adaptive truss structures. For the solution of this problem, objective functions for the minimization of the control effort and the spillover energy are formulated. The second part of this paper is concerned with the finite element analysis of the behavior of shape memory alloys. A non-linear one-dimensional finite truss element and a non-linear beam element are used for the analysis of a composite beam with embedded shape memory alloy wires, of which the temperature is varied in order to tune the eigenfrequencies.