Optimal control of shell-type structures' deformation using piezoelectric ring stiffeners

The alleviation of deformation of thin-walled shell structures by using piezoelectric ring stiffeners was demonstrated in the authors' previous work. The basic idea is to use piezoelectric ring stiffeners bonded to the surface of the shell to counteract the deformation caused by external loads such as gravity, internal pressure, and temperature change. The important issue of how to properly select control voltages within the piezoelectric ring stiffeners is discussed in this article. Instead of using a trial-and-error method, as in the past, here an optimal mechanism is used. By forcing the final deformation to approach a pre-specified deformation, the authors determine a set of optimal control voltages within the piezo-stiffeners. A thin-walled cylindrical shell, subject to its own weight, a non-uniform pressure distribution, and a high temperature increase were designed for computer simulation. Eighteen identical piezoelectric rings disposed along the length of the shell at equal spacing are considered, but there is no limitation on the number, location, and size of the rings in the analysis. Efficient control of the shell's deformation by the piezoelectric rings can be readily achieved through the optimization procedure. The numerical results illustrate that a controllable alleviation of shells' deformation is attainable.