A piezolaminated composite degenerated shell finite element for active control of structureswith distributed piezosensors and actuators

Abstract

This paper deals with the formulation of a nine-noded piezolaminated degenerated shellfinite element for modeling and analysis of multilayer composite general shell structureswith bonded/embedded distributed piezoelectric sensors and actuators. The distributedPZT sensors and actuators used in the composite smart structures are relatively thin andcould have arbitrary variation of curvatures and thicknesses. They cannot be modeled withshell elements based on curvilinear shell theories which would need the specification ofconstant shell curvatures and thicknesses. Modeling them with piezo finite elementsavailable in popular commercial codes like ABAQUS, ANSYS, MARC, etc, would needrelatively greater computational effort as they are based on solid element formulation. Inview of these, the present proposed degenerated piezoelectric shell element would be abetter choice giving good computational accuracy and efficiency. The main advantageof a degenerate shell element is that it is not based on any shell theories andis applicable over a wide range of curvatures and thicknesses. This element isdeveloped by using the degenerate solid approach based on Reissner–Mindlinassumptions which allow the shear deformation and rotary inertia effect to be consideredand the 3D field is reduced to a 2D field in terms of mid-surface nodal variables.Uniformly reduced integration is carried out to overcome membrane locking and shearlocking and the numerical integration is carried out in all three directions toobtain accurate results. The present element has 45 elastic degrees of freedomand 10 electric degrees of freedom per piezoelectric layer in the element. Thepotential induced due to bending deformation is more accurately represented byassuming quadratic variation of the electric potential through the thickness of eachpiezoelectric layer. This is achieved by interpolating using nodal mid-plane electricpotentials and one electric degree of freedom representing the potential differencebetween the top and bottom surfaces of the piezoelectric layer. Few case studiesof composite general shells with piezoelectric sensors and actuators have beenconsidered by modeling them with the above elements and the active vibration controlperformance has been studied using linear quadratic Gaussian (LQG) control.