Assessment of improved zigzag and smeared theories for smart cross-ply composite cylindrical shells including transverse normal extensibility under thermoelectric loading

Abstract

The improved zigzag theory recently developed by the authors for smart, piezoelectric, and laminated cylindrical shells is assessed for the response of finite-length cross-ply shells and shell panels under mechanical, potential, and thermal loading, in direct comparison with the exact three-dimensional (3D) piezothermoelasticity solution. This theory has the unique features of including the transverse normal strain due to thermoelectric loading without introducing additional deflection variables, capturing the nonlinear potential field and actual temperature profile across laminate thickness, accounting for the layerwise (zigzag) variation of inplane displacements, and satisfying the conditions on transverse shear stresses at the layer interfaces and at the inner and outer surfaces. For the assessment, new results are obtained for the 3D exact solution for smart cylindrical shells having a test laminate with widely different material properties across layers, a piezo-composite laminate and a piezo-sandwich laminate. To ascertain the contribution of the layerwise terms in the inplane displacements, the theory is compared with its smeared counterpart with the same number of primary variables. The effect of inclusion of transverse normal extensibility in these theories is established by comparing with their conventional counterparts that assume constant deflection across the thickness. The effect of span angle (for shell panels), length, and thickness parameters on the error of the 2D theories is illustrated.

Creative design for sandwich structures: A review

“…The development of smart core sandwich structure is pursued in parallel with the development of smart materials. 11 –17,36,148 –160 Currently, piezoelectrics, SMAs, electrorheological, and magnetorheological fluids are widely used smart materials. Figure 18 shows some typical smart core structures.…”

“…The geometrically nonlinear dynamic performance of functionally graded sandwich plates using one to three piezoelectric composites was investigated by Kumar 150 and Ray and Ghosh. 151 Nath and Kapuria 152 developed an improved zigzag theory for mart, piezoelectric, and laminated cylindrical shells. Beheshti-Aval and Lezgy-Nazargah 153 developed a coupled refined high-order global-local theory for predicting fully coupled behavior of smart multilayered/sandwich beams under electromechanical conditions.…”

“…Smart core sandwich structure: (a) SMP 11,14,15,17,142,143 , (b) SMA, (c) piezoelectrics 150,152,153 , and (d) magnetorheological fluids. 36 SMP: shape memory polymer; SMA: shape memory alloy.…”