Analytical and numerical simulations of a pressurized functionally graded smart spherical cap

Abstract

To measure changes in pressure, strain or force in pressurized spherical shells used in caps and nose of a spacecraft, piezoelectric layers as sensors are used. In this article, axisymmetric bending analysis of a hybrid piezoelectric layered functionally graded spherical cap is analytically investigated. The piezoelectric face layers behave as sensors. Using thin shell theory in a polar coordinate as well as a new decoupling method, the differential equations for the shell with electrical and mechanical coupling are exactly solved. The pressurized spherical cap is subjected to external pressure and properties of the functionally graded material are changed through the thickness of the shell. The displacement, stress, and electric potential of the hybrid piezoelectric layered functionally graded spherical cap are analytically derived and then, the accuracy and performance of these results are validated by a finite element model and literature. Finally, the effects of various parameters such as piezoelectricity, material grading index, thickness to radius and curvature ratios are examined.