Stress distribution of a cylindrical sandwich sector with FG-CNT core and piezoelectric face sheets subjected to low-velocity impact

Abstract

A new theoretical solution based on Layerwise theory is presented to determine the stress distribution in a simply-supported cylindrical sandwich sector with a functionally graded carbon nanotube core and piezoelectric face sheets subjected to low-velocity impact. The spherical elastic ball hits the top face sheet of the sector at an initial velocity of 50 m/s. The classical non-adhesive elastic contact theory and Hunter's relationship were used to determine the normal contact pressure distribution in terms of time and distance of the contact location. Moreover, Hamilton's principle and Maxwell's static equation were used to obtain the nineteen equations of motion. The numerical code was written to solve these nonlinear equations and the stress components in each layer were calculated in terms of time. In addition, it was assumed that the out-of-shell displacement of the sector at each layer is a quadratic polynomial function of the radial component in addition to a function of the coordinate components within the shell. Due to this assumption, the normal out-of-shell strain is not only zero, or not even a constant, but it changes in the form of a linear function along with the thickness of each layer.