Impact dynamic response of stiffened porous functionally graded materials sandwich doubly-curved shells with Arc-type auxetic core

Abstract

The Arc-type auxetic core is based on the traditional concave hexagonal core and incorporates a bending configuration, facilitating a smooth transition of the cell elements. This modification proves highly effective in alleviating stress concentration. To extend its use in sandwich structures, the dynamic behavior of stiffened porous functionally graded materials (PFGMs) doubly-curved sandwich shell with Arc-type auxetic core under low-velocity impact is a concern that this research addresses. The material properties of external PFGM panels are controlled by two grading patterns (P-FGM and E-FGM) and has four different porosity distributions. The core layer is made of Arc-type auxetic core. A theoretical model that utilizes Hertzian elasticity theory and first-order shear deformation theory (FSDT) is proposed, and the equations of motions are derived using the Hamilton's principle. In addition, to simulate the contact force interaction in dynamic process, the spring-mass model is employed. The analytical solution is presented by using Duhamel's principle and Navier's method to anticipate the transverse displacement. The effectiveness of the obtained data is verified by comparing the findings with those of the existing literature and the numerical results established by the Abaqus commercial software. On this basis, efficient methods for optimizing the PFGM doubly-curved sandwich shell are presented by analyzing the effect of porosity, porosity distribution, gradient index, grading pattern, auxetic core inclined angle and circular arc radius on the energy absorption capability, wherein the sandwich shell of P-FGM reduces the transverse displacement by 24.5 % over E-FGM, and the corresponding gain effects for different porosity distributions are Type B > Type D > Type C > Type A.