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The purpose of this study is to extract the response of the simultaneous low-velocity impact of multiple impactors on a porous functionally graded (FG) aluminum plate.

To design a porous FG structure, a series of functions are applied using the porosity coefficient, and mechanical properties including Young’s modulus, shear modulus and the density of the porous structure are presented as a function of the axis placed in the direction of the plate thickness. The first-order shear deformation theory of the plate is used. To simulate the contact process between each impactor and the plate, a nonlinear Hertz contact force is considered for that impactor independently.

ABAQUS finite element software is used for the verification process of the theorical equations. The effects of porous function type, radius and initial velocity of impactor are investigated for the simultaneous impact of five impactors on porous FG aluminum plate with a simply supported boundary condition. Histories of contact force and displacement of the impactor placed in the center of the beam are analyzed in detail with the changes of the mentioned parameters.

Due to the advantages of porous aluminum plate such as high energy absorption and low weight, such structures may be subjected to the simultaneous impact of multiple impactors, which is studied in this research.

The main objective of this article is to develop a theoretical formulation for predicting the response of CNTs reinforced beam under multiple impactors with general boundary conditions, using first-order shear deformation beam theory.

The rule of mixtures is implemented to derive the material properties of the beam. The nonlinear Hertz contact law is applied for simulation between impactors and the surface of the beam. A combination of approaches includes energy method, Ritz method and generalized Lagrange equations are used to extract the matrix form of equations of motion. The time-domain solution is obtained using implementing the well-known Runge Kutta 4th order method.

After examining the accuracy of the present method, the effects of the number of impactors include one impactor, and three impactors in various CNTs volume fraction are studied for CNTs reinforced beam with clamped-clamped, clamped-free and simply supported boundary conditions under the low-velocity impact. The most important finding of this article is that contact force and beam indentation at the middle of the beam in the case of one impactor are greater than those reported in the case of three impactors.

This article fulfills an identified need to study how CNTs reinforced beam behaviour with general boundary conditions under multiple low-velocity impacts can be enabled.

This paper aims to present the potential of using aligned single-layer graphene sheets to reinforce the methyl methacrylate cantilever beam in low-velocity impact problem.

The Halpin–Tsai law is applied to compute the mechanical properties of isotropic polymer beam reinforced by aligned graphene sheet. Using both longitudinal and lateral displacements in composite beam, all components of the stress and strain fields are written. The equations of motion are derived by applying energy method, generalized Lagrange equations and Ritz method.

The analytical formulation accuracy is corroborated by comparing the present results with those available in the literature. Numerical examples indicate that the contact duration is decreased with increasing of graphene volume fraction, whereas the values of peak contact force, shear strain and shear stress at peak contact force tend to be vice versa. Also, among the results, shear stress at the peak contact force has the most effect with graphene volume fraction changes.

This research fulfils an identified need to investigate how graphene-reinforced beam behavior subjected to low-velocity impact can be enabled.