PurposeThe 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.Design/methodology/approachThe 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.FindingsAfter 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.Originality/valueThis article fulfills an identified need to study how CNTs reinforced beam behaviour with general boundary conditions under multiple low-velocity impacts can be enabled.

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value This research fulfils an identified need to investigate how graphene-reinforced beam behavior subjected to low-velocity impact can be enabled.

This study has two main aims; firstly, investigating the behavior of slabs that are strengthened with different types of reinforcements and with Slurry-Infiltrated Mat Concrete (SIMCON) laminates, having different dimensions and thicknesses and subjected to static and dynamic (impact) loads. Secondly, the development of a non-linear finite element (FE) model to simulate the behavior of the tested slabs utilizing the ABAQUS/Standard package. The modeling of the NSC slabs strengthened with either SIMCON or steel plates involves using three-dimensional solid elements that are partially integrated with the modeling of concretes using the 8-node brick element (C3D8R). The results of the experimental and numerical investigations are compared to examine whether the slab modeling is sufficient. The comparison includes the element type, material characteristics, real constants, and convergence study. The predicted ultimate load-carrying capacity versus vertical deformation response is compared with the lab results that correspond with it, as obtained via the FE analysis of all tested slabs. In addition, the results of the FE analysis of slab specimens that are strengthened with steel plates were compared to the results of the ones strengthened using SIMCON laminates. The obtained results have led to a number of significant observations. Considering the punching shear strength, it was found that using SIMCON strengthening in different dimensions increased the slab’s punching shear capacity and outperformed steel-strengthened slabs. As for the plate stiffness, SIMCON-strengthened slabs presented higher stiffness rates than steel-strengthened slabs, to the extent that even 20 mm SIMCON strengthening outperformed the steel plate-strengthened slabs of any thickness or dimensions. The axial load-displacement relationships indicate that all the numerical models show a stiffer behavior when compared with the experimental axial load-displacement relationships. The slab thickness of SIMCON significantly affects the load-carrying capacity, and it increases with the increase in thickness. Likewise, using strengthening from steel plates gives a higher load-carrying capacity. Finally, since the results of the yield line analyses for these slabs are found to match the experimental results closely, this method is considered to be suitable for practical use in determining the strength of plated slabs. Therefore, the conclusion is drawn that the proposed FE model can be sufficiently used in evaluating the dynamic responses of slabs strengthened with SIMCON or steel plates and subjected to cyclic and impact load.