Analytical analysis of jute–epoxy beams subjected to low-velocity impact loading

Abstract

PurposeIn the article, analytical model of first-order shear deformation (FSDT) beams made of jute–epoxy is presented to study the low-velocity impact response.Design/methodology/approachThe nonlinear Hertz contact law is applied to identify the contact between projectile and beam. The energy method, Lagrange's equations and Ritz method are applied to derive the nonlinear governing equation of the beam and impactor-associated boundary condition. The motion equations are then solved simultaneously by the Runge–Kutta fourth-order method.FindingsAlso, a comparison is performed to validate the model predictions. The contact force and beam indentation histories of the jute–epoxy simply supported beam under spherical impactor with different radius and initial velocity are investigated in detail. It is found that in response to impactor radius increase, the utilization of the contact force law has resulted in a same increasing trend of peak contact force, impact duration and beam indentation, while in response to impactor initial velocity increase, the maximum contact force and beam indentation increase while impact time has vice versa trend.Originality/valueThis paper fulfills an identified need to study how jute–epoxy beam behavior with simply supported boundary conditions under low-velocity impact can be enabled.

Porosity-dependent impact study of a plate with Winkler-Pasternak elastic foundations reinforced with agglomerated CNTs

“…In this article, FSDT is used to present the plate displacements defined as follows (Sobamowo et al , 2020): In this equation, parameters UT , VT and WT are functions of variables x , y , z and t , while five unknowns include displacements u 0 , v 0 and w 0 , and rotations ϕ x and ϕ y of the midplane are functions of variables x , y and t . The amount of strain energy stored in the plate ( U P ) is obtained through the following equation (Jasim et al , 2021): Also, the stored strain energy of the Winkler–Pasternak foundations ( U E ) is as follows (Selim and Liu, 2021): where K w is Winkler modulus and K p is the Pasternak modulus of the elastic foundations. What is clear is that because of the collision between the impactor and the plate, strain energy occurred ( U C ) and is also obtained through the following relation (Ranjbar and Feli, 2018): where K imp is the contact stiffness.…”

“…In this equation, parameters UT, VT and WT are functions of variables x, y, z and t, while five unknowns include displacements u 0 , v 0 and w 0 , and rotations f x and f y of the midplane are functions of variables x, y and t. The amount of strain energy stored in the plate (U P ) is obtained through the following equation (Jasim et al, 2021):…”

Low velocity impact study of a sandwich beams using Ritz method and finite element modelling

“…where K s shows shear correction factor, s xx and « xx are stress and strain along the x direction, s xz and g xz are shear stress and shear strain in the xz plane, x i is impact location, C i is impact stiffness because of the impact between projectile tip and beam and y and M i are impactor displacement and impactor mass. In this article, the non-linear Hertz contact force is used to identify the impact mechanism between projectile and beam Feli, 2019a, Alhusseini et al, 2020;Jasim et al, 2020;Hassan et al, 2021):…”

Multi-layer polymer beam reinforced by graphene platelets on low velocity impact response

“…The motion equations can be derived using the generalized Lagrange equations given by (Ranjbar and Feli, 2019b; Qanber Ali Sadik et al , 2020; Jasim et al , 2020): …”