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

• Published in: Journal of engineering, design and technology design and technology, 2024-03, Vol.22 (2), p.516-531
• Main Authors: Ali Mohammed Ali, Manar Hamid Jasim, Bashar Dheyaa Hussein Al-Kasob
• Format: Article
• Language: English
• Subjects: Aircraft; Beams (structural); Carbon fibers; Composite materials; Computer simulation; Construction accidents & safety; Contact force; Contact stresses; Energy; Equations of motion; Exact solutions; Finite element method; Impact loads; Investigations; Low speed; Mathematical models; Numerical analysis; Projectiles; Ritz method; Runge-Kutta method; Sandwich structures; Shear deformation; Shear strain; Simulation; Velocity; Vibration analysis
• ISSN: 1726-0531; 1758-8901
• DOI: 10.1108/JEDT-10-2021-0584

PurposeThe purpose of this paper is to present an applied method to design the low-speed contact between a mass and surface of a beam using an analytical solution based on the first-order shear deformation beam theory. Also, a simulation of impact process is carried out by ABAQUS finite element (FE) code.Design/methodology/approachIn theoretical formulation, first strains and stresses are obtained, then kinetic and potential energies are written, and using a combination of Ritz and Lagrange methods, a set of system of motion equations in the form of mass, stiffness and force matrices is obtained. Finally, the motion equations are solved using Runge–Kutta fourth order method.FindingsThe von Mises stress contours at the impact point and contact force from the ABAQUS simulation are illustrated and it is revealed that the theoretical solution is in good agreement with the FE code. The effect of changes in projectile speed, projectile diameter and projectile mass on the results is carefully examined with particular attention to evaluate histories of the impact force and beam recess. One of the important results is that changes in projectile speed have a greater effect on the results than changes in projectile diameter, and also changes in projectile mass have the least effect.Originality/valueThis paper presents a combination of methods of energy, Ritz and Lagrange and also FE code to simulate the problem of sandwich beams under low velocity impact.