Numerical Analysis of Composite Beams under Impact by a Rigid Particle
الموضوعات :
1 - Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science Technology, Tehran, Iran
2 - Departmen of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
الکلمات المفتاحية: Impact, Composite beam, Large deformation, Rigid mass,
ملخص المقالة :
Analysis of a laminated composite beam under impact by a rigid particle is investigated. The importance of this project is to simulate the impact of objects on small scale aerial structures. The stresses are considered uni- axial bending with no torsion loading. The first order shear deformation theory is used to simulate the beam. After obtaining kinematic and potential energy for a laminated composite beam, the motion equations, boundary conditions and initial conditions are obtained by using Hamilton’s principle. The deformation of beam is considered large so these equations are nonlinear. Then by using the numerical methods such as generalize differential quadrature (GDQ) and Newmark methods, the equations will be converted in to a set of nonlinear algebraic equations. These nonlinear equations are solved by numerical methods such as Newton- Raphson. By solving the equations, the displacement of beam and rotation of cross section in terms of time for different number of points of beam for variety of orientation angle of layers are obtained. Then the displacements of impacted point of beam, stresses and contact forces in different times for variety of orientation of layers for different situations of impact are compared.
[1] Abrate S., 2011, Impact Engineering of Composite Structures, Springer Science & Business Media.
[2] Zener C., 1941, The intrinsic inelasticity of large plates, Physical Review 59(8): 669-673.
[3] Müller P., Böttcher R., Russell A., Trüe M., Aman S., Tomas J., 2016, Contact time at impact of spheres on large thin plates, Advanced Powder Technology 27(4): 1233-1243 .
[4] Boettcher R., Russell A., Mueller P., 2017, Energy dissipation during impacts of spheres on plates: Investigation of developing elastic flexural waves, International Journal of Solids and Structures 106: 229-239.
[5] Hunter S., 1957, Energy absorbed by elastic waves during impact, Journal of the Mechanics and Physics of Solids 5(3): 162-171.
[6] Reed J., 1985, Energy losses due to elastic wave propagation during an elastic impact, Journal of Physics D: Applied Physics 18(12): 2329.
[7] Weir G., Tallon S., 2005, The coefficient of restitution for normal incident, low velocity particle impacts, Chemical Engineering Science 60(13): 3637-3647.
[8] Kelly J. M., 1967, The impact of a mass on a beam, International Journal of Solids and Structures 3(2): 191-196.
[9] Sun C., Huang S., 1975, Transverse impact problems by higher order beam finite element, Computers & Structures 5 (5-6): 297-303.
[10] Yufeng X., Yuansong Q., Dechao Z., Guojiang S., 2002, Elastic impact on finite Timoshenko beam, Acta Mechanica Sinica 18(3): 252-263.
[11] Kiani Y., Sadighi M., Salami S. J., Eslami M., 2013, Low velocity impact response of thick FGM beams with general boundary conditions in thermal field, Composite Structures 104: 293-303.
[12] Rezvanian M., Baghestani A., Pazhooh M. D., Fariborz S., 2015, Off-center impact of an elastic column by a rigid mass, Mechanics Research Communications 63: 21-25.
[13] Ghatreh Samani K., Fotuhi A. R., Shafiei A. R., 2017, Analysis of composite beam, having initial geometric imperfection, subjected to off-center impact, Modares Mechanical Engineering 17(5): 185-192.
[14] Singh H., Mahajan P., 2016, Analytical modeling of low velocity large mass impact on composite plate including damage evolution, Composite Structures 149: 79-92.
[15] Shivakumar K. N., Elber W., Illg W., 1985, Prediction of impact force and duration due to low-velocity impact on circular composite laminates, Journal of Applied Mechanics 52(3): 674-680.
[16] Lam K., Sathiyamoorthy T., 1999, Response of composite beam under low-velocity impact of multiple masses, Composite Structures 44(2-3): 205-220.
[17] Ugural A. C., 2009, Stresses in Beams, Plates, and Shells, CRC Press.
[18] Elshafei M. A., 2013, FE Modeling and analysis of isotropic and orthotropic beams using first order shear deformation theory, Materials Sciences and Applications 4(01): 77.
[19] Reddy J. N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
[20] Newmark N. M., 1959, A method of computation for structural dynamics, Journal of the Engineering Mechanics Division 85(3): 67-94.
[21] Hilber H. M., Hughes T. J., Taylor R. L., 1977, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engineering & Structural Dynamics 5(3): 283-292.
[22] Shu C., Wang C., 1999, Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates, Engineering Structures 21(2): 125-134.
[23] Reddy J., 2004, An Introduction to Nonlinear Finite Element Analysis, United State, Oxford.