Extended Finite Element Method for Statics and Vibration Analyses on Cracked Bars and Beams
Subject Areas : EngineeringF Mottaghian 1 , A Darvizeh 2 , A Alijani 3
1 - Department of Mechanical Engineering, University of Guilan, Rasht, Iran
2 - Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
3 - Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
Keywords:
Abstract :
[1] Wriggers P., 2008, Nonlinear Finite Element Methods, Springer Science & Business Media.
[2] Reddy J. N., 2014, An Introduction to Nonlinear Finite Element Analysis: with Applications to Heat Transfer, Fluid Mechanics, and Solid Mechanics, OUP Oxford.
[3] Logan D. L., 2011, A First Course in the Finite Element Method, Cengage Learning.
[4] Leissa A. W., Qatu M. S., 2011, Vibrations of Continuous Systems, McGraw-Hill.
[5] Rao S. S., Yap F. F., 2011, Mechanical Vibrations, Prentice Hall Upper Saddle River.
[6] Cook R. D., 1994, Finite Element Modeling for Stress Analysis, Wiley.
[7] Kahya V., Turan M., 2017, Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory, Composites Part B: Engineering 109: 108-115.
[8] Darvizeh M. Darvizeh A., Ansari R., Alijani A., 2015, Pre-and post-buckling analysis of functionally graded beams subjected to statically mechanical and thermal loads, Scientia Iranica, Transaction B, Mechanical Engineering 22: 778-791.
[9] Alijani A., Darvizeh M., Darvizeh A., Ansari R., 2015, Elasto-plastic pre-and post-buckling analysis of functionally graded beams under mechanical loading, Proceedings of the Institution of Mechanical Engineers, Journal of Materials Design and Applications 229: 146-165.
[10] Mohammadi S., 2008, Extended Finite Element Method: for Fracture Analysis of Structures, John Wiley & Sons.
[11] Khoei A. R., 2014, Extended Finite Element Method: Theory and Applications, John Wiley & Sons.
[12] Biondi B., Caddemi S., 2005, Closed form solutions of Euler–Bernoulli beams with singularities, International Journal of Solids and Structures 42: 3027-3044.
[13] Nakhaei A., Dardel M., Ghasemi M., Pashaei M., 2014, A simple method for modeling open cracked beam, International Journal of Engineering-Transactions B: Applications 28: 321-329.
[14] Skrinar M., 2009, Elastic beam finite element with an arbitrary number of transverse cracks, Finite Elements in Analysis and Design 45: 181-189.
[15] Xiao Y., Huang J., Ouyang Y., 2016, Bending of Timoshenko beam with effect of crack gap based on equivalent spring model, Applied Mathematics and Mechanics 37: 513-528.
[16] Dolbow J., Belytschko T., 1999, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46: 131-150.
[17] Moës N., Belytschko T., 2002, Extended finite element method for cohesive crack growth, Engineering Fracture Mechanics 69: 813-833.
[18] Sukumar N., Moës N., Moran B., Belytschko T., 2000, Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering 48: 1549-1570.
[19] Borst R. d., Remmers J. J., Needleman A., Abellan M. A., 2004, Discrete vs smeared crack models for concrete fracture: bridging the gap, International Journal for Numerical and Analytical Methods in Geomechanics 28: 583-607.
[20] Kang Z., Bui T. Q., Saitoh T., Hirose S., 2017, Quasi-static crack propagation simulation by an enhanced nodal gradient finite element with different enrichments, Theoretical and Applied Fracture Mechanics 87: 61-77.
[21] Alijani A., Mastan Abadi M., Darvizeh A., Abadi M. K., 2018, Theoretical approaches for bending analysis of founded Euler-Bernoulli cracked beams, Archive of Applied Mechanics 88: 875-895.
[22] Mottaghian F., Darvizeh A., Alijani A., 2018, A novel finite element model for large deformation analysis of cracked beams using classical and continuum-based approaches, Archive of Applied Mechanics 2018: 1-36.
[23] Matbuly M., Ragb O., Nassar M., 2009, Natural frequencies of a functionally graded cracked beam using the differential quadrature method, Applied Mathematics and Computation 215: 2307-2316.
[24] Nahvi H., Jabbari M., 2005, Crack detection in beams using experimental modal data and finite element model, International Journal of Mechanical Sciences 47: 1477-1497.
[25] Orhan S., 2007, Analysis of free and forced vibration of a cracked cantilever beam, NDT & E International 40: 443-450.
[26] Attar M., Karrech A., Regenauer-Lieb K., 2014, Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model, Journal of Sound and Vibration 333: 2359-2377.
[27] Behzad M., Ebrahimi A., Meghdari A., 2008, A new continuous model for flexural vibration analysis of a cracked beam, Polish Maritime Research 15: 32-39.
[28] Shifrin E., Ruotolo R., 1999, Natural frequencies of a beam with an arbitrary number of cracks, Journal of Sound and Vibration 222: 409-423.
[29] Bachene M., Tiberkak R., Rechak S., 2009, Vibration analysis of cracked plates using the extended finite element method, Archive of Applied Mechanics 79: 249-262.
[30] Natarajan S., Baiz P. M., Bordas S., Rabczuk T., Kerfriden P., 2011, Natural frequencies of cracked functionally graded material plates by the extended finite element method, Composite Structures 93: 3082-3092.
[31] Nguyen-Thoi T., Rabczuk T., Lam-Phat T., Ho-Huu V., Phung-Van P., 2014, Free vibration analysis of cracked Mindlin plate using an extended cell-based smoothed discrete shear gap method (XCS-DSG3), Theoretical and Applied Fracture Mechanics 72: 150-163.