- Volume 44 Issue 3
DOI QR Code
Slope variation effect on large deflection of compliant beam using analytical approach
- Khavaji, A. ;
- Ganji, D.D. ;
- Roshan, N. ;
- Moheimani, R. ;
- Hatami, M. ;
- Hasanpour, A.
- Received : 2012.10.24
- Accepted : 2012.10.24
- Published : 2012.11.10
In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.
compliant beam;homotopy perturbation method;large deflection;slope variation;non-linear problem
- Ananthasuresh, G.K. and Kota, S. (1995), "Designing compliant mechanisms", J. Mech. Eng., 117, 93-96.
- Ananthasuresh, G.K. and Saggere, L. (1994), "Compliant stapler", University of Michigan Mechanical Engineering and Applied Mechanics Technical Report, UM-MEAM-95-20.
- Bathe, K.J. (1996), Finite Element Procedures, Prentice-Hall, NJ.
- Byers, F.K. and Midha, A. (1991), "Design of a compliant gripper mechanism", Proceedings of the 2nd National Applied Mechanisms & Robotics Conference, Cincinnati, Ohio, XC.1-1-1-12.
- Crane, N.B., Howell, L.L. and Weight, B.L. (2000), "Design and testing of a compliant floating-opposing-arm (FOA) centrifugal clutch", Proceedings of DETC, MECH-14451.
- Esmaeilpour, M.D. and Ganji, D. (2010), "Solution of the Jeffery Hamel flow problem by optimal homotopy asymptotic method", Comp. Math. Appl., 59, 3405-3411. https://doi.org/10.1016/j.camwa.2010.03.024
- Ganji, D.D., Ashory nezhad, H.R. and Hasanpour, A. (2011), "Effect of variable viscosity and viscous dissipation on the hagen-poiseuille flow and entropy generation", Numer. Meth. In Part. Differ. E., 27(3), 529-540. https://doi.org/10.1002/num.20536
- Ganji, D.D. (2006), "The application of he's homotopy perturbation method to nonlinear equations arising in heat transfer", Phys. Lett. A., 355, 337-341. https://doi.org/10.1016/j.physleta.2006.02.056
- Ganji, S.S., Barari, A. and Ganji, D.D. (2011), "Approximate analysis of two-mass-spring systems and buckling of a column", Comp. Math. Appl., 61(4), 1088-1095. https://doi.org/10.1016/j.camwa.2010.12.059
- Golley, B.W. (1997), "The solution of open and closed elastics using intrinsic coordinate finite elements, Comput", Meth. Appl. Mech. Eng., 146, 127-134. https://doi.org/10.1016/S0045-7825(96)01231-5
- Hasanpour, A., Omran, M.P., Ashorynejad, H.R., Ganji, D.D., Hussein, A.K. and Moheimani, R. (2011), "Investigation of heat and mass transfer of MHD flow over the movable permeable plumb surface using HAM", Mid.-East J. Sci. Res., 510-515.
- He, J.H. (1999), "Homotopy perturbation technique", Comput. Meth. Appl. Mech. Eng., 178, 257-262. https://doi.org/10.1016/S0045-7825(99)00018-3
- Howell, L.L. (2001), Compliant Mechanisms, JohnWiley & Sons, New York, USA.
- Howell, L.L. and Midha, A.A. (1994), "Method for the design of compliant mechanisms with small-length flexural pivots", ASME J. Mech. Eng., 116, 280-290. https://doi.org/10.1115/1.2919359
- Jutte, C.V. and Kota, S. (2008), "Design of single, multiple, and scaled nonlinear springs for prescribed nonlinear response", ASME J. Mech. Des., 132, 011003-011007.
- Jutte, C.V. and Kota, S. (2008), "Design of nonlinear springs for prescribed load-displacement functions", ASME J. Mech. Des., 130(8), 081403-081409. https://doi.org/10.1115/1.2936928
- Kacianauskas, R., Stupak, E. and Stupak, S. (2005), "Application of adaptive finite elements for solving elasticplastic problem of SENB specimen", MECHANIKA. Nr., 1(51), 18-22.
- Kimiaeifar, A., Lund, E., Thomsen, O.T. and Suensen, J.D. (2011), "Application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co-planar loading", Comput. Math. Appl., 62(12), 4646-4655. https://doi.org/10.1016/j.camwa.2011.10.050
- Kota, S., Ananthasuresh, G.K., Crary, S.B. and Wise, K.D. (1994), "Design and fabrication of microelectromechanical systems", ASME J. Mech., 116(4), 1081-1088. https://doi.org/10.1115/1.2919490
- Lan, C.C. and Lee, K.M. (2006), "Generalized shooting method for analyzing compliant mechanisms with curved members", Int. J. Mech., 128, 765-775.
- Lange, D., Langelaar, M. and Herder, J.L. (2008), "Design of a statically balanced compliant grasper using topology optimization", DETC ASME Design Engineering Technical Conferences, New York, August.
- Liao, S.J. (1992), "The proposed homotopy analysis technique for the solution of nonlinear problem", PhD Thesis, Shanghai Jiao Tong University.
- Liaoa, S. (2009), "Series solution of large deformation of a beam with arbitrary variable cross section under an axial load", The ANZIAM J., 51, 10-33. https://doi.org/10.1017/S1446181109000339
- Massa, F., Tison, T., Lallemand, B. and Cazier, O. (2011), "Structural modal reanalysis methods using homotopy perturbation and projection techniques", Comput. Meth. Appl. Mech. Eng., 2971-2982.
- Mattiasson, K. (1981), "Numerical results from large deflection beam and frame problems analyses by means of elliptic integrals", Int. J. Numer. Meth. Eng., 17, 145-153. https://doi.org/10.1002/nme.1620170113
- Moulton, T. and Ananthasuresh, G.K. (2001), "Micromechanical devices with embedded electro-thermalcompliant actuation", Sens. Actuators A., 90, 38-48. https://doi.org/10.1016/S0924-4247(00)00563-X
- Ohtsuki, A. and Ellyin, F. (2001), "Analytical approach to large deformation problems of frame structures (in case of a square frame with rigid joints)", JSME Int., 44, 89-93.
- Pirbodaghi, T., Ahmadian, M.T. and Fesanghary, M. (2009), "On the homotopy analysis method for nondeflection of a cantilever beam under a terminal follower force", Mech. Res. Comm., 36(2), 143-148. https://doi.org/10.1016/j.mechrescom.2008.08.001
- Saje, M. and Srpcic, S. (1985), "Large deformations of in-plane beams", Int. J. Solids Struct., 21, 1181-1186. https://doi.org/10.1016/0020-7683(85)90003-4
- Safari, M., Ganji, D.D. and Sadeghi, E.M.M. (2010), "Application of He's homotopy perturbation and He's variational iteration methods for solution of Benney-Lin equation", Int. J. Comput. Math., 87(8), 1872-1884. https://doi.org/10.1080/00207160802524770
- Saje, M. and Srpcic, S. (1985), "Large deformations of thin curved plane beam of constant initial curvature", Int. J. Mech., 28, 275-282.
- Shabana, A.A. (1998), Dynamics of Multi Body Systems, Wiley, New York.
- Tolou, N. and Herder, J.L. (2009), "A seminalytical approach to large deflections in compliant beams under point load", Math. Prob. in Eng., 2009, 1-13.
- Wang, C.M., Lam, K.Y., He, X.Q. and Chucheepsakul, S. (1997), "Large deformation of an end supported beam subjected to a point load", Int. J. Nonlin. Mech., 32, 63-72. https://doi.org/10.1016/S0020-7462(96)00017-0
- Wang, Y.G., Lin, W.H. and Liu, N. (2012), "A homotopy perturbation-based method for large deflection of a cantilever beam under a terminal follower force", Int. J. Comput. Meth. Eng. Sci. Mech., 13(3), 197-201. https://doi.org/10.1080/15502287.2012.660229
- Wanga, J.I., Chena, J.K. and Liao, S. (2008), "An explicit solution of the large deformation of a cantilever beam under point load at the free tip", J. Comput. Appl. Math., 212, 320-330. https://doi.org/10.1016/j.cam.2006.12.009
- Yin, X., Lee, K.M. and Lan, C.C. (2004), "Computational models for predicting the deflected shape of a nonuniform, flexible finger", IEEE ICRA, 3, 2963-2968.
- Pasharavesh, A., Vaghasloo, Y.A., Ahmadian, M.T. and Moheimani, R. (2011), "Nonlinear vibration analysis of nano to micron scale beams under electric force using nonlocal theory", ASME Conference Proceedings, DETC2011-47615, 145-151.
- Deflection prediction of a cantilever beam subjected to static co-planar loading by analytical methods vol.10, pp.2, 2014, https://doi.org/10.1016/j.hbrcj.2013.11.003
- Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM vol.4, pp.4, 2014, https://doi.org/10.2478/s13531-013-0175-9