A Homotopy Perturbation-Based Method for Large Deflection of a Cantilever Beam Under a Terminal Follower Force

REFERENCES

• Rao , B. N. and Rao , G. V. 1986 . On the Large Deflections of Cantilever Beams with End Rotational Load . ZAMM , 66 : 507 – 508 .
   Web of Science ®Google Scholar
• Rao , B. N. and Rao , G. V. 1988 . Large Deflections of a Nonuniform Cantilever Beam with End Rotational Load . Forsch. Ing. Wes. , 54 : 24 – 26 .
   Web of Science ®Google Scholar
• Rao , B. N. and Rao , G. V. 1989 . Large Deflections of a Cantilever Beam Subjected to a Rotational Distributed Loading . Forsch. Ing. Wes. , 55 : 116 – 120 .
   Web of Science ®Google Scholar
• Argyris , J. and Symeonidis , S. 1981 . Nonlinear Finite Element Analysis of Elastic Systems under Nonconservative Loading: Natural Formulation, Part 1, Quasistatic Problems . Comput. Methods Appl. Mech. Eng. , 26 : 75 – 123 .
   Web of Science ®Google Scholar
• Shvartsman , B. S. 2007 . Large Deflections of a Cantilever Beam Subjected to a Follower Force . J. Sound Vib. , 304 : 969 – 973 .
   Web of Science ®Google Scholar
• Kounadis , A. N. 1980 . Static Stability Analysis of Elastically Restrained Structures under Follower Forces . AIAA Journal , 18 : 473 – 476 .
   Web of Science ®Google Scholar
• Navaee , S. and Elling , R. E. 1992 . Equilibrium Configurations of Cantilever Beams Subjected to Inclined End Loads, . J. Appl. Mech. , 59 : 572 – 579 .
   Web of Science ®Google Scholar
• Mohyud-Din , S. T. , Noor , M. A. and Jabeen , F. 2011 . Modified Variational Iteration Method for Traveling Wave Solutions of Seventh-order Generalized KdV Equations . Int. J. Comput. Methods Eng. Sci. Mech. , 12 : 107 – 113 .
   Google Scholar
• Jalaal , M. , Ganji , D. D. and Ahmadi , G. 2010 . An Analytical Study on Settling of Non-spherical Particles . Asia-Pacific J. Chem. Eng. , DOI:10.1002/apj.492
   Web of Science ®Google Scholar
• Miansari , M. O. , Miansari , M. E. , Barari , A. and Domairry , G. 2010 . Analysis of Blasius Equation for Flat-plate Flow with Infinite Boundary Value . Int. J. Comput. Methods Eng. Sci. Mech. , 11 : 79 – 84 .
   Google Scholar
• Jalaal , M. and Ganji , D. D. 2010 . An Analytical Study on Motion of a Sphere Rolling Down an Inclined Plane Submerged in a Newtonian Fluid . Powder Technol. , 198 : 82 – 92 .
   Web of Science ®Google Scholar
• He , J. H. 1999 . Homotopy Perturbation Technique . Comput. Methods Appl. Mech. Eng. , 178 : 257 – 262 .
   Web of Science ®Google Scholar
• He , J. H. 2003 . Homotopy Perturbation Method: A New Nonlinear Analytical Technique . Appl. Math. Comput. , 135 : 73 – 79 .
   Web of Science ®Google Scholar
• He , J. H. 2000 . A Coupling Method of Homotopy Technique and Perturbation Technique for Nonlinear Problems . Int. J. Non-Linear Mech. , 35 ( 1 ) : 37 – 43 .
   Web of Science ®Google Scholar
• He , J. H. 2000 . A Review on Some New Recently Developed Nonlinear Analytical Techniques . Int. J. Nonlinear Sci. Numer. Simul. , 1 ( 1 ) : 51 – 70 .
   Google Scholar
• Jalaal , M. , Ganji , D. D. and Ahmadi , G. 2010 . Analytical Investigation on Acceleration Motion of a Vertically Falling Spherical Particle in Incompressible Newtonian Media . Adv. Powder Technol. , 21 : 298 – 304 .
   Web of Science ®Google Scholar
• Jalaal , M. and Ganji , D. D. 2011 . On Unsteady Rolling Motion of Spheres in Inclined Tubes Filled with Incompressible Newtonian Fluids . Adv. Powder Technol. , 22 : 58 – 67 .
   Web of Science ®Google Scholar
• Esmaeilpour , M. , Ganji , D. D. , Davodi , A. G. and Sadoughi , N. 2010 . Application of He's Methods for Laminar Flow in a Porous-saturated Pipe . Math. Methods. Appl. Sci. , 33 : 1112 – 1121 .
   Web of Science ®Google Scholar
• 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 : 1872 – 1884 .
   Web of Science ®Google Scholar
• He , J. H. 2005 . Homotopy Perturbation Method for Bifurcation of Nonlinear Problems . Int. J. Nonlinear Sci. Numer. Simul. , 6 ( 2 ) : 207 – 208 .
   Web of Science ®Google Scholar
• He , J. H. 2006 . Homotopy Perturbation Method for Solving Boundary Value Problems . Phys. Lett. , A350 ( 1–2 ) : 87 – 88 .
   Google Scholar
• Noor , M. A. and Mohyud-Din , S. T. 2007 . An Efficient Algorithm for Solving Fifth-order Boundary Value Problems . Math. Comput. Model. , 45 : 954 – 964 .
   Web of Science ®Google Scholar
• Odibat , Z. M. 2007 . A New Modification of the Homotopy Perturbation Method for Linear and Nonlinear Operators . Appl. Math. Comput. , 189 : 746 – 753 .
   Web of Science ®Google Scholar
• Ghasemi , M. , Kajani , M. T. and Babolian , E. 2007 . Application of He's Homotopy Perturbation Method to Nonlinear Integro-differential Equations . Appl. Math. Comput. , 188 : 538 – 548 .
   Web of Science ®Google Scholar
• Ghasemi , M. , Kajani , M. T. and Davari , A. 2007 . Numerical Solution of Two-dimensional Nonlinear Differential Equation by Homotopy Perturbation Method . Appl. Math. Comput. , 189 : 341 – 345 .
   Web of Science ®Google Scholar