Analytical Solution for Large Deflections of a Cantilever Beam Under Nonconservative Load Based on Homotopy Analysis Method

被引：16

作者：

Kimiaeifar, A. ^{[2
]}

Domairry, G. ^{[1
]}

Mohebpour, S. R. ^{[3
]}

Sohouli, A. R. ^{[1
]}

Davodi, A. G. ^{[4
]}

机构：

[1] Babol Univ Technol, Dept Civil Engn & Mech, Babol Sar, Iran

[2] Shahid Bahonar Univ Kerman, Dept Mech Engn, Kerman, Iran

[3] Persian Gulf Univ, Dept Mech Engn, Bushehr, Iran

[4] Shahrood Univ Technol, Dept Civil Engn, Shahrood, Iran

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 27卷 / 03期

关键词：

homotopy analysis method; nonconservative load; large deformation; nonlinear differential equation; FLUID; FLOW; SOLVE;

D O I：

10.1002/num.20538

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, large deflection and rotation of a nonlinear beam subjected to a coplanar follower static loading is studied. It is assumed that the angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation. The governing equation of this problem is solved analytically for the first time using a new kind of analytic technique for nonlinear problems, namely, the homotopy analysis method (HAM). The present solution can be used in wide range of load and length for beams under large deformations. The results obtained from HAM are compared with those results obtained by fourth order Range Kutta method. Finally, the load-displacement characteristics of a uniform cantilever under a follower force normal to the deformed beam axis are presented. (c) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 541-553, 2011

引用

页码：541 / 553

页数：13

共 31 条

[1] MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel
Abbas, Z.
Sajid, M.
Hayat, T.
[J]. THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, 2006, 20 (04) : 229 - 238
[2] The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation
Abbasbandy, S.
[J]. PHYSICS LETTERS A, 2007, 361 (06) : 478 - 483
[3] The application of homotopy analysis method to nonlinear equations arising in heat transfer
Abbasbandy, S.
[J]. PHYSICS LETTERS A, 2006, 360 (01) : 109 - 113
[4] EXTENDED VARIATIONAL FORMULATIONS AND FE MODELS FOR NONLINEAR BEAMS UNDER NONCONSERVATIVE LOADING
ALLINEY, S
TRALLI, A
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1984, 46 (02) : 177 - 194
[5] [Anonymous], INT J NONLINEAR DYNA
[6] NON-LINEAR FINITE-ELEMENT ANALYSIS OF ELASTIC-SYSTEMS UNDER NON-CONSERVATIVE LOADING NATURAL FORMULATION .1. QUASISTATIC PROBLEMS
ARGYRIS, JH
SYMEONIDIS, S
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1981, 26 (01) : 75 - 123
[7] On a new reliable modification of homotopy analysis method
Bataineh, A. Sami
Noorani, M. S. M.
Hashim, I.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (02) : 409 - 423
[8] Bolotin V.V., 1963, NONCONSERVATIVE PROB
[9] The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow
Domairry, G.
Mohsenzadeh, A.
Famouri, M.
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (01) : 85 - 95
[10] Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation
Domairry, G.
Nadim, N.
[J]. INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, 2008, 35 (01) : 93 - 102

← 1 2 3 4 →