Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied. In order to derive the fully non-linear equations governing the non-linear deformation, a curvilinear coordinate system is introduced. A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities, infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials. The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam. The effects of taper ratio, inclined end load angle and material property gradient on large deflection of the beam are evaluated. The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.

[1]  A. Nayfeh,et al.  Linear and Nonlinear Structural Mechanics , 2002 .

[2]  Jia-Zhen Hong,et al.  An exact nonlinear hybrid-coordinate formulation for flexible multibody systems , 2007 .

[3]  I. Hashim.  Adomian decomposition method for solving BVPs for fourth-order integro-differential equations , 2006 .

[4]  D. Ganji,et al.  TRAVELING WAVE SOLUTIONS OF THE SINE-GORDON AND THE COUPLED SINE-GORDON EQUATIONS USING THE HOMOTOPY-PERTURBATION METHOD , 2009 .

[5]  Youhe Zhou,et al.  THERMAL POST-BUCKLING OF A HEATED ELASTIC ROD WITH PINNED-FIXED ENDS , 2002 .

[6]  Guo-Ping Cai,et al.  Model study and active control of a rotating flexible cantilever beam , 2004 .

[7]  杜强,et al.  Modal test and analysis of cantilever beam with tip mass , 2002 .

[8]  Marta B. Rosales,et al.  A further study on the postbuckling of extensible elastic rods , 2000 .

[9]  Nesbitt W. Hagood,et al.  Modelling of Piezoelectric Actuator Dynamics for Active Structural Control , 1990 .

[10]  Youlun Xiong,et al.  High-order model and slide mode control for rotating flexible smart structure , 2008 .

[11]  Edward F. Crawley,et al.  Intelligent structures for aerospace - A technology overview and assessment , 1994 .

[12]  Jialing Yang,et al.  Inverse problem of elastica of a variable-arc-length beam subjected to a concentrated load , 2005 .

[13]  G. K. Ananthasuresh,et al.  Designing compliant mechanisms , 1995 .

[14]  G. Rahimi,et al.  LARGE DEFLECTION OF FUNCTIONALLY GRADED CANTILEVER FLEXIBLE BEAM WITH GEOMETRIC NON-LINEARITY: ANALYTICAL AND NUMERICAL APPROACHES , 2010 .

[15]  Michael J. Brennan,et al.  Two simple methods to suppress the residual vibrations of a translating or rotating flexible cantilever beam , 2008 .

[16]  Rubens Sampaio,et al.  Vibrations of axially moving flexible beams made of functionally graded materials , 2008 .

[17]  Bhavani V. Sankar,et al.  AN ELASTICITY SOLUTION FOR FUNCTIONALLY GRADED BEAMS , 2001 .

[18]  L. Tsai,et al.  Modeling of Flexural Beams Subjected to Arbitrary End Loads , 2002 .

[19]  A. Midha,et al.  Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms , 1995 .

[20]  M. A. Abdou,et al.  New applications of variational iteration method using Adomian polynomials , 2008 .

[21]  Frederick Bloom,et al.  Elastica solution for the hygrothermal buckling of a beam , 1999 .

[22]  R. Barboni,et al.  TECHNICAL NOTE: Static adjustment of beam deflections by means of induced strain actuators , 1999 .

[23]  A. Banerjee,et al.  Large deflection of cantilever beams with geometric non-linearity: Analytical and numerical approaches , 2008 .

[24]  K. E. Bisshopp,et al.  Large deflection of cantilever beams , 1945 .

[25]  G. Rahimi,et al.  THERMAL BEHAVIOR ANALYSIS OF THE FUNCTIONALLY GRADED TIMOSHENKO'S BEAM , 2008 .

[26]  S. Suresh,et al.  Fundamentals of functionally graded materials , 1998 .

[27]  Abdul-Majid Wazwaz,et al.  A reliable algorithm for solving boundary value problems for higher-order integro-differential equations , 2001, Appl. Math. Comput..

[28]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[29]  B. Shvartsman,et al.  Direct method for analysis of flexible cantilever beam subjected to two follower forces , 2009 .

[30]  P. Frank Pai,et al.  Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams , 2000 .

[31]  Anupam Saxena,et al.  A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments , 1998 .