A superconvergent finite element for composite beams with embedded magnetostrictive patches

A superconvergent finite element formulation for a composite beam with embedded magnetostrictive patches is presented in this paper. The element uses linear properties of magnetostrictive materials, which can act both as sensors and actuators. A refined 2-node beam element is derived based on the Euler–Bernoulli and First Order Shear Deformation Theory for axial–flexural-shear coupled deformation in asymmetrically stacked laminated composite beams with magnetostrictive patches. The element has an interpolating function, which is derived by solving the static part of the governing equations of motion exactly, where a general ply-stacking is considered. Thus, the element has superconvergent properties for static problems. The formulated consistent mass matrix, however, is approximate. Since the stiffness matrix is exact for static analysis, the formulated element predicts natural frequency to greater level of accuracy with smaller discretization compared to any other conventional finite elements. Numerical experiments are performed for static and natural frequency calculation and the superconvergent property of the formulated element is shown by comparing the solution with the standard 1-D FE beam element and 2-D FEM.

[1]  Brian Culshaw,et al.  Smart Structures and Materials , 2004 .

[2]  D. P. Ghosh,et al.  Role of coupling terms in constitutive relationships of magnetostrictive materials , 2004 .

[3]  Srinivasan Gopalakrishnan,et al.  A refined higher order finite element for asymmetric composite beams , 2005 .

[4]  J. N. Reddy,et al.  Transient analysis of laminated composite plates with embedded smart-material layers , 2004 .

[5]  D. Roy Mahapatra,et al.  Active feedback control of multiple waves in helicopter gearbox support struts , 2001 .

[6]  J. N. Reddy,et al.  An exact solution for the bending of thin and thick cross-ply laminated beams , 1997 .

[7]  B Balachandran,et al.  Analytical study of active control of wave transmission through cylindrical struts , 2001 .

[8]  Srinivasan Gopalakrishnan,et al.  Coupled analysis of composite laminate with embedded magnetostrictive patches , 2005 .

[9]  Srinivasan Gopalakrishnan,et al.  A deep rod finite element for structural dynamics and wave propagation problems , 2000 .

[10]  K. Y. Lam,et al.  Active vibration control of composite laminated cylindrical shells via surface-bonded magnetostrictive layers , 2003 .

[11]  Srinivasan Gopalakrishnan,et al.  Poisson's Contraction Effects in a Deep Laminated Composite Beam , 2003 .

[12]  Moshe Eisenberger,et al.  An exact high order beam element , 2003 .

[13]  J. N. Reddy,et al.  A new beam finite element for the analysis of functionally graded materials , 2003 .

[14]  Kiyoshi Tanaka,et al.  Development of active six-degrees-of-freedom microvibration control system using giant magnetostrictive actuators , 2000 .

[15]  Z. Wang,et al.  Sensing of Delaminations in Composite Laminates using Embedded Magnetostrictive Particle Layers , 1999 .

[16]  J. N. Reddy,et al.  Free vibration of cross-ply laminated beams with arbitrary boundary conditions , 1994 .

[17]  James R. Downer,et al.  Terfenol-D driven flaps for helicopter vibration reduction , 1996 .

[18]  M Anjanappa,et al.  Magnetostrictive mini actuators for smart structure applications , 1994 .

[19]  M. Anjanappa,et al.  Magnetostrictive particulate actuators: configuration, modeling and characterization , 1997 .

[20]  Robert G. Loewy,et al.  REVIEW ARTICLE: Recent developments in smart structures with aeronautical applications , 1997 .

[21]  Ted Belytschko,et al.  Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems , 1991 .

[22]  G. Narayana Naik,et al.  An Experimental Investigation of a Smart Laminated Composite Beam with a Magnetostrictive Patch for Health Monitoring Applications , 2003 .

[23]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[24]  D. Roy Mahapatra,et al.  Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities , 2002 .

[25]  J. N. Reddy,et al.  On vibration suppression of magnetostrictive beams , 2000 .

[26]  M. Seetharama Bhat,et al.  A new super convergent thin walled composite beam element for analysis of box beam structures , 2004 .

[27]  Alessandro Russo,et al.  Unlocking with residual-free bubbles , 1997 .

[28]  Gangan Prathap,et al.  Reduced integration and the shear-flexible beam element , 1982 .

[29]  Gerard Franklyn Fernando.  Smart materials and systems , 2007 .

[30]  J. Reddy.  ON LOCKING-FREE SHEAR DEFORMABLE BEAM FINITE ELEMENTS , 1997 .

[31]  G. Prathap.  The Finite Element Method in Structural Mechanics , 1993 .

[32]  H. Stolarski,et al.  Assumed strain formulation for triangular C0 plate elements based on a weak form of the Kirchhoff constraints , 1989 .

[33]  D. Kleinke,et al.  A noncontacting magnetostrictive strain sensor , 1993 .

[34]  S. Elliott,et al.  A non-intrusive fluid-wave actuator and sensor pair for the active control of fluid-borne vibrations in a pipe , 1996 .