Finite element modeling of smart plates/shells using higher order shear deformation theory

Abstract The finite element formulation of a degenerate shell element, using higher order shear deformation theory taking the piezo-electric effect into account is presented. An eight-noded element is used to derive global coupled electro elastic behavior of the overall structure. The model incorporates the warping of cross section due to transverse shear stresses and assumes a parabolic shear strain variation over the thickness. The static deflections of bimorph beam are compared with the literature. Active vibration control performance of the piezolaminated curved beam with distributed sensors and actuators is studied. The variation of the damping effect with different gains and actuator coverage is studied.

[1]  H. Tiersten.  Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates , 1969 .

[2]  Aditi Chattopadhyay,et al.  Dynamics of delaminated smart composite cross-ply beams , 1999 .

[3]  Tarun Kant,et al.  Higher-order shear deformable theories for flexure of sandwich plates—Finite element evaluations , 1988 .

[4]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[5]  Nagi G. Naganathan,et al.  A finite-element static analysis of smart turbine blades , 1997 .

[6]  W. Hwang,et al.  Finite Element Modeling of Piezoelectric Sensors and Actuators , 1993 .

[7]  C. I. Tseng,et al.  Distributed vibration control and identification of coupled elastic/piezoelectric systems: Finite element formulation and applications , 1991 .

[8]  Singiresu S Rao,et al.  Analysis of distributed thermopiezoelectric sensors and actuators in advanced intelligent structures , 1993 .

[9]  Shu Xiao-ping.  An improved simple higher-order theory for laminated composite shells , 1996 .

[10]  J. Reddy.  A Simple Higher-Order Theory for Laminated Composite Plates , 1984 .

[11]  H. S. Tzou,et al.  Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements , 1996 .

[12]  Maenghyo Cho,et al.  A postprocess method using a displacement field of higher-order shell theory , 1996 .

[13]  B. Samanta,et al.  Static analysis of an intelligent structure by the finite element method , 1994 .

[14]  Tarun Kant,et al.  ESTIMATION OF INTERLAMINAR STRESSES IN FIBRE REINFORCED COMPOSITE CYLINDRICAL SHELLS , 1991 .

[15]  Tarun Kant,et al.  Higher-order theories for composite and sandwich cylindrical shells with C0 finite element , 1989 .

[16]  Grant P. Steven,et al.  A mixed model for composite beams with piezoelectric actuators and sensors , 1999 .

[17]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[18]  K. Bathe.  Finite Element Procedures , 1995 .