Static analysis of an intelligent structure by the finite element method

Abstract Static analysis of an intelligent structure, i.e., a structure integrated with distributed actuators and sensors, is presented by the finite element method. The distributed actuator and sensor layers are made of a piezoelectric polymer called PVDF and are perfectly bonded to the top and bottom surfaces of the substrate of the intelligent structure. The substrate is a laminated rectangular plate, composed of a graphite/epoxy composite material. In order to demonstrate the distributed actuation and sensing the overall structure is considered as the plies of the laminated plate. A two-dimensional eight-noded isoparametric finite element is derived for modeling the distributed coupled electromechanical behavior using higher order displacement theory. To verify the accuracy of the finite element modeling the results obtained by the present finite element method for a given distributed mechanical load and with or without describing the electric potential on the surface of the actuator are compared with the exact solution.

[1]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[2]  C. I. Tseng,et al.  Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach , 1990 .

[3]  Satya N. Atluri,et al.  Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading , 1989 .

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

[5]  D. H. Robbins,et al.  Analysis of piezoelectrically actuated beams using a layer-wise displacement theory , 1991 .

[6]  Craig A. Rogers,et al.  Laminate Plate Theory for Spatially Distributed Induced Strain Actuators , 1991 .

[7]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[8]  C. Fuller,et al.  Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates , 1991 .

[9]  M. C. Ray,et al.  Exact analysis of coupled electroelastic behaviour of a piezoelectric plate under cylindrical bending , 1992 .

[10]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[11]  D. Griffiths.  Introduction to Electrodynamics , 2017 .

[12]  C. I. Tseng,et al.  Distributed structural dynamics control of flexible manipulators—II. Distributed sensor and active electromechanical actuator , 1990 .

[13]  R. Christensen,et al.  Stress solution determination for high order plate theory , 1978 .

[14]  R. Christensen,et al.  A High-Order Theory of Plate Deformation—Part 2: Laminated Plates , 1977 .

[15]  Fu-Kuo Chang,et al.  Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators , 1992 .

[16]  Kenneth B. Lazarus,et al.  Induced strain actuation of isotropic and anisotropic plates , 1991 .