A mixed variational principle is suggested for electromechanical analysis, in which the displacements, the transverse stresses and the electric potential are taken as the primary variables, and a three-dimensional hybrid element approach is built on the principle. Two kinds of specific element, namely the bimaterial interface element and the surface element, are developed so that the interlayer traction-continuity and surface traction-free conditions of transverse stresses can be imposed exactly. Two numerical examples of intelligent laminates with piezoelectric layers bonded to the upper and lower surfaces are presented to demonstrate the efficiency of the present approach.
SpilkerR. L.A hybrid-stress finite element formulation for thick multilayer laminates. Computers Structs, 1980, 11, 507–514.
2.
SpilkerR. L.Hybrid-stress eight-node elements for thin and thick multilayer laminated plates. Int. J. Numer. Meth. Engng, 1982, 18, 801–828.
3.
PianT. H.H.LiM. S.Stress analysis of laminated composites by hybrid finite elements. In Discretization Methods in Structural Mechanics (Eds KuhnG.MangH.) (IUTAM/IACM Symposium, Vienna, 1989), 1990, pp. 363–372 (Springer-Verlag, Berlin and Heidelberg).
4.
JingH. S.LiaoM. L.Partial hybrid stress element for the analysis of thick laminated composite plates. Int. J. Numer. Meth. Engng, 1989, 2, 2813–2827.
5.
SpilkerR. L.ChouS. C.OrringerO.Alternate hybrid-stress elements for analysis of multilayer composite plates. J. Composite Mater., 1977, 11, 51–70.
6.
HuangY. Q.LiuM.WuC. C.A 3D penalty-hybrid finite element method for the analysis of laminated system. Chin. J. Comput. Mechanics, 1997, 14, 83–86.
HeyligerP.BrooksS.Free vibration of piezoelectric laminates in cylindrical bending. Int. J. Solids Structs, 1995, 32, 29452960.
9.
LeeJ. S.JiangL. Z.Exact electroelastic analysis of piezoelectric laminae via state space approach. Int. J. Solids Structs, 1996, 33, 977990.
10.
RayM. C.BhattacharyaR.SamantaB.Exact solutions for static analysis of intelligent structures. Am. Inst. Aeronaut. Astronaut. J., 1993, 31, 16841691.
11.
RayM. C.RaoK. M.SamantaB.Exact solution for static analysis of an intelligent structure under cylindrical bending. Computers Structs, 1993, 47, 10311042.
12.
ReissnerE.On a mixed variational theorem and on deformable plate theory. Int. J. Numer. Meth. Engng, 1986, 23, 193198.
13.
SunK.ZhangF. X.Piezoelectricity, 1984 (National Defense Industry Press, Beijing).
14.
HuangY. Q.Hybrid element method for composite and piezoelectric laminated structures. PhD thesis, University of Science and Technology of China, 1997.
