Bending Problems On Piezoelectric Laminated Plates Containing An Elliptic Hole

Piezoelectric composite material is widely used in engineering due to its unique mechanic-electric coupling characteristics. Many studies have been focused on the coupling effect of piezoelectric materials in recent years. Especially, the bending deformation of laminated piezoelectric plates is very common in practical applications. Thus, it is of great importance to study the bending problems of piezoelectric laminated plates.Based on Lekhniskii's complex-variable-methods, the bending problems of an infinite piezoelectric laminated plate containing an elliptic hole are investigated in this thesis. The main works are as follows:In Chapter 1, we give a brief introduction of engineering applications of piezoelectric material and plates, and then summarized the recent studies on piezoelectric laminates problem. In Chapter 2, basic assumptions and related theories about bending problems of thin plates are given and basis equations for piezoelectricity and laminated plates are presented.In Chapters 3 and 4, given are mainly the theoretical analyses for the bending problems of piezoelectric laminated plates. The stress potentials, deflection and electric potentials are firstly derived for the plate which is subjected to uniform bending moments at infinity. Then, the solutions of the bending moments, electric displacement and membrane stress are obtained, respectively. Moreover, the explicit expressions for the stresses and electric displacements around the elliptic hole are also obtained. In addition, numerical results for the stress distribution, electric potential and electric intensity around the elliptic hole are also presented.In Chapter 5, given are mainly the numerical simulations, FEM software ANSYS is applied to study the bending problems of piezoelectric laminated plates containing an elliptical hole. The stress distribution in a piezoelectric plate containing a circular hole subjected to bending moment was further researched. For different ratio of long axis to short axis of the elliptical hole, the effects of the hole geometry is studied on the distribution of stress, electric intensity and electric flux density. Finally, as an example of a two-layer piezoelectric plate containing a circular hole, numerical results are presented for stress, electric potential and electric field, and then they were compared with theoretical results above.Finally, conclusions are given and future works are proposed in Chapter 6.This work was partially supported by the National Natural Science Foundation of China under Grant No. 10972103.