Research On Bending Problems Of Piezoelectric-piezomagnetic Laminated Plates With An Elliptical Hole

Piezoelectric and piezomagnetic materials have wide applications in engineering due to theirunique capability of converting the system energies from one form (among magnetic, electric andmechanical energies) to the other. Holed structures are very common in engineering. Undercomplicated loading conditions, the so-called “stress concentration” phenomenon will be induced inthis kind of structures, and it may lead to the damage of the structures. And, the piezoelectric andpiezomagnetic devices are usually used in form of laminated plates. Therefore, it is of greattheoretical and engineering significance to investigate the bending problems of piezoelectric andpiezomagnetic laminated plates with holes.Based on exact boundary conditions, this paper presents the Lekhnitskii solutions for the bendingproblems of the infinite piezoelectric as well as piezoelectric/piezomagnetic laminated platescontaining an elliptic hole. Below are the main contents of this work: a brief introduction onpiezoelectric-piezomagnetic materials and previous works is given in Chapter1. Basic equations,assumptions and boundary conditions are outlined in Chapter2. Chapter3-4are the maincontributions of the work. Using the extended Kirchhoff assumptions, the form of the displacements,electric fields and/or magnetic fields are all be expressed as a linear distribution along the thicknessdirection, and then with the classical Mushhelishvili-Lekhnitskii complex variable method, theconformal mapping method and the Cauchy integration, the explicit solutions for the stresses,moments, electric displacements and magnetic inductions are derived, respectively. In addition,numerical results for the distributions of the field quantities around the elliptic hole are presented todiscuss the bending-streching coupling effects and piezoelectric and piezomagnetic effects on the fieldvariables as well as the variation of stress concentration around the elliptical hole by changing theratio of the major and minor axis. Finally, ANSYS is applied to confirm the rightness of theLekhnitskii solutions by a simple example. According to the above results, it is found that the stressconcentration near the hole depends on the material constants and the geometry of the hole. InChapter5, this work is concluded and future works are proposed.