双周期圆柱形压电夹杂反平面问题的精确解及其应用

AN EXACT SOLUTION FOR DOUBLY PERIODIC PIEZOELECTRIC INCLUSIONS UNDER ANTIPLANE SHEAR AND ITS APPLICATIONS

研究无限压电介质中双周期圆柱形压电夹杂的反平面问题.借鉴Eshelby等效夹杂原理,通过引入双周期非均匀本征应变和本征电场,构造了一个与原问题等价的均匀介质双周期本征应变和本征电场问题.利用双准周期Riemann边值问题理论,获得了夹杂内外严格的电弹性解.作为压电纤维复合材料的一个重要模型,预测了压电纤维复合材料的有效电弹性模量.

Doubly periodic piezoelectric inclusions in an infinite piezoelectric medium under antiplane shear is dealt with. Reference to Eshelby＇s equivalent inclusion principle, by introducing periodic non-uniform eigenstrain and eigen-electrical-field, an equivalent to the originally heterogeneous materials problem is constructed. Employing the theory of doubly quasi-periodic Riemann boundary value problem, the strictly analytical solutions of electroelastic field in the inclusions and matrix are obtained in series form. As application of this important model of piezoelectric composites, the effective electro-elastic moduli is evaluated.