精化杂交压电固体单元的研究

基于力、电耦合问题的三类交量广义交分原理，提出了广义杂交压电单元列式。为了进一步改进单元的性能和保证单元能够通过分片检验，通过引入非协调模式、放松电学方程约束条件和单元间的弱连续性条件，建立了新的、修正的广义交分原理，在此基础上成功地引入了应力、应交的正交化插值模式，从而建立了精化杂交压电单元法，它继承了常规精化杂交单元的全部优点。文中所推导的八节点精化杂交压电固体单元列式完全避免了矩阵求逆运算，较广义杂交压电单元和杂交应力压电单元均显著提高了计算效率。数值算例表明，与同类型其他单元相比，该单元明显具有更好的对歪斜网格的适应性。

Investigation of refined hybrid piezoelectric solid element

Starting from the Hu-Washizu generalized variational principle for the coupling electromechanical problems; this paper presents a generalized hybrid piezoelectric element formulation. In order to improve the element property and guarantee its passing the patch test, an modified generalized variational principle was proposed by incorporating the non-conforming modes and relaxing electrical equations and weaker continuity condition. Based on this new functional and orthogonal interpolation mode, a general formulation of a refined hybrid piezoelectric element method was established, which inherits all the merits of the conventional refined hybrid element. In this paper, an 8-node refined hybrid piezoelectric solid element was derived, which absolutely avoids the computation of matrix inversion and are very reliable, more accurate. Its computational efficiency is superior to that of generalized hybrid piezoelectric elements and hybrid stress piezoelectric elements. The numerical examples show that this element has more adaptability to mesh distortion compared with other state-of-art piezoelectric solid elements.