为了应用弹性力学中的Hamilton 正则方程研究压电材料的灵敏度系数问题,基于压电材料的H-R(Hellinger-Reissner)变分原理,简要地导出Hamilton正则方程算子表达式,建立了四边简支板静力学控制方程.根据灵敏度定义,在静力学控制方程的基础上联立灵敏度控制方程,得到了增维的齐次压电材料静力响应和灵敏度系数混合控制方程.应用该方程可以同时求得压电层合板的力学、电学参量及其灵敏度.该算法过程简单、运算效率和稳定性好.数值算例结果与有限差分法的结果比较表明本文方法切实有效.
In order to analyze the sensitivity coefficients of piezoelectric lamina in terms of Hamilton canonical equation, based on the H -R (Hellinger- Reissner) variational principle of piezoelectric materials, the expression of operator was deduced for Hamilton canonical equation, and the governing equations of static response were established for piezoelectric plates simply supported on four sides as well. According to the definition of sensitivity analysis, the hybrid governing equation of static response and sensitivity coefficients was obtained by uniting Hamilton canonical equation and the equation of sensitivity. The mechanic, electric parameters and the sensitivity coefficients of static response would be gained by this hybrid governing equations at the same time. This algorithm simplifies the process and improves the efficiency of calculation and stability. The results of numerical examples, compared with those of the finite difference methods, show that the present solution is efficient.
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