A novel strong-form numerical algorithm, piezoelectric vibration element differential method (PVEDM), is proposed for simulating the static deflection and forced vibration of the structure integrated with piezoelectric layers, with the host structure being homogeneous or functionally graded materials. A unified manner for the steady-state and dynamic responses of piezoelectric structures is set up by the proposed method, which draws on the merits of the finite element method and collocation method. In the whole process of assembling the system of equations, variational principle and integration are not required. Furthermore, the influence of boundary conditions on static deflection, and static shape control are investigated. Three examples of static and dynamic responses from one-layer structure, bimorph structure to the structure bonded with piezoelectric layers are given in turn. By comparing with analytical solution or ABAQUS, precise results are achieved, which verifies the the accuracy of the method.

提出了一种新的强形式数值算法，即压电振动元件微分法（PVEDM），用于模拟与压电层集成的结构的静态偏转和受迫振动，主体结构为均质或功能梯度材料。该方法借鉴了有限元法和搭配法的优点，建立了压电结构稳态和动态响应的统一方法。在组装方程组的整个过程中，不需要变分原理和积分。此外，还研究了边界条件对静态挠度和静态形状控制的影响。三层结构的静态和动态响应的三个示例，依次给出了双晶结构到与压电层结合的结构。通过与解析解或ABAQUS的比较，得到了精确的结果，验证了方法的准确性。