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压电复合材料层板由压电片与纤维层叠合而成。基于等效单层理论的位移场和电势场,针对正交铺层压电复合材料层板柱面弯曲问题,建立了力电耦合平衡方程,获得了一般边界的解析解。解析解由特解和通解两部分组成,特解对应于简支边界条件,通解由其他各类边界条件确定。平衡方程的变量仅4个,且不随层数变化。如采用相应的位移和电势分布函数,可以得到一阶理论、高阶理论、指数型理论等多种理论的解析解。算例中给出了各种边界条件下位移、应力和电势的解,讨论了各种理论的精度,观察到了固支边界的应力奇异现象。
Piezoelectric composite laminates are composed of piezoelectric sheets and fiber layers. Based on the displacement field and the potential field of the equivalent single-layer theory, a force-electric coupling equation is established for the cylinder bending of the orthogonally laminated piezoelectric composite laminates, and an analytical solution of the general boundary is obtained. The analytical solution is composed of the special solution and the general solution. The special solution corresponds to the simple support boundary condition, and the general solution is determined by other kinds of boundary conditions. The equilibrium equation has only four variables and does not vary with the number of layers. Such as the use of the corresponding displacement and potential distribution function, you can get first-order theory, high-order theory, exponential theory and other theories of analytic solution. The examples show the solution of displacements, stresses and potentials under various boundary conditions. The accuracy of various theories is discussed and the stress singularity of the boundary is observed.