Abstract

In this article, a 3D semi-analytical procedure is elaborated for static behavior of simply supported functionally graded magnetoelectroelastic laminated plates subjected to various types of loads. An arbitrary graded formulation is considered in the thickness direction. The laminated plates have been divided into some layers in which the materials properties vary through the thickness. In each layer, the solution has been established using the state-space approach coupled with the Gauss-Tchybechev integration. The predicted solution has been propagated from the bottom to the top layers of the plate using the propagator matrix method. The presented methodological procedure is general and allow considering various types of graded functionalities in the thickness direction. For the computation process, the piezoelectric material $\mathit{BaTi}{O}_3$ and the piezomagnetic material $Co{Fe}_2{O}_4$ are used. Two kinds of functionally graded materials have been hindered. First, the polynomial variation of the materials properties through the thickness direction of the plate is considered. The effective properties of functionally graded materials are assumed to follow the law of mixture. Second, the exponential variation of the materials properties through the thickness of the plate was used. The obtained numerical results have been well compared with the available ones obtained by the 3D asymptotic approach, the modified Pagano method, the pseudo-Stroh formalism, and the finite elements method, respectively. The convergence study showed the accuracy, the efficiency, and the reliability of the presented methodological procedure.

摘要

本文详细介绍了简支功能梯度磁电弹性叠层板在各种载荷作用下的静态行为的 3D 半解析程序。在厚度方向上考虑任意梯度公式。层压板已分为一些层，其中材料特性随厚度而变化。在每一层中，都使用状态空间方法和 Gauss-Tchybechev 积分建立了解决方案。预测的解已经使用传播矩阵方法从板块的底部传播到顶层。所提出的方法过程是通用的，并允许在厚度方向考虑各种类型的分级功能。对于计算过程，压电材料$\mathit{钡钛}{○}_3$和压磁材料$C○{Fe}_2{○}_4$被使用。两种功能梯度材料受到阻碍。首先，考虑材料特性沿板厚方向的多项式变化。假设功能梯度材料的有效特性遵循混合定律。其次，使用了通过板厚度的材料特性的指数变化。所获得的数值结果分别与通过 3D 渐近方法、改进的 Pagano 方法、伪 Stroh 形式和有限元方法获得的可用结果进行了很好的比较。收敛性研究表明了所提出的方法过程的准确性、效率和可靠性。