Abstract

In this study, an analytical model is developed to research on the time-varying performance of multilayer functionally graded plates glued by viscoelastic interlayers. In the plate, the elastic modulus in each graded layer is exponentially distributed along the thickness, and its mechanical property is modeled on the basis of the three-dimensional (3D) elasticity theory. The viscoelastic property in the interlayer is described by the standard linear solid model considering hereditary nature of viscoelasticity. By using the series expansion and the Laplace transformation, the solutions of stress and displacement for the multilayer plate are analytically derived out. The comparison analysis indicates that the finite element solution and the present one have a good agreement. The Kirchhoff-Love solution becomes imprecise as the thickness or the gradient index increases, because the transverse shear deformation is ignored. In the parameter analysis, the effects of the time variable, the gradient index and the viscoelastic constants on the time-varying performance of the multilayer functionally graded plate are analyzed in detail. The results show that the stress and displacement distributions of the multilayer functionally graded plate can be optimized by changing the gradient index.

摘要

在这项研究中，开发了一个分析模型来研究粘弹性夹层粘合的多层功能梯度板的时变性能。在板中，每个梯度层的弹性模量沿厚度呈指数分布，其力学性能基于三维 (3D) 弹性理论建模。考虑粘弹性的遗传性质，通过标准线性实体模型描述夹层中的粘弹性。利用级数展开和拉普拉斯变换，解析推导出了多层板的应力和位移解。对比分析表明，有限元解与现有解具有良好的一致性。随着厚度或梯度指数的增加，Kirchhoff-Love 解变得不精确，因为忽略了横向剪切变形。在参数分析中，详细分析了时间变量、梯度指数和粘弹性常数对多层功能梯度板时变性能的影响。结果表明，通过改变梯度指数可以优化多层功能梯度板的应力和位移分布。