A two-dimensional (2-D) elasticity solution is developed to investigate the time-dependent response of laminated functionally graded beam with viscoelastic interlayer. The elastic modulus in each functionally graded layer varies through the thickness following an exponential function, and the mechanical property of each layer is described by the exact 2-D elasticity equations. Viscoelastic property in the interlayer is simulated by the Maxwell–Wiechert model, in which the memory effect of it is neglected. By virtue of the recursive matrix method, the solution of stress and deformation can be obtained efficiently. The comparison studies indicate that the relative error of the Euler–Bernoulli solution is slight for slender beam with small gradient factor, but it significantly increases as the beam thickness or the gradient factor grows. The finite element solution is close to the present one with large number of sub-layers in FE modeling and small gradient factor of FG layer, while the error of FE solution increases as the number of sub-layers decrease or the gradient factor increases. Besides, the influences of material parameters upon the time-dependent behavior and the optimization for the stress and deformation in the beam are discussed in detail.

中文翻译：

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基于弹性理论的粘弹性夹层粘结的功能梯度层合梁的时变行为

开发了二维（2-D）弹性解决方案，以研究具有粘弹性夹层的层状功能梯度梁的时变响应。每个功能渐变层中的弹性模量随厚度的变化遵循指数函数，并且每个层的机械性能由精确的二维弹性方程式描述。中间层的粘弹性是通过Maxwell-Wiechert模型进行模拟的，其中忽略了它的记忆效应。借助于递归矩阵方法，可以有效地获得应力和变形的解。比较研究表明，对于具有较小梯度因子的细长光束，Euler–Bernoulli解的相对误差很小，但随着光束厚度或梯度因子的增大，其相对误差会显着增加。有限元解决方案与目前的有限元解决方案非常接近，有限元建模中的子层数较多，FG层的梯度因子较小，而有限元解的误差随子层数的减少或梯度因子的增加而增加。此外，详细讨论了材料参数对随时间变化的行为的影响以及梁中应力和变形的优化。