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Exact solutions for multilayer functionally graded beams bonded by viscoelastic interlayer considering memory effect

机译：考虑记忆效应，通过粘弹性中间层粘合的多层功能渐变梁的精确解决方案

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摘要

This work proposes exact solutions for simply supported multilayer functionally graded (FG) beams with viscoelastic interlayer to predict its time-dependent mechanical behavior. The stresses and deformations of FG layers are described by the two-dimensional (2-D) elasticity theory. The viscoelastic property of the interlayer is simulated by the standard linear solid model, and its constitutive relation is expressed in the convolution form which considers the strain memory effect. The general solutions of FG layers involving undetermined coefficients are obtained by virtue of the Fourier series expansion. By the use of the Laplace transform method, the solutions of stresses and deformations are determined analytically. The present solutions including Fourier series possess good convergence property. The comparison studies indicate that the finite element (FE) solutions approach the present ones when each FG layer is divided into many isotropic sub-layers in FE model and the gradient factor is taken as small value. The relative error of the one-dimensional (1-D) Euler-Bernoulli solutions is slight for slender beam with small gradient factor, but it significantly increases as the beam thickness or the gradient factor grows. Finally, the influences of the material constants on the time-dependent behavior in the beam are investigated in detail.
机译：这项工作提出了简单地支持的多层功能梯度（FG）光束的精确解决方案，其具有粘弹性层间以预测其时间依赖的机械行为。通过二维（2-D）弹性理论描述FG层的应力和变形。中间层的粘弹性由标准的线性固体模型模拟，其本构体关系是以卷积形式表示的，其考虑应变记忆效应。涉及未确定系数的FG层的一般溶液通过傅立叶级展开而获得。通过使用拉普拉斯变换方法，分析确定应力和变形的溶液。目前的解决方案包括傅里叶系列具有良好的收敛性。比较研究表明，当将每个FG层分成许多Fe模型中的各向同性子层时，有限元（Fe）溶液接近本发明的溶液，并且梯度因子被视为小值。一维（1-D）Euler-Bernouli溶液的相对误差对于具有小梯度因子的细长梁轻微，但随着光束厚度或梯度因子的增长，它显着增加。最后，详细研究了材料常数对光束中的时间依赖性行为的影响。

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