The mechanical responses of viscoelastic structures are evaluated by using finite beam elements based on different kinematical assumptions. The governing equations related to the structural theories are obtained with the Carrera Unified Formulation. The viscoelastic constitutive law is expressed in an integral form, which relates the viscous moduli with the strain rate. The solution of the governing equations is obtained in the Laplace domain and then transformed in the time domain through a numerical inversion procedure. The numerical simulations are performed on slender, squat, isotropic, and orthotropic beams in order to examine the actual differences between the results obtained with low-order theories and the refined models. The current results are validated with classical and higher-order solutions available in the literature. Moreover, comparisons between the equivalent-single layer and the layer-wise approach are reported and discussed.

中文翻译：

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具有低阶和高阶一维有限元的粘弹性三维梁状结构的应力分析

通过使用基于不同运动学假设的有限梁单元来评估粘弹性结构的机械响应。与结构理论相关的控制方程是通过 Carrera 统一公式获得的。粘弹性本构定律以积分形式表示，它将粘性模量与应变率联系起来。在拉普拉斯域中获得控制方程的解，然后通过数值反演程序在时域中进行变换。数值模拟在细长梁、深蹲梁、各向同性梁和正交各向异性梁上进行，以检查低阶理论获得的结果与改进模型之间的实际差异。当前的结果已通过文献中可用的经典和高阶解决方案进行了验证。而且，