论文标题
在带有ARX模型的台阶拉普拉斯变换方法中解决粘弹性问题：升级有限元或光谱代码的一种方法
Solving viscoelastic problems in a step-inverse Laplace transform approach supplanted with ARX models: a way to upgrade Finite Element or spectral codes
论文作者
论文摘要
用于求解与（时间依赖性）粘弹性介质相关的瞬态问题的机械平衡方程的有限元代码通常依赖于所选本构定律的时间消化版。最近对使用非全能微分方程来描述粘弹性或基于直接在频域中的动态机械分析（DMA）实验得出的行为定律（DMA）实验来描述粘弹性或有良好想法的关注点可以使Laplace域方法可能使Laplace域方法特别有吸引力，如果嵌入到时间否认的方案中。基于拉普拉斯变换的反转，本文表明，这种目标不仅可能是可能的，而且还会引起一种简单的算法，在计算时间和精度方面具有良好的性能。这种方法完全依赖于拉普拉斯定义的行为传递函数（LTBF），如果它使用ARX参数模型完全可以替换为真实的LTBF，则可以促进它。他们避免了迄今为止不得不将所有过去数据存储在计算机内存中的陷阱，同时保持相等的计算精度。
Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent concerns about the use of non-integer differential equations to describe viscoelasticity or well-founded ideas based upon the use of a behavior's law directly derived from Dynamic Mechanical Analysis (DMA) experiments in frequency domain, could make the Laplace domain approach particularly attractive if embedded in a time discretized scheme. Based upon the inversion of Laplace transforms, this paper shows that this aim is not only possible but also gives rise to a simple algorithm having good performances in terms of computation times and precision. Such an approach, which fully relies on the Laplace-defined Behavioral Transfer Function (LTBF) can be promoted if it uses ARX parametric models perfectly substitutable to the real LTBF. They avoid the hitherto prohibitive pitfall of having to store all past data in the computer's memory while maintaining an equal computation precision.
