摘要
针对多个弹性元件和黏性元件以任意连接方式组成的线性黏弹性模型,本文探究了其本构方程的通用矩阵形式表述。首先将研究问题扩展为由Maxwell基本单元构成的标准模型,然后转化为有向图,根据独立路径和闭包围的形式表征出基本应力方程和应变方程,进一步推导得到了任意线性黏弹性模型的微分型本构方程的一般矩阵形式。论文最后总结并建立了一套适合计算机编程的固定范式,利用Python编程实现了该算法、获得了一些数值计算结果。
This paper derived the general matrix form for the linear viscoelastic model for arbitrarily linked springs and dampers. Firstly, the underlying linear viscoelastic problem is modeled through the standard model composed of basic Maxwell units. Then the standard model is transformed into a directed graph, and the basic stress equation and strain equation are expressed in the form of independent path and closed enclosure. And then the general matrix form of a differential constitutive equation for an arbitrary viscoelastic model is derived.Finally, a universal paradigm suitable for computer programming is developed, and the relevant algorithm is realized with the Python language along with numerical results.
作者
彭培火
黄朝军
PENG Peihuo;HUANG Chaojunt(School of Science,Beijing University of Civil Engineering&Architecture,Beijing 102612,China;China Construction Second Engineering Bureau Co.,Ltd,Beijing 100160,China)
出处
《力学与实践》
北大核心
2022年第2期358-367,共10页
Mechanics in Engineering
基金
北京市属高校基本科研业务费专项资金项目(X20049)。
关键词
黏弹性
数学模型
微分形式
本构方程
矩阵形式
viscoelasticity
mathematical model
differential form
constitutive equation
matrix form
