黏弹性边界理论演进与自动化实现

Evolution and Automation of Viscoelastic Boundary Theory

摘要:

系统回顾了黏弹性边界理论的发展，并阐述了在不同维度模型中边界应力平衡方程的建立。采用先进的数值模拟软件ABAQUS，对一维、二维及三维条件下黏弹性理论的适用性进行了验证。研究发现：在一维模型中，简单的黏性边界条件即可满足所需的吸收精度；在二维剪切柱面波模型中，则需要引入黏弹性边界条件来达到同样的精度要求；对于二维垂直入射模型，其特性在于输入与吸收边界的统一，采用等效节点力的方法施加可以确保入射波不被黏弹性边界所影响，并且在反射时仍能保持良好的吸收效果。在三维条件下，从斜入射波场分解理论引入到角点入射，并详述了利用Python编程实现黏弹性边界条件自动化的施加过程。所得研究成果为桥梁和路基等工程结构在地震作用下的动力响应分析提供了有效的技术手段。

Abstract:

The development of viscoelastic boundary theory is systematically reviewed and the establishment of boundary stress equilibrium equations in different dimensional models is expounded. The applicability of viscoelastic theory under one-dimensional, two-dimensional and three-dimensional conditions is verified by using the advanced numerical simulation software ABAQUS. It is found that in the one-dimensional model， the simple viscous boundary condition can meet the required absorption accuracy. In the two-dimensional shear cylindrical wave model, the viscoelastic boundary conditions need to be introduced to achieve the same accuracy requirements. For the two-dimensional vertical incidence model, its characteristic is the unity of the input and absorption boundary. The equivalent nodal force method can be used to ensure that the incident wave is not affected by the viscoelastic boundary, and can still maintain a good absorption effect during reflection. Under three-dimensional condition, the theory of oblique incident wave field decomposition is introduced to angular incident, and the process of automatic application of viscoelastic boundary conditions using Python programming is described in detail. The studied results provide an effective technical means for the dynamic response analysis of engineering structures such as bridges and roadbeds under earthquake.