AI 中文总结
该研究提出综合高阶VEM框架，整合先进稳定策略与VC-VEM方法，将其应用于三类结构分析并通过验证，为先进结构设计提供灵活易实现的工具。
AI 中文摘要
本文提出了一种用于创新型变刚度板结构分析的综合高阶（p版本）虚拟单元法（Virtual Element Method, VEM）框架。VEM因能处理包含曲边的任意多边形网格，特别适合复杂构型，但它的数学公式可能阻碍其在工程界的推广。本研究展示了一种采用熟知的有限元法（FEM）符号、便于实现的公式，同时整合了一系列新的先进功能，具体采用了标准稳定化策略和先进自稳定化策略。为进一步提高VEM在变系数存在时的鲁棒性，采用了考虑系数的多项式投影，该方法被称为变系数VEM方法（Variable Coefficients-VEM approach, VC-VEM）。此统一框架应用于线性静力学、自由振动和屈曲分析，并通过解析解和数值基准进行验证，特别研究了带开孔的板和具有高梯度解的问题，证明所提出的综合方法为先进结构设计提供了一种灵活且易于实现的工具。
英文摘要
This paper presents a comprehensive, high-order (p-version) Virtual Element Method (VEM) framework for the structural analysis of innovative variable stiffness plates. VEM is particularly suited for complex configurations due to its ability to handle arbitrary polygonal meshes, including curved edges. However, its mathematical formulation may hinder its spread in the engineering community. This work illustrates a formulation with an accessible implementation using well-known FEM notation and integrating at the same time a set of new advanced capabilities. Specifically, both standard stabilized and advanced self-stabilized strategies are adopted. To further improve the robustness of VEM in the presence of variable coefficients, polynomial projections taking into account the coefficients are employed. This approach is referred to as Variable Coefficients-VEM approach (VC-VEM). This unified framework is applied to linear static, free-vibration, and buckling analyses, and validated against analytical solutions and numerical benchmarks. In particular, plates with cutouts and problems featuring high-gradient solutions are investigated, demonstrating that the proposed comprehensive approach provides a flexible and ready-to-implement tool for advanced structural design.
Comments55 pages, 24 figures, 6 tables
