意大利都灵理工大学（Politecnico di Torino）Erasmo Carrera 教授（都灵科学院院士、意大利航空航天学会主席）、Enrico Zappino副教授和Matteo Filippi助理教授一行，应浙江大学应用力学研究所邀请，于2025年5月14日和17日分别访问浙江大学，并与浙江大学航空航天学院、建筑工程学院，以及来自香港城市大学、浙江农林大学、沈阳大学的师生，以及来自校外研究机构和企业的工程师、技术负责人进行了广泛的学术交流与讨论。
5月17日下午，Carrera教授作了题为“A CUF-based Framework for Next Generation Theory of Structures and Finite Elements Applications”的学术报告。他指出，众所周知，经典的梁、板和壳理论由于基本假设的限制，往往导致其所得解与精确解之间存在较大偏差。另一方面，当结构的变形程度显著偏离初始未变形状态时，若仍采用简化的几何非线性关系（如von Kármán近似），则可能引入显著误差，难以准确捕捉结构的真实平衡路径。从计算实现的角度来看，现有的有限元方法（包括商业软件中广泛采用的方案）通常在每个节点上仅设置固定且有限的自由度：结构单元一般为6个自由度，三维实体单元则为3个自由度。这种自由度设定在处理局部化应力/场分布、层合复合材料或金属结构、力-电耦合问题，以及多物理场载荷作用下的结构响应时，常常带来较大局限。
报告中，Carrera教授详细介绍了他与合作团队成功提出并发展的一种统一结构理论建模框架——Carrera Unified Formulation（即CUF列式）。CUF方法基于分层建模思想，能够系统地构建任意阶数的梁、板和壳结构理论，适用于层合结构以及多场耦合问题，并已被推广应用于多类线性与非线性问题，展现出优异而独特的计算精度。基于CUF的有限元应用已被广泛开展，Carrera教授介绍了CUF方法在若干关键问题中的应用与成果，包括层合梁、板和壳结构中的高精度应力与振动响应分析，薄壁结构的屈曲与后屈曲行为，以及复合材料的塑性响应、渐进破坏过程和低速冲击响应等。
报告进一步指出，在采用传统商业软件的情况下，只有使用三维实体有限元方法，才能达到CUF所实现的分析精度，但其计算代价往往极其高昂，难以满足实际工程对效率的要求。CUF提供了一种兼顾精度与效率的优选方案。
报告结束后，现场师生与Carrera教授展开了热烈交流，围绕报告内容探讨了相关科学问题，并就CUF有限元的模拟能力与实际应用、面临的挑战与机遇、未来的发展趋势与合作方向等话题进行了深入讨论。
5月14日下午，Zappino副教授在题为“CUF Based Numerical Modeling and AI Integration for Predicting and Mitigating Process-Induced Deformations in Composite Aerospace Structures”的学术报告中指出，精确预测与控制复合材料中的工艺诱导变形（PIDs）是航空航天制造领域的关键挑战。报告介绍了一种基于CUF的建模框架，该框架通过精细化分层有限元模拟，能够解析厚度方向的复杂应力场。结合CHILE本构模型，可准确模拟碳纤维增强聚合物（CFRP）层压板在固化过程中的热化学演化过程，包括残余应力、回弹变形和翘曲现象。
为解决不确定性条件下的设计优化问题并降低实验成本，研究引入了代理建模技术，尤其是高斯过程回归（GPR）及其空间加权变体（SWGPR）。这些基于概率的机器学习工具结合多保真度仿真数据和实验验证，能够高效探索堆叠顺序与工艺参数的影响。此外，该方法进一步扩展至嵌入压电传感器的先进复合材料结构，通过多物理场分层模型，分析结构局部的力学和电学行为，以评估传感器集成效果并实现固化过程的实时监测策略。
紧接着，Filippi助理教授作了题为“High-order Finite Elements for Propagation Analyses of Arbitrary-Shaped Waveguides”的学术报告。他指出，波动传播问题在多个工程领域具有关键研究价值——通过揭示结构部件中的能量传递机制，可以预测声发射水平和振动强度，并据此设计有效的减振策略。他提出了一种基于先进运动学的梁和壳模型，用于计算一维和二维波导的频散特性，具体方法是在波导的横截面和厚度方向上采用高阶函数对主变量进行插值。该模型采用泰勒型和拉格朗日型展开描述截面变形，同时利用拉格朗日型函数在传播方向上近似位移场。
基于波有限元法，对不同结构理论下构建的刚度矩阵和质量矩阵进行后处理，从而构建代表性结构单元的传递矩阵，其中矩阵的计算基于CUF理论完成。该方法已成功应用于周期性结构和复合超材料的动态特性分析。报告还概述了基于CUF的梁单元在其他领域的应用，特别是在转子动力学、热弹性问题和几何非线性动力学分析等方面的拓展。
报告结束后，与会师生踊跃参与，与Zappino副教授和Filippi助理教授展开了深入的讨论与交流，共同探讨CUF有限元方法在实际工程应用中的潜力及面临的关键挑战。
此次受邀访问，Carrera教授一行还得到了软物质力学学科创新引智基地的部分资助。
Erasmo Carrera教授个人简介
Dr Erasmo Carrera is a Professor of Aeronautics and Astronautics at Politecnico di Torino. He acts as the President of the Italian Association of Aeronautics and Astronautics (A.I.D.A.A.), a member of the Accademia delle Scienze di Torino and of the Académie de l’Air et de l’Espace. He has been a Visiting Professor at the University of Stuttgart, Virginia Tech, Royal Melbourne Institute of Technology, Tambov University, Supméca and ENSAM, and PMU. Carrera has been responsible for various research contracts granted by public and private national and international institutions, including the European Community, European Space Agency, Thales Alenia Space, and Embraer. He is the founder and Editor-in-Chief of Advances in Aircraft and Spacecraft Science, Editor-in-Chief of Mechanics of Advanced Materials and Structures, and Section Editor of Journal of Sound and Vibration. He has introduced the Unified Formulation, or Carrera Unified Formulation (CUF), as a tool to establish a new framework to develop theories of beams, plates, and shells for metallic and composite multilayered structures. CUF has been applied to meshless and finite element methods, to classical and mixed variational frameworks, as well as to linear and nonlinear problems. In particular, CUF has originated the so-called NDK-FE, Node-Dependent Kinematics version of finite elements. He has been the author and co-author of about 800 papers on the above topics. Carrera has been the recipient of various ‘Best Paper Awards’ and of the ‘J.N. Reddy Medal’. He has been listed among the Highly Cited Researchers (Top 100 Scientists) by Thomson Reuters in two categories: Engineering and Materials. He was confirmed as a HiCI in 2015 in the Engineering category—the only aerospace engineer worldwide to receive this distinction. Due to his scientific achievements, Carrera has been awarded the title of ‘Honorary Commendator’ by the President of the Italian Republic. He has been appointed Local Chair of IAC 2024 (Milan), ICAS 2024 (Florence), and General Chair of SSDM, ASME 2025 (Long Beach, CA).
Enrico Zappino副教授个人简介
Enrico Zappino is an Associate Professor at Politecnico di Torino, where he specializes in structural analysis and advanced computational modeling. Since joining Professor Carrera’s research group in 2010, he has co-authored numerous publications in leading international journals. His research interests include multifield modeling, structural mechanics, manufacturing process simulations, and additive manufacturing of aerospace-grade materials. He holds a PhD in Aerospace Engineering, during which he developed innovative one-, two-, and three-dimensional models for the analysis of aerospace structures using the CUF. He has been involved in multiple collaborative research projects funded by the European Union and the European Space Agency, working closely with both academic and industrial partners. A member of the Italian Association of Aeronautics and Astronautics (AIDAA) for over a decade, he has been active in higher education since 2011. In 2024, he assumed the role of Executive Project Manager for the organization of the International Astronautical Congress (IAC).
Matteo Filippi助理教授个人简介
Matteo Filippi is an Assistant Professor in the Department of Mechanical and Aerospace Engineering at Politecnico di Torino, Turin, Italy. He received a Bachelor’s degree in Aerospace Engineering in 2009, followed by a Master’s degree in 2011. He subsequently obtained his Ph.D. from the same university in 2015. His research primarily focuses on the development of high-fidelity finite elements for stress and dynamic analyses of structures made of advanced materials, axial rotors, and rotary-wing configurations, as well as coupled thermoelastic formulations and geometric and dynamic stability analyses. Matteo has co-authored more than 100 scientific papers on these topics, which have been published in peer-reviewed international journals. He serves as an editorial board member of Mechanics of Advanced Materials and Structures and Shock and Vibration.
