意大利都靈理工大學（Politecnico di Torino）Erasmo Carrera 教授（都靈科學院院士、意大利航空航天學會主席）、Enrico Zappino副教授和Matteo Filippi助理教授一行，應浙江大學應用力學研究所邀請，于2025年5月14日和17日分別訪問浙江大學，并與浙江大學航空航天學院、建筑工程學院，以及來自香港城市大學、浙江農(nóng)林大學、沈陽大學的師生，以及來自校外研究機構和企業(yè)的工程師、技術負責人進行了廣泛的學術交流與討論。
5月17日下午，Carrera教授作了題為“A CUF-based Framework for Next Generation Theory of Structures and Finite Elements Applications”的學術報告。他指出，眾所周知，經(jīng)典的梁、板和殼理論由于基本假設的限制，往往導致其所得解與精確解之間存在較大偏差。另一方面，當結構的變形程度顯著偏離初始未變形狀態(tài)時，若仍采用簡化的幾何非線性關系（如von Kármán近似），則可能引入顯著誤差，難以準確捕捉結構的真實平衡路徑。從計算實現(xiàn)的角度來看，現(xiàn)有的有限元方法（包括商業(yè)軟件中廣泛采用的方案）通常在每個節(jié)點上僅設置固定且有限的自由度：結構單元一般為6個自由度，三維實體單元則為3個自由度。這種自由度設定在處理局部化應力/場分布、層合復合材料或金屬結構、力-電耦合問題，以及多物理場載荷作用下的結構響應時，常常帶來較大局限。
報告中，Carrera教授詳細介紹了他與合作團隊成功提出并發(fā)展的一種統(tǒng)一結構理論建模框架——Carrera Unified Formulation（即CUF列式）。CUF方法基于分層建模思想，能夠系統(tǒng)地構建任意階數(shù)的梁、板和殼結構理論，適用于層合結構以及多場耦合問題，并已被推廣應用于多類線性與非線性問題，展現(xiàn)出優(yōu)異而獨特的計算精度。基于CUF的有限元應用已被廣泛開展，Carrera教授介紹了CUF方法在若干關鍵問題中的應用與成果，包括層合梁、板和殼結構中的高精度應力與振動響應分析，薄壁結構的屈曲與后屈曲行為，以及復合材料的塑性響應、漸進破壞過程和低速沖擊響應等。
報告進一步指出，在采用傳統(tǒng)商業(yè)軟件的情況下，只有使用三維實體有限元方法，才能達到CUF所實現(xiàn)的分析精度，但其計算代價往往極其高昂，難以滿足實際工程對效率的要求。CUF提供了一種兼顧精度與效率的優(yōu)選方案。
報告結束后，現(xiàn)場師生與Carrera教授展開了熱烈交流，圍繞報告內(nèi)容探討了相關科學問題，并就CUF有限元的模擬能力與實際應用、面臨的挑戰(zhàn)與機遇、未來的發(fā)展趨勢與合作方向等話題進行了深入討論。
5月14日下午，Zappino副教授在題為“CUF Based Numerical Modeling and AI Integration for Predicting and Mitigating Process-Induced Deformations in Composite Aerospace Structures”的學術報告中指出，精確預測與控制復合材料中的工藝誘導變形（PIDs）是航空航天制造領域的關鍵挑戰(zhàn)。報告介紹了一種基于CUF的建模框架，該框架通過精細化分層有限元模擬，能夠解析厚度方向的復雜應力場。結合CHILE本構模型，可準確模擬碳纖維增強聚合物（CFRP）層壓板在固化過程中的熱化學演化過程，包括殘余應力、回彈變形和翹曲現(xiàn)象。
為解決不確定性條件下的設計優(yōu)化問題并降低實驗成本，研究引入了代理建模技術，尤其是高斯過程回歸（GPR）及其空間加權變體（SWGPR）。這些基于概率的機器學習工具結合多保真度仿真數(shù)據(jù)和實驗驗證，能夠高效探索堆疊順序與工藝參數(shù)的影響。此外，該方法進一步擴展至嵌入壓電傳感器的先進復合材料結構，通過多物理場分層模型，分析結構局部的力學和電學行為，以評估傳感器集成效果并實現(xiàn)固化過程的實時監(jiān)測策略。
緊接著，Filippi助理教授作了題為“High-order Finite Elements for Propagation Analyses of Arbitrary-Shaped Waveguides”的學術報告。他指出，波動傳播問題在多個工程領域具有關鍵研究價值——通過揭示結構部件中的能量傳遞機制，可以預測聲發(fā)射水平和振動強度，并據(jù)此設計有效的減振策略。他提出了一種基于先進運動學的梁和殼模型，用于計算一維和二維波導的頻散特性，具體方法是在波導的橫截面和厚度方向上采用高階函數(shù)對主變量進行插值。該模型采用泰勒型和拉格朗日型展開描述截面變形，同時利用拉格朗日型函數(shù)在傳播方向上近似位移場。
基于波有限元法，對不同結構理論下構建的剛度矩陣和質(zhì)量矩陣進行后處理，從而構建代表性結構單元的傳遞矩陣，其中矩陣的計算基于CUF理論完成。該方法已成功應用于周期性結構和復合超材料的動態(tài)特性分析。報告還概述了基于CUF的梁單元在其他領域的應用，特別是在轉(zhuǎn)子動力學、熱彈性問題和幾何非線性動力學分析等方面的拓展。
報告結束后，與會師生踴躍參與，與Zappino副教授和Filippi助理教授展開了深入的討論與交流，共同探討CUF有限元方法在實際工程應用中的潛力及面臨的關鍵挑戰(zhàn)。
此次受邀訪問，Carrera教授一行還得到了軟物質(zhì)力學學科創(chuàng)新引智基地的部分資助。
Erasmo Carrera教授個人簡介
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副教授個人簡介
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助理教授個人簡介
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.
