意大利都靈理工大學(xué)（Politecnico di Torino）Erasmo Carrera 教授（都靈科學(xué)院院士、意大利航空航天學(xué)會(huì)主席）、Enrico Zappino副教授和Matteo Filippi助理教授一行，應(yīng)浙江大學(xué)應(yīng)用力學(xué)研究所邀請(qǐng)，于2025年5月14日和17日分別訪問浙江大學(xué)，并與浙江大學(xué)航空航天學(xué)院、建筑工程學(xué)院，以及來自香港城市大學(xué)、浙江農(nóng)林大學(xué)、沈陽大學(xué)的師生，以及來自校外研究機(jī)構(gòu)和企業(yè)的工程師、技術(shù)負(fù)責(zé)人進(jìn)行了廣泛的學(xué)術(shù)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(xué)術(shù)報(bào)告。他指出，眾所周知，經(jīng)典的梁、板和殼理論由于基本假設(shè)的限制，往往導(dǎo)致其所得解與精確解之間存在較大偏差。另一方面，當(dāng)結(jié)構(gòu)的變形程度顯著偏離初始未變形狀態(tài)時(shí)，若仍采用簡(jiǎn)化的幾何非線性關(guān)系（如von Kármán近似），則可能引入顯著誤差，難以準(zhǔn)確捕捉結(jié)構(gòu)的真實(shí)平衡路徑。從計(jì)算實(shí)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(gè)節(jié)點(diǎn)上僅設(shè)置固定且有限的自由度：結(jié)構(gòu)單元一般為6個(gè)自由度，三維實(shí)體單元?jiǎng)t為3個(gè)自由度。這種自由度設(shè)定在處理局部化應(yīng)力/場(chǎng)分布、層合復(fù)合材料或金屬結(jié)構(gòu)、力-電耦合問題，以及多物理場(chǎng)載荷作用下的結(jié)構(gòu)響應(yīng)時(shí)，常常帶來較大局限。

報(bào)告中，Carrera教授詳細(xì)介紹了他與合作團(tuán)隊(duì)成功提出并發(fā)展的一種統(tǒng)一結(jié)構(gòu)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(gòu)建任意階數(shù)的梁、板和殼結(jié)構(gòu)理論，適用于層合結(jié)構(gòu)以及多場(chǎng)耦合問題，并已被推廣應(yīng)用于多類線性與非線性問題，展現(xiàn)出優(yōu)異而獨(dú)特的計(jì)算精度。基于CUF的有限元應(yīng)用已被廣泛開展，Carrera教授介紹了CUF方法在若干關(guān)鍵問題中的應(yīng)用與成果，包括層合梁、板和殼結(jié)構(gòu)中的高精度應(yīng)力與振動(dòng)響應(yīng)分析，薄壁結(jié)構(gòu)的屈曲與后屈曲行為，以及復(fù)合材料的塑性響應(yīng)、漸進(jìn)破壞過程和低速?zèng)_擊響應(yīng)等。

報(bào)告進(jìn)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(shí)體有限元方法，才能達(dá)到CUF所實(shí)現(xiàn)的分析精度，但其計(jì)算代價(jià)往往極其高昂，難以滿足實(shí)際工程對(duì)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(bào)告結(jié)束后，現(xiàn)場(chǎng)師生與Carrera教授展開了熱烈交流，圍繞報(bào)告內(nèi)容探討了相關(guān)科學(xué)問題，并就CUF有限元的模擬能力與實(shí)際應(yīng)用、面臨的挑戰(zhàn)與機(jī)遇、未來的發(fā)展趨勢(shì)與合作方向等話題進(jìn)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(xué)術(shù)報(bào)告中指出，精確預(yù)測(cè)與控制復(fù)合材料中的工藝誘導(dǎo)變形（PIDs）是航空航天制造領(lǐng)域的關(guān)鍵挑戰(zhàn)。報(bào)告介紹了一種基于CUF的建模框架，該框架通過精細(xì)化分層有限元模擬，能夠解析厚度方向的復(fù)雜應(yīng)力場(chǎng)。結(jié)合CHILE本構(gòu)模型，可準(zhǔn)確模擬碳纖維增強(qiáng)聚合物（CFRP）層壓板在固化過程中的熱化學(xué)演化過程，包括殘余應(yīng)力、回彈變形和翹曲現(xiàn)象。

為解決不確定性條件下的設(shè)計(jì)優(yōu)化問題并降低實(shí)驗(yàn)成本，研究引入了代理建模技術(shù)，尤其是高斯過程回歸（GPR）及其空間加權(quán)變體（SWGPR）。這些基于概率的機(jī)器學(xué)習(xí)工具結(jié)合多保真度仿真數(shù)據(jù)和實(shí)驗(yàn)驗(yàn)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(jìn)一步擴(kuò)展至嵌入壓電傳感器的先進(jìn)復(fù)合材料結(jié)構(gòu)，通過多物理場(chǎng)分層模型，分析結(jié)構(gòu)局部的力學(xué)和電學(xué)行為，以評(píng)估傳感器集成效果并實(shí)現(xiàn)固化過程的實(shí)時(shí)監(jiān)測(cè)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(xué)術(shù)報(bào)告。他指出，波動(dòng)傳播問題在多個(gè)工程領(lǐng)域具有關(guān)鍵研究?jī)r(jià)值——通過揭示結(jié)構(gòu)部件中的能量傳遞機(jī)制，可以預(yù)測(cè)聲發(fā)射水平和振動(dòng)強(qiáng)度，并據(jù)此設(shè)計(jì)有效的減振策略。他提出了一種基于先進(jìn)運(yùn)動(dòng)學(xué)的梁和殼模型，用于計(jì)算一維和二維波導(dǎo)的頻散特性，具體方法是在波導(dǎo)的橫截面和厚度方向上采用高階函數(shù)對(duì)主變量進(jìn)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(shí)利用拉格朗日型函數(shù)在傳播方向上近似位移場(chǎng)。

基于波有限元法，對(duì)不同結(jié)構(gòu)理論下構(gòu)建的剛度矩陣和質(zhì)量矩陣進(jìn)行后處理，從而構(gòu)建代表性結(jié)構(gòu)單元的傳遞矩陣，其中矩陣的計(jì)算基于CUF理論完成。該方法已成功應(yīng)用于周期性結(jié)構(gòu)和復(fù)合超材料的動(dòng)態(tài)特性分析。報(bào)告還概述了基于CUF的梁?jiǎn)卧谄渌I(lǐng)域的應(yīng)用，特別是在轉(zhuǎn)子動(dòng)力學(xué)、熱彈性問題和幾何非線性動(dòng)力學(xué)分析等方面的拓展。

報(bào)告結(jié)束后，與會(huì)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(shí)際工程應(yīng)用中的潛力及面臨的關(guān)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(xué)學(xué)科創(chuàng)新引智基地的部分資助。

Erasmo Carrera教授個(gè)人簡(jiǎn)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(gè)人簡(jiǎn)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(gè)人簡(jiǎn)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.