报告主题：A Short Course on CUF and Related Applications Including FEM.2.0
报告人：Erasmo Carrera教授（意大利都灵理工大学）
报告地点：明故宫校区18-529报告厅
主办单位：航空学院、航空航天结构力学及控制全国重点实验室、国际合作处
报告内容简介：
It is a well know fact that assumptions of classical beam, plate and shell theories often lead to solutions that could deviate significantly from the exact ones. In the recent years, the author and co-workers have successfully introduced and extended the Carrera Unified Formulation, CUF, which is a hierarchical framework to develop any theory of structures for beams, plates and shells including laminated structures and multifield loadings. Equivalent Single Layers, Layer-Wise, Component-Wise, Node-Dependent Kinematics approaches have been successfully applied via CUF to composite structures. Many articles have been extended to various mechanical, thermal and electromechanical problems with excellent and unique accuracy. FEs applications have been developed extensively to both linear and nonlinear problems. The lecture describes the X-DOF method to develop structural theories which can exhibit di ‘any’ X-assumptions for each displacement components (Degree Of Freedom DOF). Applications are given to beams, plates and shells made by metallic and laminated composites. It is concluded that X-DOF combined with NDK provide the most natural way to describe the deformation which is herein denoted as FEM 2.0, that is the next generation Finite Element Method: that is in each point/direction of the structures the FEM 2.o has the most appropriate structural models in the nodes by leading to the most successful and effective method to build the ‘best’ computational model of a given problem related to any structural analysis.
报告时间：2026年9月9日（周三）下午16:00-18：00
报告1：Origin of CUF vs Laminate Theories
This lecture will discuss the origins of the CUF in the analysis of theories of laminates made of unidirectional composite layers. Multilayer plates and shells will be considered. The topics of shear deformability, interlaminar continuity, and the zigzag effect will be examined in detail. Some classical theories will be discussed up to the introduction of higher-order theories and layer-wise and/or equivalent single-layer models. The governing equations will be obtained in terms of the fundamental kernels ‘nuclei’ of the Carrera Unified Formulation. These ‘nuclei’ will allow the definition of any structural theory with just a few instructions, based on nine formulas. This is a unique result never before achieved in structural theory. Finally, the Reissner Mixed Principle will be introduced as a natural extension of the Principle of Virtual Work to laminate structures.
报告2：CUF as a Tool for Multifield Structural Problems
This lecture will discuss the fundamental elements that make the CUF approach absolutely essential in multifield problems, where mechanical charges are replaced or combined with field loads. This is the case in thermodynamic analysis, structures with layers and piezoelectric and/or piezomagnetic materials.
报告时间：2026年9月11日（周五）上午9:00-11：00
报告3: FEM 2.0 Concept and Applications
The applications of CUF to finite elements are extremely significant and allow the formulation of elements capable of solving problems that cannot be solved with commercial codes. We abandon the scheme derived from rigid body mechanics with 6 degrees of freedom (6-DOF) per node and move on to the revolutionary concept of X-DOF, where the number of degrees of freedom of the node is a free parameter of the problem.
报告4: Selected applications and two CUF available Software
This lesson focuses on the use of some simple software, available online, that demonstrates some of the basic capabilities of CUF. A closed-form analytical case and a FEM code for isotropic beams will be discussed first as an example.
报告人简介：
Erasmo Carrera is Professor of Aerospace Structures and Aeroleasticity at Politecnico di Torino, Italy. He graduated in Aeronautics in 1986 and Space Engineering in 1988 at the Politecnico di Torino. He obtained a Ph.D. in Aerospace Engineering in 1991. Carrera has introduced the Reissner Mixed Variational Theorem, RMVT, as a natural extension of the Principle of Virtual Displacement to layered structure analysis. He introduced the Unified Formulation, or CUF (Carrera Unified Formulation), as a tool to establish a new framework in which to develop linear and nonlinear theories of beams, plates and shells for metallic and composite multilayered structures loaded by mechanical, thermal electrical and magnetic loadings. Carrera has been author and coauthor of about 800 papers on the above topics, most of which have been published in first rate international journals, including a few recent books. Professor Carrera is founder and leader of the MUL2 group at the Politecnico di Torino. The MUL2 group has acquired a significant international reputation in the field of multilayered structures subjected to multifield loadings, see also www.mul2.com.
Professor Carrera has been recognized as Highly Cited Researchers (Top 100 Scientist) by Thompson Reuters in the two Sections: Engineering and Materials (2013) and Engineering (2015).
He is Editor-in-Chief of Mechanics of Advanced Materials and Structures.
He is founder and Editor-in-Chief of Advanced in Aircraft and Spacecraft Sciences.
Member of Accademia delle Scienze di Torino, International Academy of Astronautics e Academie de l’Air et l’Espace.
He currently acts as President of A.I.D.A.A. (Associazione Italiana di Aeronautica ed Astronautica). He has been Local Chair of IAC Milano 2024, ICAS Florence 2024, AIAA-CEAS Aeroacoustic Rome, 2024. He is currently General Chair of ASME-SDDM, Long Beach, CA, 2026 and Local Chair of CEAS-AIDAA Conference, Torino 2025 and AIAA-AIDAA 2026 Hypersonic Conference in Naples.
