Implementation of Beam-Type Finite Elements Based on Carrera Unified Formulation
Description
This book offers a comprehensive exploration of advanced finite element methods for modeling and analyzing beam-like structures. Moving beyond traditional 1D finite elements, it introduces the Carrera Unified Formulation (CUF), a versatile framework that unifies various structural behaviors under a single mathematical approach.
The work addresses key challenges in finite element modeling, particularly shear locking, and provides practical solutions through techniques such as reduced and selectively reduced integration and mixed formulations. It also introduces Node-Dependent Kinematics (NDK), enabling localized refinement for high-accuracy results without excessive computational costs.
Designed for students, researchers, and professionals, the book includes MATLAB scripts to aid in deriving stiffness matrices for beam structures, bridging the gap between theoretical foundations and practical application. Clear, step-by-step instructions make complex concepts accessible, fostering both analytical understanding and hands-on skills.
Whether you are an engineering student, a researcher in structural mechanics, or a practicing engineer, this book serves as an invaluable resource for mastering finite element techniques and applying CUF in real-world scenarios.
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Persons
Erasmo Carrera is a Professor of Aerospace Engineering at Politecnico di Torino, holding degrees in Aeronautics and Aerospace Engineering , as well as a PhD in Aerospace Engineering. He has held research and visiting positions at institutions including the University of Stuttgart and Virginia Tech, focusing on advanced theories for composites, finite elements, and aeroelasticity. Carrera has authored over 700 articles and serves as a reviewer and editor for leading journals in his field.
Gerlando Augello is an Italian engineer with over 30 years of experience in mechanical and structural analysis, primarily in aerospace. He holds a Master's Degree in Mechanical Engineering and has led Mechanical Computer Aided Engineering teams at Thales Alenia Space, contributing to major space projects such as EXOMARS, Space Rider, and EUCLID. Recognized as a "Maestro del Lavoro" in 2014, he continues to develop advanced methods in structural analysis and design.
Riccardo Augello is a Marie Sklodowska-Curie Postdoctoral Fellow who earned his Ph.D. in Mechanical Engineering from Politecnico di Torino in 2021. Specializing in nonlocal mechanics and nonlinear analysis of composite structures, he has collaborated with the City University of Hong Kong and joined Caltech to advance modeling for ultra-thin, deployable space systems.
Content
Introduction.- Stiffness matrix of a bar element.- Stiffness matrix of a beam bending around z axis.- Numerical remedies against shear locking.- Stiffness matrix of a beam bending around x axis.- Stiffness matrix of a beam subjected by a torsion.- Stiffness matrix of a beam under combined load.- Fundamental Nucleus using Unified Formulation.- Stiffness Matrix with Node-Dependent Kinematic.- Application to the analysis of real structures.
