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.

Implementation of Beam-Type Finite Elements Based on Carrera Unified Formulation

教材
发表日期：

2026年

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Erasmo Carrera,
Gerlando Augello,
Riccardo Augello

摘要

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.