An Introduction to the Finite Element Method with the Variational Approach
Prakash Mahadeo Dixit · Sachin Singh Gautam
Oct 2025 · Elsevier
Ebook
850
Pages
family_home
Eligible
info
infoThis book will become available on October 1, 2025. You will not be charged until it is released.
About this ebook
An Introduction to the Finite Element Method with the Variational Approach offers a comprehensive solution to the gaps often found in introductory texts on the Finite Element Method (FEM). The book provides a thorough introduction to the fundamental principles of linear and time-independent FEM within the variational framework. It meticulously covers the derivation of 1-D FEM equations based on variational functionals, encompassing both linear and higher-order elements, and shape functions driven by convergence criteria. Furthermore, it explores 1-D numerical integration, outlines coding procedures, and provides insights into handling material nonlinearity and time-dependent scenarios.Expanding into 2-D problems, the book offers derivations of 2-D FEM equations tailored to diverse engineering disciplines, including Steady-State Heat Conduction, Solid Mechanics (covering torsion, plane strain/axisymmetric cases, and the bending, stability, and vibrations of thin plates), as well as Fluid Mechanics (addressing incompressible inviscid and viscous fluids). It includes detailed discussions on element continuity, numerical integration techniques, and even includes 2-D codes for selected problems. The book concludes by delving into recent advancements in FEM, with a specific focus on applications in machine learning and isogeometric analysis. - Explains the fundamentals of the Finite Element Method (FEM) with a focus on linear and time-independent aspects, employing a variational approach - Covers variational FEM formulations for 1-D and 2-D scenarios in solid mechanics, fluid mechanics, and heat conduction problems - Explores the application of 1-D Galerkin FEM to address challenges presented by material nonlinearity and time-dependent problems - Delves into the intricacies of FEM algorithms and provides a comprehensive overview of coding implementation - Offers insights into Machine Learning and includes a section on Isogeometric analysis
About the author
Prof. Prakash Mahadeo Dixit earned a BTech in Aeronautical Engineering from the Indian Institute of Technology Kharagpur in 1974 and a PhD in Mechanics from the University of Minnesota, USA, in 1979. His teaching journey began as a Lecturer in Aerospace Engineering at IIT Kharagpur in 1980 and ended as a Professor in Mechanical Engineering at IIT Kanpur in 2018. His research work is in the areas of metal forming processes, ductile fracture and damage mechanics, contact-impact problems and dynamic, large deformation, damage-coupled, thermo-elasto-plastic, contact finite element formulation.Dr. Sachin Singh Gautam is an Associate Professor in Mechanical Engineering at the Indian Institute of Technology Guwahati, specializing in computational mechanics. He completed his Ph.D. from IIT Kanpur in 2010 and worked as a post-doctoral fellow in AICES, RWTH Aachen University, Germany till 2013 before joining his current position. His research encompasses isogeometric analysis, contact-impact problems, GPU computing, and machine learning's application in finite elements.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
