Computational Continuum Mechanics

Computational Continuum Mechanics

Author: Ahmed A. Shabana

Publisher: Cambridge University Press

Published: 2011-12-12

Total Pages: 341

ISBN-13: 1139505424

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This second edition presents the theory of continuum mechanics using computational methods. The text covers a broad range of topics including general problems of large rotation and large deformations and the development and limitations of finite element formulations in solving such problems. Dr Shabana introduces theories on motion kinematics, strain, forces and stresses and goes on to discuss linear and nonlinear constitutive equations, including viscoelastic and plastic constitutive models. General nonlinear continuum mechanics theory is used to develop small and large finite element formulations which correctly describe rigid body motion for use in engineering applications. This second edition features a new chapter that focuses on computational geometry and finite element analysis. This book is ideal for graduate and undergraduate students, professionals and researchers who are interested in continuum mechanics.


Large Strain Finite Element Method

Large Strain Finite Element Method

Author: Antonio Munjiza

Publisher: John Wiley & Sons

Published: 2014-11-19

Total Pages: 486

ISBN-13: 1118535804

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An introductory approach to the subject of large strains and large displacements in finite elements. Large Strain Finite Element Method: A Practical Course, takes an introductory approach to the subject of large strains and large displacements in finite elements and starts from the basic concepts of finite strain deformability, including finite rotations and finite displacements. The necessary elements of vector analysis and tensorial calculus on the lines of modern understanding of the concept of tensor will also be introduced. This book explains how tensors and vectors can be described using matrices and also introduces different stress and strain tensors. Building on these, step by step finite element techniques for both hyper and hypo-elastic approach will be considered. Material models including isotropic, unisotropic, plastic and viscoplastic materials will be independently discussed to facilitate clarity and ease of learning. Elements of transient dynamics will also be covered and key explicit and iterative solvers including the direct numerical integration, relaxation techniques and conjugate gradient method will also be explored. This book contains a large number of easy to follow illustrations, examples and source code details that facilitate both reading and understanding. Takes an introductory approach to the subject of large strains and large displacements in finite elements. No prior knowledge of the subject is required. Discusses computational methods and algorithms to tackle large strains and teaches the basic knowledge required to be able to critically gauge the results of computational models. Contains a large number of easy to follow illustrations, examples and source code details. Accompanied by a website hosting code examples.


Integration of Large Deformation Finite Element Formulations in Flexible Multibody System Algorithms

Integration of Large Deformation Finite Element Formulations in Flexible Multibody System Algorithms

Author:

Publisher:

Published: 2010

Total Pages: 11

ISBN-13:

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This project deals with the new and challenging problem of implementing large deformation finite element (FE) formulations in flexible multibody system (MBS) algorithms. Successful integration of large deformation FE and MBS algorithms will lead to a new generation of simulation codes that can be used in the analysis, design and performance evaluation of mechanical and aerospace systems. Specifically, the objectives of this project are (1) Different formulations used in the dynamic modeling of flexible MBS will be reviewed and evaluated in order to identify the advantages and drawbacks of each method; (2) The constrained nonlinear equations of motion expressed in terms of different sets of coordinates that can be efficiently used to describe the dynamics of rigid, flexible, and very flexible bodies will be developed; (3) Large deformation Cholesky coordinates will be used to develop a new form of the MBS dynamic equations with optimum sparse matrix structure; (4) Quantitative and qualitative evaluation of the effect of the nonlinear dynamic coupling between the reference motion and the large deformation modes will be performed; (5) The use of the computational methodology developed in this research project in the analysis of mechanical systems will be demonstrated. This report summarizes the main accomplishments made in this research project.


Finite Element Analysis of Solids and Structures

Finite Element Analysis of Solids and Structures

Author: Sudip S. Bhattacharjee

Publisher: CRC Press

Published: 2021-07-18

Total Pages: 341

ISBN-13: 100041230X

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Finite Element Analysis of Solids and Structures combines the theory of elasticity (advanced analytical treatment of stress analysis problems) and finite element methods (numerical details of finite element formulations) into one academic course derived from the author’s teaching, research, and applied work in automotive product development as well as in civil structural analysis. Features Gives equal weight to the theoretical details and FEA software use for problem solution by using finite element software packages Emphasizes understanding the deformation behavior of finite elements that directly affect the quality of actual analysis results Reduces the focus on hand calculation of property matrices, thus freeing up time to do more software experimentation with different FEA formulations Includes chapters dedicated to showing the use of FEA models in engineering assessment for strength, fatigue, and structural vibration properties Features an easy to follow format for guided learning and practice problems to be solved by using FEA software package, and with hand calculations for model validation This textbook contains 12 discrete chapters that can be covered in a single semester university graduate course on finite element analysis methods. It also serves as a reference for practicing engineers working on design assessment and analysis of solids and structures. Teaching ancillaries include a solutions manual (with data files) and lecture slides for adopting professors.