Finite Element Computations in Mechanics with R : a Problem-Centered Programming Approach / Khameel Bayo Mustapha.
"Finite Element Computations in Mechanics with R: A Problem-Centred Programming Approach provides introductory coverage of the finite element method (FEM) with the R programming language, emphasizing links between theory and implementation of FEM for problems in engineering mechanics. Useful fo...
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Full Text (via Taylor & Francis) |
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
2018.
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| Edition: | First edition. |
| Subjects: |
Table of Contents:
- Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; Author; 1: Overview of the R Programming Environment, Installations, and Basic Syntax; 1.1 Introduction; 1.2 Downloading and Installing R; 1.3 Downloading and Installing RStudio; 1.4 Getting Started with R and RStudio; 1.4.1 Basic Interaction with RStudio; 1.4.2 Getting Help in R; 1.4.3 In-Built Examples and Demos; 1.4.4 Packages and Modularity in R; References; 2: Vectors and Matrices; 2.1 Introduction; 2.2 Creating Vectors; 2.2.1 The Sequence Operator; 2.2.2 The Colon Operator.
- 2.2.3 The Combine Function2.2.4 Other Sequence Functions; 2.2.5 The Repeat Function; 2.2.6 The Vector Function; 2.3 Operations on Vectors; 2.3.1 Assessing the Element of a Vector; 2.3.2 Length of a Vector; 2.3.3 Creating Row and Column Vectors; 2.3.4 Transpose of Vectors; 2.3.5 Assigning and Modifying the Elements of Vectors; 2.3.6 Adding of Vectors; 2.3.7 Multiplication of Vectors; 2.3.8 Reversing and Ordering a Vector; 2.3.9 Recycling; 2.4 Vectorized Functions of R; 2.5 Creating Matrices; 2.5.1 The Matrix Function; 2.5.2 The Diagonal Function; 2.5.3 The Vector-Binding Functions.
- 2.5.4 Building a Matrix by Repeating a Vector2.6 Operations on Matrices; 2.6.1 Indexing; 2.6.2 Diagonal, Trace, and Dimension; 2.6.3 Determinant, Inverse, and Transpose; 2.6.4 Eigenvalues and Eigenvectors; 2.6.5 Arithmetic Operations on Matrices; 2.6.6 Matrix Multiplication; References; 3: Linear Spring Elements; 3.1 Introduction; 3.2 The Spring Element; 3.2.1 Element Matrix Equation Using the Direct Method of Formulation; 3.2.2 Element Matrix from the Principle of Minimum Potential Energy; 3.3 Computer Implementation.
- 3.3.1 Systematic Procedure for Solving Static Problems of Connected Linear Springs3.3.1.1 Precomputation Phase; 3.3.1.2 Computation Phase; 3.3.2 Implemented R Subroutines for Linear Spring Elements; 3.4 Examples; 3.4.1 Example 3.1; 3.4.1.1 Solution; 3.4.2 Example 3.2; 3.4.2.1 Solution; 3.5 Exercises; References; 4: Linear and Quadratic Bar Elements; 4.1 Introduction; 4.2 Finite Element Equations for Bar Elements; 4.2.1 The Two-Node Linear Bar Element; 4.2.2 The Three-Node Quadratic Bar Element; 4.3 Computer Implementation.
- 4.3.1 Systematic Procedure for Solving Static Problems of Longitudinally Connected Elastic Bars4.3.1.1 Precomputation Phase; 4.3.1.2 Computation Phase; 4.3.2 Implemented R Functions for the Linear Bar Element; 4.3.3 Implemented R Functions for the Quadratic Bar Element; 4.4 Examples; 4.4.1 Example 4.1; 4.4.1.1 Solution; 4.4.2 Example 4.2; 4.4.2.1 Solution; 4.4.3 Example 4.3; 4.4.3.1 Solution; 4.5 Exercises; References; 5: Plane and Space Truss Elements; 5.1 Introduction; 5.2 Finite Element Equations for the Plane Truss Element; 5.2.1 Displacement Function.