| Description |
1 online resource (xi, 99 pages) |
| Series |
SpringerBriefs in applied sciences and technology, Computational mechanics, 2191-5342 |
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SpringerBriefs in applied sciences and technology. Computational mechanics.
|
| Contents |
Intro; Preface; Acknowledgements; Contents; About the Author; 1 A Brief Introduction to R, R Studio and MicrofiniteR; 1.1 The R Programming Language; 1.2 Tools for Getting Started; 1.2.1 R Installer; 1.2.2 RStudio; 1.3 Overview of Basic Operations; 1.3.1 Using RStudio Console as a Calculator; 1.3.2 Getting Help; 1.3.3 Using RStudio's Editor; 1.4 Packages in R; 1.5 Package-MicrofiniteR; 1.6 Summary; References; 2 Bending of Microstructure-Dependent MicroBeams and Finite Element Implementations with R; 2.1 Introduction; 2.2 Governing Differential Equations |
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2.2.1 Classical Versus Non-classical Strain Density Function2.2.2 Displacement-Strain Relations; 2.2.3 Stress-Strain Relations; 2.2.4 Timoshenko Beam Theory and Reduced Displacement Field; 2.3 Finite Element Formulations; 2.3.1 The 6 Degrees of Freedom Finite Element Model; 2.3.2 The 4 Degrees of Freedom Reduced-Order Model; 2.4 R Functions for Static Analysis; 2.5 Using the Implemented Functions for Static Problems; 2.6 Summary; References; 3 Vibration and Buckling of Microstructure-Dependent Timoshenko MicroBeams and Finite Element Implementations with R; 3.1 Introduction |
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3.2 Governing Differential Equations3.2.1 Displacement Field; 3.2.2 The Extended Hamilton's Principle; 3.3 Finite Element Formulations; 3.4 R Functions for Free Vibration and Buckling Analyses; 3.5 Free Vibration and Buckling Problems with the Implemented R Functions; 3.6 Summary; References; 4 Bending and Vibration of Microstructure-Dependent Kirchhoff Microplates and Finite Element Implementations with R; 4.1 Introduction; 4.2 Governing Differential Equations; 4.2.1 The Extended Hamilton's Principle; 4.3 Finite Element Formulations; 4.3.1 Stiffness Matrix; 4.3.2 Equivalent Load Vector |
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4.3.3 Mass Matrix4.4 R Functions for Static and Vibration Analyses; 4.5 Bending and Free Vibration Analyses with the Implemented R Functions; 4.6 Summary; References |
| Summary |
This book addresses the static and dynamic analysis of linear elastic size-dependent structures based on the modified couple stress theory. It focuses on establishing the governing equations of the size-dependent structures, deriving the associated finite element models, and implementing those models using the R programming language. The implemented functions are employed to develop a special R package (equivalent to a MATLAB toolbox) called microfiniteR for this book. In each chapter, the governing equations are formulated using the variational method, and the behaviour of the structures is examined on the basis of their load-deformation characteristics (in the case of static analyses) and by evaluating their eigenvalues (in the case of dynamics and buckling problems). The first chapter introduces readers to the R programming language, beginning with the resources needed to make use of the language and ending with a list of recommended texts. The remaining chapters cover the requisite linear elastic theory and highlight the implemented R functions. Each chapter concludes with a brief summary and relevant references |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed March 27, 2019) |
| Subject |
Finite element method.
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R (Computer program language)
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Finite element method
|
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R (Computer program language)
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| Form |
Electronic book
|
| ISBN |
9789811370144 |
|
9811370141 |
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9789811370151 |
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981137015X |
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