R for Finite Element Analyses of Size-dependent Microscale Structures

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.

• microfiniteR
• Timoshenko Microscale Beams
• Microstructure-dependent Beams
• Kirchhoff Microscale Beams
• R Programming Language
• Buckling Analysis
• Bending Analysis

• Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham Malaysia Campus, Semenyih, Malaysia

  Khameel B. Mustapha

Khameel Mustapha is an Assistant Professor at the Department of Mechanical, Materials and Manufacturing Engineering at the University of Nottingham (Malaysia Campus). He currently offers courses on the Mechanics of Solids and Advanced Solid Mechanics (Stress Analysis Techniques), and co-teaches Computer Modelling Techniques, Additive Manufacturing and 3D Printing and Design, Manufacture & Project. In a previous role as a lecturer with Swinburne University of Technology (Malaysia Campus), he convened and taught the following courses: Solid Mechanics, Structural Mechanics, Computer Aided Engineering, and Computer Modelling, Analysis and Visualization.

He holds a Ph.D. in Mechanical Engineering from Nanyang Technological University (Singapore), B.Eng. (Mechanical Engineering) from the University of Ilorin, a GCLT from Swinburne University of Technology (Australia) and a PGCHE from the University of Nottingham (UK). He is a Fellow of the Higher Education Academy (UK) and a member of the American Society of Mechanical Engineers. His research interests include the mechanics of composite materials; mechanics of additively manufactured components; mechanics of small-scale structures; mechanics of biological structures and energy materials; and computational methods for the simulation of mechanical systems.