Introduction

The chapter serves as the introduction to a MATLAB® primer oriented for scientists, specialists, and students of mechanical and tribological (M&T) sciences. The objectives of the book and the principal audience are outlined and accompanied by a brief description of the topics and structure of the book chapters and its appendices. The history of MATLAB® is briefly described together with the advantages of the software. In addition, the order of studying the material of the book is discussed.

Curve Fitting for Mechanical and Tribological Problems

This chapter devoted to matching the data with mathematical expressions. Here the functions using fitting by polynomial and non-polynomial expressions is represented by examples from the mechanics and tribology (M&T) fields. The Basic Fitting tool and examples of its use are described. Single and multivariate fitting through optimization are discussed. Application examples are demonstrate the curve fitting for the following data: fuel efficiency-velocity, yield strength-grain diameter, friction coefficient-time, and machine diagnostic parameter.

Basics of Graphics With Applications

The basic, special, and additional commands for generating two- and three-dimensional graphs are presented. It describes formatting commands for inserting labels, headings, texts, and symbols into a plot, as well as color, marker, and line qualifiers. Graphs with more than one curve and graphs with two Y axes are discussed. The possibilities of creating multiple plots on one page are shown. All the commands studied are presented with examples from the field of mechanics and tribology (M&T). At the end of the chapter, applications are given; they illustrate how to generate 2D and 3D graphs for engine piston velocity, power screw efficiency, engine oil viscosity, and a number of other M&T problems.

The ODE- and BVP-Solvers With M&T Applications

The chapter introduces solvers for solving initial and boundary value problems (IVP&BVP) of the ordinary differential equation (ODE). It begins with a description of the ODE solver commands applied to the initial value problem and presents the steps for solving the actual ODE. Further, the chapter presents the BVP-solver commands and steps for their usage. The solutions are presented through real examples. In the final part, the studied ODE and BVP commands are applied, mainly to problems oriented for mechanics and tribology (M&T). At the end of the chapter, applications to the M&T problems are presented; they illustrate how to solve IVP for the spring-mass system and particle falling, as well as BVP for a single clamped beam and hydrodynamic lubrication of a sliding surface covered with semicircular pores.

Solving One-Dimensional Partial Differential Equations

This chapter describes the pdepe command, which is used to solve spatially one-dimensional partial differential equations (PDEs). It begins with a description of the standard forms of PDEs and its initial and boundary conditions that the pdepe solver uses. It is shown how various PDEs and boundary conditions can be represented in standard forms. Applications to the mechanics are presented in the final part of the chapter. They illustrate how to solve: heat transfer PDE with temperature dependent material properties, startup velocities of the fluid flow in a pipe, Burger's PDE, and coupled FitzHugh-Nagumo PDE.

Statistical Calculations

This chapter presents statistical commands and its applications to various problems of the mechanics and tribology (M&T). Descriptive statistics, data statistics tool, specialized statistical graphs, probability distributions, and hypothesis tests are discussed. The solutions of various applied problems are given. In particular, surface roughness indices are calculated by the measured data using the descriptive statistics command; the histogram generated by a runout data are matched with the theoretical distribution; capability plot generation is shown by the data for the piston ring gaps; friction torques for two different oil additives are compared using a hypothesis test.

Solving Two-Dimensional Partial Differential Equations

This chapter describes the PDE Modeler tool, which is used to solve spatially two-dimensional partial differential equations (PDE). It begins with a description of the standard forms of PDEs and its initial and boundary conditions that the tool uses. It is shown how various PDEs and boundary conditions can be represented in standard forms. Applications to the mechanics and tribology are presented in the final part of the chapter. They illustrate the use of PDE Modeler to solve the Reynolds equation describing the hydrodynamic lubrication, to implement the mechanical stress modeler application for a plate with an elliptical hole, to solve the transient heat equation with temperature-dependent material properties, and to study vibration of a rectangular membrane.

Symbolic Calculations

The chapter is devoted to symbolic calculations in which the variables and commands operate on mathematical expressions containing symbolic variables. The representation of a symbolic expression, its simplification, the solution of algebraic expressions, symbolic differentiation and integration, and conversion of the symbolic numbers to their decimal form are described. ODEs solutions are also presented. The final sections of the chapter give examples of the symbolic calculation implementation for some mechanical and tribological problems that were solved numerically in previous chapters, namely lengthening a two-spring scale, shear stress in a lubrication film, a centroid of a certain plate, and two-way solutions of the ODE describing the second order dynamical system – traditional and using the Laplace transform.

Basics of Software Used to Solve M&T Problems

At the beginning of the chapter, the desktop of the software, its toolbars, and main windows are introduced. Examples of interactive calculations with MATLAB® language are presented. Elementary functions, input and output commands, numbers and strings, vectors, matrices and arrays, flow control commands, relational and logical operators are discussed. Each command is presented in its most applicable form and with practical examples. At the end of each subsection, the commands studied are applied to elementary problems in the field of mechanical and tribological (M&T) sciences and technology, in particular to such as stress intensity factor, stiffness of a threaded bolt, adhesive force in contact between two spheres, and many others.

Script-, Function-Files and Program Managing

The Editor window for writing scripts and user-defined functions are presented, as well as the Live Editor window for writing live scripts and functions. All commands, regular and live scripts, and functions are explained by examples from the mechanics and tribology (M&T) fields. After that, the application examples are given; they include the stress unit converters, computing of the stress factor of a shaft with a transverse hole, gear warm K-parameter calculations, installation, and operation stresses on the piston ring.