Applied Engineering Analysis

**A resource book applying mathematics to solve engineering problems**__Applied Engineering Analysis__is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls.Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors.**__Key features:__**Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems. Examples and problems of a practical nature with illustrations to enhance student's self-learning. Numerical methods and techniques, including finite element analysis. Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC).__Applied Engineering Analysis__is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making. Title Page 17 Copyright 18 Dedication 19 Preface 21 Suggestions to instructors 24 About the companion website 26 Chapter 1: Overview of Engineering Analysis 27 1.1 Introduction 29 1.2 Engineering Analysis and Engineering Practices 30 1.3 “Toolbox” for Engineering Analysis 34 1.4 The Four Stages in Engineering Analysis 38 1.5 Examples of the Application of Engineering Analysis in Design 43 1.6 The “Safety Factor” in Engineering Analysis of Structures 51 Problems 53 Chapter 2: Mathematical Modeling 54 2.1 Introduction 56 2.2 Mathematical Modeling Terminology 63 2.3 Applications of Integrals 77 2.4 Special Functions for Mathematical Modeling 99 2.5 Differential Equations 108 Problems 111 Chapter 3: Vectors and Vector Calculus 119 3.1 Vector and Scalar Quantities 121 3.2 Vectors in Rectangular and Cylindrical Coordinate Systems 124 3.3 Vectors in 2D Planes and 3D Spaces 130 3.4 Vector Algebra 132 3.5 Vector Calculus 145 3.6 Applications of Vector Calculus in Engineering Analysis 151 3.7 Application of Vector Calculus in Rigid Body Dynamics 154 Problems 178 Chapter 4: Linear Algebra and Matrices 181 4.1 Introduction to Linear Algebra and Matrices 183 4.2 Determinants and Matrices 185 4.3 Different Forms of Matrices 190 4.4 Transposition of Matrices 193 4.5 Matrix Algebra 194 4.6 Matrix Inversion, [A]−1 199 4.7 Solution of Simultaneous Linear Equations 201 4.8 Eigenvalues and Eigenfunctions 214 Problems 223 Chapter 5: Overview of Fourier Series 225 5.1 Introduction 226 5.2 Representing Periodic Functions by Fourier Series 228 5.3 Mathematical Expression of Fourier Series 230 5.4 Convergence of Fourier Series 243 5.5 Convergence of Fourier Series at Discontinuities 246 Problems 252 Chapter 6: Introduction to the Laplace Transform and Applications 254 6.1 Introduction 255 6.2 Mathematical Operator of Laplace Transform 256 6.3 Properties of the Laplace Transform 260 6.4 Inverse Laplace Transform 264 6.5 Laplace Transform of Derivatives 272 6.6 Solution of Ordinary Differential Equations Using Laplace Transforms 277 6.7 Solution of Partial Differential Equations Using Laplace Transforms 289 Problems 293 Chapter 7: Application of First-order Differential Equations in Engineering Analysis 295 7.1 Introduction 296 7.2 Solution Methods for First-order Ordinary Differential Equations 297 7.3 Application of First-order Differential Equations in Fluid Mechanics Analysis 303 7.4 Liquid Flow in Reservoirs, Tanks, and Funnels 306 7.5 Application of First-order Differential Equations in Heat Transfer Analysis 319 7.6 Rigid Body Dynamics under the Influence of Gravitation 338 Problems 343 Chapter 8: Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis 348 8.1 Introduction 349 8.2 Solution Method for Typical Homogeneous, Second-order Linear Differential Equations with Constant Coefficients 350 8.3 Applications in Mechanical Vibration Analyses 356 8.4 Mathematical Modeling of Free Mechanical Vibration: Simple Mass–Spring Systems 359 8.5 Modeling of Damped Free Mechanical Vibration: Simple Mass–Spring Systems 365 8.6 Solution of Nonhomogeneous, Second-order Linear Differential Equations with Constant Coefficients 371 8.7 Application in Forced Vibration Analysis 381 8.8 Near Resonant Vibration 392 8.9 Natural Frequencies of Structures and Modal Analysis 397 Problems 400 Chapter 9: Applications of Partial Differential Equations in Mechanical Engineering Analysis 403 9.1 Introduction 405 9.2 Partial Derivatives 406 9.3 Solution Methods for Partial Differential Equations 408 9.4 Partial Differential Equations for Heat Conduction in Solids 413 9.5 Solution of Partial Differential Equations for Transient Heat Conduction Analysis 422 9.6 Solution of Partial Differential Equations for Steady-state Heat Conduction Analysis 432 9.7 Partial Differential Equations for Transverse Vibration of Cable Structures 439 9.8 Partial Differential Equations for Transverse Vibration of Membranes 454 Problems 463 Chapter 10: Numerical Solution Methods for Engineering Analysis 466 10.1 Introduction 468 10.2 Engineering Analysis with Numerical Solutions 469 10.3 Solution of Nonlinear Equations 470 10.4 Numerical Integration Methods 479 10.5 Numerical Methods for Solving Differential Equations 496 10.6 Introduction to Numerical Analysis Software Packages 513 Problems 516 Chapter 11: Introduction to Finite-element Analysis 519 11.1 Introduction 521 11.2 The Principle of Finite-element Analysis 523 11.3 Steps in Finite-element Analysis 524 11.4 Output of Finite-element Analysis 544 11.5 Elastic Stress Analysis of Solid Structures by the Finite-element Method 547 11.6 General-purpose Finite-element Analysis Codes 562 Problems 566 Chapter 12: Statistics for Engineering Analysis 569 12.1 Introduction 571 12.2 Statistics in Engineering Practice 573 12.3 The Scope of Statistics 575 12.4 Common Concepts and Terminology in Statistical Analysis 578 12.5 Standard Deviation (σ) and Variance (σ2) 584 12.6 The Normal Distribution Curve and Normal Distribution Function 586 12.7 Weibull Distribution Function for Probabilistic Engineering Design 590 12.8 Statistical Quality Control 600 12.9 Statistical Process Control 602 12.10 The “Control Charts” 604 Problems 611 Bibliography 614 Appendix 1: Table for the Laplace Transform 618 Appendix 2: Recommended Units for Engineering Analysis 620 Appendix 3: Conversion of Units 622 Appendix 4: Application of MATLAB Software for Numerical Solutions in Engineering Analysis: Contributed by Vaibhav Tank 624 Index 639 End User License Agreement 672

Applied Engineering Analysis

Tai-Ran Hsu, San Jose State University, USA

A resource book applying mathematics to solve engineering problems

Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls.

Drawing on the author’s extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors.

Key features:

• Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems.
• Examples and problems of a practical nature with illustrations to enhance student’s self-learning.
• Numerical methods and techniques, including finite element analysis.
• Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC).

Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.