This volume presents an introduction to the three numerical methods most commonly used in the mechanical analysis of deformable solids, viz. the finite element method (FEM), the linear iteration method (LIM), and the finite difference method (FDM). The book has been written from the point of view of simplicity and unity; its originality lies in the comparable emphasis given to the spatial, temporal and nonlinear dimensions of problem solving. This leads to a neat global algorithm. Chapter 1 addresses the problem of a one-dimensional bar, with emphasis being given to the virtual work principle. Chapters 2--4 present the three numerical methods. Although the discussion relates to a one-dimensional model, the formalism used is extendable to two-dimensional situations. Chapter 5 is devoted to a detailed discussion of the compact combination of the three methods, and contains several sections concerning their computer implementation. Finally, Chapter 6 gives a generalization to two and three dimensions of both the mechanical and numerical aspects. For graduate students and researchers whose work involves the theory and application of computational solid mechanics.

Prominent scientists present the latest achievements in computational methods and mechanics in this book. These lectures were held at the CMM 2009 conference.

While various software packages have become essential for performing unit operations and other kinds of processes in chemical engineering, the fundamental theory and methods of calculation must also be understood to effectively test the validity of these packages and verify the results. Computer Methods in Chemical Engineering, Second Edition presents the most used simulation software along with the theory involved. It covers chemical engineering thermodynamics, fluid mechanics, material and energy balances, mass transfer operations, reactor design, and computer applications in chemical engineering. The highly anticipated Second Edition is thoroughly updated to reflect the latest updates in the featured software and has added a focus on real reactors, introduces AVEVA Process Simulation software, and includes new and updated appendixes. Through this book, students will learn the following: What chemical engineers do The functions and theoretical background of basic chemical engineering unit operations How to simulate chemical processes using software packages How to size chemical process units manually and with software How to fit experimental data How to solve linear and nonlinear algebraic equations as well as ordinary differential equations Along with exercises and references, each chapter contains a theoretical description of process units followed by numerous examples that are solved step by step via hand calculation and computer simulation using Hysys/UniSim, PRO/II, Aspen Plus, and SuperPro Designer. Adhering to the Accreditation Board for Engineering and Technology (ABET) criteria, the book gives chemical engineering students and professionals the tools to solve real problems involving thermodynamics and fluid-phase equilibria, fluid flow, material and energy balances, heat exchangers, reactor design, distillation, absorption, and liquid extraction. This new edition includes many examples simulated by recent software packages. In addition, fluid package information is introduced in correlation to the numerical problems in book. An updated solutions manual and PowerPoint slides are also provided in addition to new video guides and UniSim program files.

This text is aimed at helping engineering students develop expertise in numerical methods and use them to solve problems of practical interest. It provides students with a treatment of numerical methods for important operations such as integration, differentiation and root solving.

Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.

The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial value problems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.

Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.