A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineering problems involving bars, beams, torsion, plane elasticity, trusses, and plates. It begins with a review of the basic equations of mechanics, the concepts of work and energy, and key topics from variational calculus. It presents virtual work and energy principles, energy methods of solid and structural mechanics, Hamilton’s principle for dynamical systems, and classical variational methods of approximation. And it takes a more unified approach than that found in most solid mechanics books, to introduce the finite element method. Featuring more than 200 illustrations and tables, this Third Edition has been extensively reorganized and contains much new material, including a new chapter devoted to the latest developments in functionally graded beams and plates. Offers clear and easy-to-follow descriptions of the concepts of work, energy, energy principles and variational methods Covers energy principles of solid and structural mechanics, traditional variational methods, the least-squares variational method, and the finite element, along with applications for each Provides an abundance of examples, in a problem-solving format, with descriptions of applications for equations derived in obtaining solutions to engineering structures Features end-of-the-chapter problems for course assignments, a Companion Website with a Solutions Manual, Instructor's Manual, figures, and more Energy Principles and Variational Methods in Applied Mechanics, Third Edition is both a superb text/reference for engineering students in aerospace, civil, mechanical, and applied mechanics, and a valuable working resource for engineers in design and analysis in the aircraft, automobile, civil engineering, and shipbuilding industries.

THE FINITE ELEMENT METHOD : Basic Concepts and ApplicationsDarrell Pepper, Advanced Projects Research, Inc. California, and Dr . JuanHeinrich, University of Arizona, TucsonTh i s introductory textbook is designed for use in undergraduate, graduate, andshort courses in structural engineering and courses devoted specifically to thefinite element method. This method is rapidly becoming the most widely usedstandard for numerical approximation for partial differential equations definingengineering and scientific problems.The authors present a simplified approach to introducing the method and a coherentand easily digestible explanation of detailed mathematical derivations andtheory Example problems are included and can be worked out manually Anaccompanying floppy disk compiling computer codes is included and required forsome of the multi-dimensional homework problems.

Practicing engineers designing civil engineering structures, and advanced students of civil engineering, require foundational knowledge and advanced analytical and empirical tools. Mechanics in Civil Engineering Structures presents the material needed by practicing engineers engaged in the design of civil engineering structures, and students of civil engineering. The book covers the fundamental principles of mechanics needed to understand the responses of structures to different types of load and provides the analytical and empirical tools for design. The title presents the mechanics of relevant structural elements—including columns, beams, frames, plates and shells—and the use of mechanical models for assessing design code application. Eleven chapters cover topics including stresses and strains; elastic beams and columns; inelastic and composite beams and columns; temperature and other kinematic loads; energy principles; stability and second-order effects for beams and columns; basics of vibration; indeterminate elastic-plastic structures; plates and shells. This book is an invaluable guide for civil engineers needing foundational background and advanced analytical and empirical tools for structural design. - Includes 110 fully worked-out examples of important problems and 130 practice problems with an interaction solution manual (http://hsz121.hsz.bme.hu/solutionmanual) - Presents the foundational material and advanced theory and method needed by civil engineers for structural design - Provides the methodological and analytical tools needed to design civil engineering structures - Details the mechanics of salient structural elements including columns, beams, frames, plates and shells - Details mechanical models for assessing the applicability of design codes

An integration of modern work in structural stability theory, this volume focuses on the Koiter postbuckling analyses, with mathematical notions of stability of motion. In relation to discrete and continuous systems, it bases the minimum energy principles for static stability upon the dynamic concepts of stability of motion. It further develops the asymptotic buckling and postbuckling analyses from potential energy considerations, with applications to columns, plates, and arches.

This book attempts to acquaint engineers who have mastered the essentials of structural mechanics with the mathematical foundation of their science, of structural mechanics of continua. The prerequisites are modest. A good working knowledge of calculus is sufficient. The intent is to develop a consistent and logical framework of theory which will provide a general understanding of how mathematics forms the basis of structural mechanics. Emphasis is placed on a systematic, unifying and rigorous treatment. Acknowledgements The author feels indebted to the engineers Prof. D. Gross, Prof. G. Mehlhorn and Prof. H. G. Schafer (TH Darmstadt) whose financial support allowed him to follow his inclinations and to study mathematics, to Prof. E. Klingbeil and Prof. W. Wendland (TH Darmstadt) for their unceasing effort to achieve the impossible, to teach an engineer mathematics, to the staff of the Department of Civil Engineering at the University of California, Irvine, for their generous hospitality in the academic year 1980-1981, to Prof. R. Szilard (Univ. of Dortmund) for the liberty he granted the author in his daily chores, to Mrs. Thompson (Univ. of Dortmund) and Prof. L. Kollar (Budapest/Univ. of Dortmund) for their help in the preparation of the final draft, to my young colleagues, Dipl.-Ing. S. Pickhardt, Dipl.-Ing. D. Ziesing and Dipl.-Ing. R. Zotemantel for many fruitful discussions, and to cando ing. P. Schopp and Frau Middeldorf for their help in the production of the manuscript. Dortmund, January 1985 Friedel Hartmann Contents Notations ........................................................... XII Introduction ........................................................ .

A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.

Structural Theorems and Their Applications is an account of the various structural theorems and their applications. Topics covered range from the principles of superposition to virtual work and energy concepts, calculation of deflections, and analysis of indeterminate structures using the compatibility and equilibrium methods. Reciprocal theorems and theorems of plastic analysis for plane frames are also discussed. This book is comprised of eight chapters and begins with an overview of the problems of structural analysis and the importance of the principle of virtual work in this regard, followed by an analysis of the principles of superposition. The next chapter is devoted to virtual work and energy concepts such as strain energy and complementary energy. The principle of virtual work is used in the subsequent chapters as the basis for all of the indirect methods of structural analysis described in the text, including the analysis of indeterminate structures using the compatibility method and the equilibrium method. The principle of virtual work is also used to prove the reciprocal theorems and to establish the various theorems of plastic and incremental collapse for framed structures. This monograph will be of interest to mechanical and structural engineers.

A popular text in its first edition, Mechanics of Solids and Structures serves as a course text for the senior/graduate (fourth or fifth year) courses/modules in the mechanics of solid/advanced strength of materials, offered in aerospace, civil, engineering science, and mechanical engineering departments. Now, Mechanics of Solid and Structure, Second Edition presents the latest developments in computational methods that have revolutionized the field, while retaining all of the basic principles and foundational information needed for mastering advanced engineering mechanics. Key changes to the second edition include full-color illustrations throughout, web-based computational material, and the addition of a new chapter on the energy methods of structural mechanics. Using authoritative, yet accessible language, the authors explain the construction of expressions for both total potential energy and complementary potential energy associated with structures. They explore how the principles of minimal total potential energy and complementary energy provide the means to obtain governing equations of the structure, as well as a means to determine point forces and displacements with ease using Castigliano’s Theorems I and II. The material presented in this chapter also provides a deeper understanding of the finite element method, the most popular method for solving structural mechanics problems. Integrating computer techniques and programs into the body of the text, all chapters offer exercise problems for further understanding. Several appendices provide examples, answers to select problems, and opportunities for investigation into complementary topics. Listings of computer programs discussed are available on the CRC Press website.

A solid introduction to basic continuum mechanics, emphasizing variational formulations and numeric computation. The book offers a complete discussion of numerical method techniques used in the study of structural mechanics.