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Energy and variational methods in applied mechanics. With an introduction to the finite element method. (English) Zbl 0635.73017

A Wiley-Interscience Publication. New York etc.: John Wiley & Sons. XIII, 545 p. (1984).
This book is intended for senior undergraduate students and beginning graduate students in aerospace, civil and mechanical engineering, and applied mechanics, who have had a course in ordinary and partial differential equations.
The text is organized into four chapters. Chapter 1 is essentially a review, especially for graduate students, of the equations of applied mechanics. Much of the chapter can be assigned as reading material to the student. The equations of bars, beams, torsion, and plane elasticity presented in Section 1.7 are used to illustrate concepts from energy and variational methods. Chapter 2 deals with the study of the basic topics from variational calculus, virtual work and energy principles, and energy methods of mechanics. The instructor can omit Section 2.4 on stationary principles and Section 2.5 on Hamilton’s principle if he or she wants to cover all of Chapter 4. Classical variational methods of approximation (e.g., the methods of Ritz, Galerkin, Kantorovich, etc.) and the finite element method are introduced and illustrated in Chapter 3 via linear problems of science and engineering, especially solid mechanics. A unified approach, more general than that found in most solid mechanics books, is used to introduce the variational methods. As a result, the student can readily extend the methods to other subject areas of solid mechanics as well as to other branches of engineering.
The classical variational methods and the finite element method are put to work in Chapter 4 in the derivation and approximate solution of the governing equations of elastic plates and shells. In the interest of completeness, and for use as a reference for approximate solutions, exact solutions of plates and shells are also included. Keeping the current developments in composite-material structurs in mind, a brief but reasonably complete, discussion of laminated plates and shells is included in Sections 4.3 and 4.4.
The book contains many examples and exercise problems that illustrate, test, and broaden the understanding of the topics covered. A long list of references, by no means complete or up-to-date, is provided in the Bibliography at the end of the book.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
74S05 Finite element methods applied to problems in solid mechanics