Titlebook: Variational Methods in Theoretical Mechanics; John T. Oden,Junuthula N. Reddy Textbook 1983Latest edition Springer-Verlag Berlin Heidelber

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0172-5939 Ai r Force Offi ce of Scientific Research. We are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gu978-3-540-11917-3978-3-642-68811-9Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Mechanics of Continua-A Brief Review,theory for problems in mechanics, and the equations of constitution, of course, involve relations between the kinematic variables (or temperatures) and their duals, and define the constitution of the material under study.

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Introduction,ns of equilibrium of elastic bodies, as well as a basis for the study of stability. Hamilton’s principle can be used in lieu of the equations governing dynamical systems, and the variational forms presented by Biot displace certain equations in linear continuum thermodynamics.

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Complementary and Dual Variational Principles in Mechanics,ement u of a Hilbert space U such that .where Λ is a linear operator from U into its dual U′ which is given as a product of three linear operators, . Here A is a continuous linear operator from . into a Hilbert space ., E is a canonical isomorphism mapping . onto its dual .′, and A* is the adjoint of A which, by definition, maps . ′ into .′.

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Variational Methods of Approximation,ticular, we discuss interpolation properties of finite element methods, existence and uniqueness of solutions to the approximate problem, and convergence and error estimates of finite element methods for linear elliptic problems. More detailed accounts of linear elliptic problems can be found in [47, 109, 135].

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