Mechanics of Structural Elements: Theory and Applications

Springer Science & Business Media, Dec 18, 2006 - Technology & Engineering - 787 pages
The presentment should be as simple as possible, but not a bit simpler. Albert Einstein Introduction The power of the variational approach in mechanics of solids and structures follows from its versatility: the approach is used both as a universal tool for describing physical relationships and as a basis for qualitative methods of analysis [1]. And there is yet another important advantage inherent in the variational approach – the latter is a crystal clear, pure and unsophisticated source of ideas that help build and establish numerical techniques for mechanics. This circumstance was realized thoroughly and became especially important after the advanced numerical techniques of structural mechanics, first of all the finite element method, had become a helpful tool of the modern engineer. Certainly, it took some time after pioneering works by Turner, Clough and Melos until the finite element method was understood as a numerical technique for solving mathematical physics problems; nowadays no one would attempt to question an eminent role played by the variational approach in the process of this understanding. It is a combination of intuitive engineer thinking and a thoroughly developed mathematical theory of variational calculus which gave the finite element method an impulse so strong that its influence can still be felt. It would be too rash to say that there are few publications or books on the subject matter discussed in this book.

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Contents

 BASIC VARIATIONAL PRINCIPLES OF STATIC 1 References 27 ADDITIONAL VARIATIONAL PRINCIPLES 98 References 132 PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL 221 PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL 312 PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL 395 References 456
 compound profile 482 References 494 VARIATIONAL PRINCIPLES IN SPECTRAL PROBLEMS 539 VARIATIONAL PRINCIPLES IN STABILITYBUCKLING 605 CONCLUSION 701 700 Curvilinear coordinates on a plane associated with 755 Crosssections of a combined profile 776 SUBJECT INDEX 783

 PARTICULAR CLASSES OF PROBLEMS IN STRUCTURAL 458