Mechanics of Structural Elements

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.

The author systematically uses the variational principle where it is most powerful constructing numerical procedures and deriving basic governing equations of applied mechanics of solids Includes supplementary material: sn.pub/extras

Klappentext

The book systematically presents variational principles and methods of analysis for applied elasticity and structural mechanics. The variational approach is used consistently for both, constructing numerical procedures and deriving basic governing equations of applied mechanics of solids; it is the derivation of equations where this approach is most powerful and best grounded by mathematics. The book is oriented towards experts in civil engineering, researchers, developers of software for mechanical strength, stability, and oscillation analysis; it can be used by practical engineers who employ software tools to do their job and who want to know more about the theoretical background of the strength analysis. The book will be useful to senior and postgraduate students of engineering, to professors of structural analysis at civil or mechanical engineering departments of technical universities.

Inhalt
Basic Variational Principles of Static and Geometry in Structural Mechanics.- Basic Variational Principles of Structural Mechanics.- Additional Variational Principles of Structural Mechanics.- Particular Classes of Problems in Structural Mechanics Part 1.- Particular Classes of Problems in Structural Mechanics Part 2.- Particular Classes of Problems in Structural Mechanics Part 3.- Particular Classes of Problems in Structural Mechanics Part 4.- Particular Classes of Problems in Structural Mechanics Part 5.- The Ritz Method and its Modifications.- Variational Principles in Spectral Problems.- Variational Principles in Stability/Buckling Analysis.