By Jan Awrejcewicz, Vadim Anatolevich Krys'ko
This quantity introduces and studies novel theoretical ways to modeling strongly nonlinear behaviour of both person or interacting structural mechanical devices equivalent to beams, plates and shells or composite structures thereof.
The process attracts upon the well-established fields of bifurcation thought and chaos and emphasizes the concept of regulate and balance of gadgets and structures the evolution of that is ruled by means of nonlinear usual and partial differential equations. Computational equipment, specifically the Bubnov-Galerkin strategy, are hence defined intimately.
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Additional resources for Chaos in structural mechanics
Sample text
Finally, the central square element, cross addition element, and perforation-type non-homogeneities are introduced. 1 Fundamental Concepts of the Theory of Elastic Stability Increasing strength properties of the traditional material characteristics that are applied for various kinds of constructions as well as the use of new composite mediums characterized by extremely high-resistance features have led in the contemporary machines and building industry to a widespread application of light and economical constructions.
Because of the absence of a minimal potential energy at this point, the appropriate equilibrium locus will not be stable. The equilibrium locus of a conservative system will be unstable for all cases in which the total potential energy of a system takes some constant but not minimal value. The total energy of the deformable conservative system is composed of both the energy U of an elastic deformation and the potential Π of external forces: E = U + Π. ) condition, the total potential energy does not change.
But after all they are the idealized formulations. Such a simplified approach to the analysis of physical phenomena turns out to be insufficient. New mathematical notions or apparatus are often required. The first notions of generalized functions were formed in the work of Dirac and other physicist’s as a type of symbolic description of the physical phenomena. To achieve a systematic method of application of the above functions it was necessary to introduce some important bases of the theory of generalized functions, which was done by Sobolev and Schwartz [267, 279], respectively.