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    Dynamical Systems. Periodic solutions near the Lagrange equilibrium points in the restricted three-body problem for mass ratios near Routh's critical value G. Lower bound on the dimension of the attractor for the Navier-Stokes equations in Space Dimension 3 J. Ghidaglia and R. Homoclinic chaos for ray optics in a fiber: years after Lagrange D. Holm and G.
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    Mechanics and Analysis of Composite Materials

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    Mathematics - Analysis and mechanics | Britannica

    This book is concerned with the topical problems of mechanics of advanced composite materials whose mechanical properties are controlled by high-strength and high-stiffness continuous fibers embedded in polymeric, metal, or ceramic matrix. Although the idea of combining two or more components to produce materials with controlled properties has been known and used from time immemorial, modern composites were only developed several decades ago and have now found intensive application in different fields of engineering, particularly in aerospace structures for which high strength-to-weight and stiffness-to-weight ratios are required. There already exist numerous publications that cover anisotropic elasticity, mechanics of composite materials, design, analysis, fabrication, and application of composite structures but the difference between this book and the existing ones is that this is of a more specific nature. It covers specific features of material behaviour such as nonlinear elasticity, plasticity, creep, and structural nonlinearity and discusses in detail the problems of material micro- and macro-mechanics that are only slightly touched in existing books, e. The authors are designers of composite structures who were involved in practically all the main Soviet and then Russian projects in composite technology, and the permission of the Russian Composite Center - Central Institute of Special Machinery CRISM to use in this book the pictures of structures developed and fabricated in CRISM as part of the joint research and design project is much appreciated. Mechanics and Analysis of Composite Materials consists of eight chapters progressively covering all structural levels of composite materials from their components through elementary plies and layers to laminates. For researchers and specialists in mechanical engineering involved with and interested in composite technology, and design and analysis of composite structures; also for engineering graduate students as a reference text.
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    Mechanics, Analysis and Geometry: 200 Years after Lagrange

    Structural mechanics or Mechanics of structures is the computation of deformations , deflections , and internal forces or stresses stress equivalents within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads , the structure's geometric representation and support conditions, and the materials' properties. Output quantities may include support reactions, stresses and displacements.
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    The scientific revolution had bequeathed to mathematics a major program of research in analysis and mechanics. With expansion came specialization as different parts of the subject acquired their own identity: ordinary and partial differential equations , calculus of variations , infinite series , and differential geometry. The applications of analysis were also varied, including the theory of the vibrating string, particle dynamics , the theory of rigid bodies, the mechanics of flexible and elastic media, and the theory of compressible and incompressible fluids.
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