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This electronic text summarizes the physical laws, mathematical methods, and computer algorithms that are used to predict the response of materials and structures to mechanical or thermal loading. Topics include: the mathematical descriptions of deformation and forces in solids; constitutive laws; analytical techniques and solutions to linear elastic and elastic-plastic boundary value problems; the use and theory of finite element analysis; fracture mechanics; and the theory of deformable rods, plates and shells. The text is intended for advanced undergraduate or graduate students, as well as practicing engineers and scientists.
It will be particularly useful to readers who wish to learn enough about solid mechanics to impress their teachers, colleagues, research advisors, or managers, but who would prefer not to study the subject in depth. A printed copy of the text has published by Taylor and Francis and is available from Amazon. For length reasons, and to minimize cost, the print version does not include the problem sets. The electronic web site will continue to be freely available. Home Contents Quick Navigation 1. Objectives and Applications 2. Governing Equations 2. Doblare, and A. Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling.
Journal of the Mechanics and Physics of Solids, 57 1 , Perzyna, The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects. Mechanics, 27 1 , Glema, T. Journal of Theoretical and Applied Mechanics, 48 4 , Sumelka and T.
Reduction of the number of material parameters by ann approximation. Computational Mechanics, , Material rate dependence and mesh sensitivityin localization problems. Computer Methods in Applied Mechanics and Engineering, , Fractional deformation gradients. Thermoelasticity in the framework of the fractional continuum mechanics. Journal of Thermal Stresses, 37 6 , More clarity on the concept of material frame-indifference in classical continuum mechanics.
Drapaca and S. A fractional model of continuum mechanics. Journal of Elasticity, , , Di Paola, G. Failla, and M.
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Physically-based approach to the mechanics of strong non-local linear elasticity theory. Journal of Elasticity, 97 2 , Atanackovic and B. Generalized wave equation in nonlocal elasticity. Carpinteri, P. Cornetti, and A.
A fractional calculus approach to nonlocal elasticity. European Physical Journal Special Topics, , , Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calculus and Applied Analysis, 5 4 , Carpinteri and F. Carpinteri and P.
- The Mechanics of Solids and Structures - Hierarchical Modeling and the Finite Element Solution.
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A fractional calculus approach to the description of stress and strain localization in fractal media. Chaos, Solitons and Fractals, , Continuous medium model for fractal media. Physics Letters A, , Fractional hydrodynamic equations for fractal media. Annals of Physics, 2 , Towards thermomechanics of fractal media. Stresses and strains in a deformable fractal medium and in its fractal continuum model.
Academic Press, Kilbas, H. Srivastava, and J. Oliveira and J. A review of definitions for fractional derivatives and integral. Atanackovic, S. Pilipovic, B. Stankovic, and D. Fractional Calculus with Applications in Mechanics, Wiley, ISBN On differential equations of nonlocal elasticity and solutions of screw dislocations and surface waves.
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Journal of Applied Physics, , Nonlocal elasticity: an approach based on fractional calculus, Meccanica, 49 11 , Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids, , Samko, A.
Kilbas, and O. Fractional integrals and derivatives: theory and applications, Gordon and Breach, Amsterdam, An introduction to fractional mechanics. Monographs No Frederico and D. Applied Mathematics and Computation, , The Marcel Riesz Memorial volume, pages , Fractional continua for linear elasticity.
Archives of Mechanics, 66 3 , Sumelka, K. Szajek, and T. Plane strain and plane stress elasticity under fractional continuum mechanics. Archive of Applied Mechanics, 89 9 , Non-local kirchhoff-love plates in terms of fractional calculus. Archives of Civil and Mechanical Engineering, Application of fractional continuum mechanics to rate independent plasticity.
Acta Mechanica, 11 , Continuum Mechanics and Theory of Materials, Springer, second edition, Approximations of fractional integrals and Caputo fractional derivatives. High-accuracy numerical integration methods for fractional order derivatives and integrals computations.
Remarks on five equivalent forms of the fractional - order backward - difference. Export Citation.
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