Abstract
Solid and structural mechanics deal with the elasticity basic concepts and the classical theories of stressed materials. Mechanical components and structures are under a stress condition if they are subjected to external loads or forces. The relationship between stresses and strains, displacements and forces, stresses and forces are of main importance in the process of modeling, simulating and designing engineered technical systems. This chapter describes the important relationships associated with the elasticity basic concepts and the classical mathematical models for solids and structures. Important field variables of solid mechanics are introduced, and the dynamic equations of these variables are derived. Mathematical models for 2D and 3D solids, trusses, Euler-beams, Timoshenko-beams, frames and plates are covered in a concise manner.
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References
Leal RP (2004) Folhas de apoio de Mecânica dos Sólidos. Departamento de Engenharia Mecânicam, Universidade de Coimbra, Coimbra, Portugal
Rekach VG (1978) Static theory of thin walled space structures. Mir Publisher, Moscow
Yu W (2012) Three-ways to derive the Euler-Bernoulli-Saint Venant beam theory. iMechanica
Wang CM, Reddy JN, Lee KH (2000) Shear deformable beams and plates: relationships with classical solutions. Elsevier Science, Amsterdam/New York
Popescu B, Hodges DH (2000) On asymptotically correct Timoshenko-like anisotropic beam theory. Int J Solids Struct 37(3):535–558. doi:10.1016/S0020-7683(99)00020-7
Bauchau OA, Craig JI (2009) Euler-Bernoulli beam theory. In: Bauchau OA, Craig JI (eds) Structural analysis, vol 163, Solid mechanics and its applications. Springer, Dordrecht, pp 173–221. doi:10.1007/978-90-481-2516-6_5
Wagner W, Gruttmann F, Sprenger W (2001) A finite element formulation for the simulation of propagating delaminations in layered composite structures. Int J Numer Method Eng 51(11):1337–1359. doi:10.1002/nme.210
Bathe K-J (1996) Finite element procedures. Prentice Hall, Princeton, New Jersey
Timoshenko SP (1921) On the correction factor for shear of the differential equation for transverse vibrations of bars of uniform cross-section. Philos Mag 744
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Neto, M.A., Amaro, A., Roseiro, L., Cirne, J., Leal, R. (2015). Mechanics of Solids and Structures. In: Engineering Computation of Structures: The Finite Element Method. Springer, Cham. https://doi.org/10.1007/978-3-319-17710-6_1
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DOI: https://doi.org/10.1007/978-3-319-17710-6_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17709-0
Online ISBN: 978-3-319-17710-6
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