New PDF release: Elasticity of Transversely Isotropic Materials (Solid

By Haojiang Ding

ISBN-10: 1402040334

ISBN-13: 9781402040337

ISBN-10: 1402040342

ISBN-13: 9781402040344

This e-book provides a complete and systematic research of difficulties of transversely isotropic fabrics that experience extensive functions in civil, mechanical, aerospace, fabrics processing and production engineering. numerous effective tools in accordance with three-d elasticity are constructed lower than a unified framework, together with the displacement strategy, the strain strategy, and the state-space approach. specifically, a third-dimensional normal resolution is derived to unravel sensible difficulties comparable to the countless area, half-space, bimaterial house, layered medium, our bodies of revolution, thermal stresses and three-d touch. detailed and analytical suggestions also are constructed for static and dynamic difficulties of plates and shells, that could be used because the benchmarks for numerical or approximate research. Coupling results of inner/outer fluids and surrounding elastic media at the loose vibration of cylindrical and round shells are mentioned intimately. New state-space formulations are tested for the research of oblong plates and round shells, from which self sustaining periods of vibrations might be simply clarified.

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51) 1, 2, , n 1) that are equal to sn2 . 3 Almansi (1899) proved the theorem that bears his name: The solution of a differential equation with multiple three-dimensional Laplace operators can be represented by a linear combination of several threedimensional harmonic functions. Eubanks and Sternberg (1953) extended Almansi’s theorem to axisymmetric problems. 2 Displacement Method 47 According to this theorem, the solution of Eq. 53) where F1 and F2 satisfy the following equations: § ∂2 ¨Λ + 2 ¨ ∂z i © · ¸ Fi = 0 , (i = 1, 2) .

69) becomes the same as Eq. 71) and Eq. 70) becomes identical to Eq. 72a) ∂ ϕ3 . ∂zz32 2 (2) A body subjected to an axisymmetric deformation Let ϕ3 = 0 , ϕ1 ϕ1 ( , 1 ) , and ϕ2 ϕ2 ( , 2 ) . When s1 ≠ s 2 , Eqs. 70b) ∂ ϕi , ∂zzi2 2 2 66 ∂ 2ϕi ∂zi2 uα = 0 , 3i i =1 ∂ 2ϕ i . ∂r ∂zi While when s1 = s 2 , Eqs. 72b) 54 Chapter 2 General Solution for Transversely Isotropic Problems § ∂ 2ϕ1 σ z / c66 = k 21 ¨¨ + z1 ∂ 2ϕ 2 · ∂ϕ ¸ + k5 2 , ∂zz1 ∂zz12 ¸¹ © ∂zz § ∂ 2ϕ1 ∂ 2ϕ 2 · ∂ϕ ¸¸ + k 6 2 . + z1 τ zr / c66 = k 31 ¨¨ ∂ ∂z ∂ ∂z r z r z ∂r 1 1 © ¹ 2 1 In these equations, ϕ i still satisfy Eq.

36) where ª1 0 0º ª0 0 0 º « » [k1 ] = «0 0 0» , [k 2 ] = ««0 1 0»» . 37) With this rearrangement, Eq. 38) 38 Chapter 2 General Solution for Transversely Isotropic Problems where ª A′ A2′ º [ A′] = « 1 » = [k ][ A][k ] , ¬ A3′ A4′ ¼ {β 4′ } = [k ]{β 4 } , f ′ = [k ]{ f } . 40) Using Eqs. 42) º c23 ∂ » c33 ∂y » » § c13c23 · ∂ 2 ¸¸ ». 43) This result is consistent with that of Zheng and Zhang (1996). 2 DISPLACEMENT METHOD We will find the solution for transversely isotropic problems using the governing equations developed above.

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Elasticity of Transversely Isotropic Materials (Solid Mechanics and Its Applications) (Solid Mechanics and Its Applications) by Haojiang Ding


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