Refined theory and decomposed theorem of transversely isotropic thermoporoelastic beam

Lu, Gui-xian; Zhao, Bin; Wu, Xiue

doi:10.1016/j.crme.2013.07.001

Cited by 8 publications

(3 citation statements)

References 14 publications

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“…Gao et al [13] got the refined theory of beams for a transversely isotropic body. Lu et al [14] got the refined theory of transversely isotropic thermoporoelastic beam. Based on a refined theory of a single layer, Zhao and others [15,16] got the refined analysis of bi-layer beams and a refined theory of sandwich beams without an ad hoc assumption.…”

Section: Introductionmentioning

confidence: 99%

Refined theory of bi-layer beams for a transversely isotropic body

Liu

Zhao

2014

Comptes Rendus. Mécanique

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Based on elastic theory, the refined theory of bi-layer beams for a transversely isotropic body is studied. Using the Elliott-Lodge (E-L) solution and Luré method, the refined theory of beams is derived from continuity conditions without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by displacements and stresses of the interface of two layers of different materials. The governing equations about the transverse displacement of the interface can be obtained directly from the refined theory under transverse surface loading. Approximate solutions are derived for beams by dropping terms of high order. In addition, one example is examined to illustrate the application of the theory proposed in this paper.

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Section: Introductionmentioning

confidence: 99%

Refined theory of bi-layer beams for a transversely isotropic body

Liu

Zhao

2014

Comptes Rendus. Mécanique

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“…Cheng (1979) presented a method for the solution of 3D elasticity equations, and established a refined theory of plates by using the Lur'e method (Lur'e, 1964). Thereafter, the refined theory is extended to the transversely isotropic plates (Wang, 1990(Wang, , 1991, beam (Gao et al, 2007;Gao and Shang, 2010;Lu et al, 2013) and circular cylinder (Zhao et al, 2011;Zhao and Wu, 2012). The true importance of using the refined theory is in the fact that the high-dimensional theory can be transformed into low-dimensional theory to study by making use of elastic general solution and symbolic operation, and the problem can be simplified further.…”

Section: Introductionmentioning

confidence: 99%

A refined theory of axisymmetric thermoporoelastic circular cylinder

Wu¹,

Yu²,

Wang³

et al. 2015

European Journal of Mechanics - A/Solids

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“…The 3D and elasticity based solutions (Alibeigloo and Zanoosi, 2013;Chang and Tarn, 2012;Yang et al, 2012) are also available in the literature, as well as the different layerwise approximations (Arya et al, 2002;Ferreira et al, 2011;Ovesy et al, 2015;Saeedi et al, 2012a Saeedi et al, ,b, 2013aLerpiniere et al, 2014;Sahoo and Singh, 2014b). Other higher-order theories (Steigmann, 2012;Xiang et al, 2012;Shi, 2007;Zhao et al, 2013;Lu et al, 2013;Shimpi and Patel, 2006) and those based on trigonometric or other appropriate functions (Thai and Vo, 2013;Thai and Choi, 2013; Singh, 2014a, 2013a,b) are useful in the case of functionally graded (FGM) plates. …”

Section: Introductionmentioning

confidence: 99%

Nonsingular crack modelling in orthotropic plates by four equivalent single layers

Szekrényes

2016

European Journal of Mechanics - A/Solids

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Keywords:Delamination Mixed mode II/III fracture Energy release rate Second-order plate theory Theoreom of autocontinuity Q3 a b s t r a c tIn this work the second-and third-order laminated plate theories are applied to model delaminated composite plates with material orthotropy. The method of four equivalent single layers is proposed and a general third-order displacement field is utilized in each layer. The kinematic continuity between the layers is established by the system of exact kinematic conditions. Apart from the continuity of the inplane displacements between the interfaces of the layers even the continuity of shear strains, their derivatives and curvatures is imposed. As a novelty a so-called shear strain control condition is introduced, which means that the shear strains at two or more points located along the thickness are imposed to be the same. Using the proposed conditions the equilibrium equations are derived for the delaminated and undelaminated regions of the plate. Plates with different boundary conditions are solved as examples and the theorem of autocontinuity is introduced, which is essentially related to the continuity conditions between the delaminated and undelaminated parts. The stress and displacement fields as well as the J-integral are determined in the examples and compared to finite element calculations. The results indicate that the control condition works very well in the case of the second-order plate theory, in contrast it is rather a disadvantage in the case of the third-order approximation.© 2015 Published by Elsevier Masson SAS. IntroductionAnisotropic composites (Chaudhuri and Balaraman, 2007; Czig any and De ak, 2012; M esz aros et al., 2013) are often utilized in air-, spacecraft (Smojver and Ivan cevi c, 2010;Ivan cevi c and Smojver, 2011; Ivan cevi c, 2011, 2012;Langdon et al., 2014) and sport industry (Jiang, 2014;Li and Jing, 2014;Su, 2014;Zhang, 2014;Tang, 2014), composite panels are also applied in cars and vehicles (Norhidayah et al., 2014;Wennberg and Stichel, 2014;Khan et al., 2014), ships (Chirica et al., 2011;Chirica, 2013), pressure vessels (Gheshlaghi et al., 2006 and many other engineering applications (Goch et al., 2012). The mechanical behavior of laminated composite plates and shells can be described by different theories. The classical laminated plate theory (CLPT) is based on the Kirchhoff assumption and so, it does not take the shear deformation into account (Radosavljevi c and Dra zi c, 2010;Eftekhari and Jafari, 2012;Hajheidari and Mirdamadi, 2013). The first-order shear deformation (FSDT or Mindlin) theory assumes constant shear strain distribution over the thickness of the plate (Kreja and Schmidt, 2006;Endo and Kimura, 2007;Assie et al., 2012;Batista, 2012;Nanda and Sahu, 2012;Sabik and Kreja, 2013;Endo, 2015). As a next step, the second-order plate theory (SSDT) proposes that the in-plane displacements are captured by quadratic functions in terms of the through-thickness coordinate (Baddour, 2011;Izadi and Tahani, 2010;Shahrjerdi et al., 2011...

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Refined theory and decomposed theorem of transversely isotropic thermoporoelastic beam

Cited by 8 publications

References 14 publications

Refined theory of bi-layer beams for a transversely isotropic body

Refined theory of bi-layer beams for a transversely isotropic body

A refined theory of axisymmetric thermoporoelastic circular cylinder

Nonsingular crack modelling in orthotropic plates by four equivalent single layers

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