Variational solutions to stresses in cracked cross-ply laminates under bending

Kuriakose, Sunil; Talreja, Ramesh

doi:10.1016/j.ijsolstr.2003.11.022

Cited by 18 publications

(34 citation statements)

References 19 publications

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“…Therefore, for cracked general cross-ply laminates under in-plane biaxial loading as well as out-of-plane bendings, with a uniform distribution of ply cracks in a single orientation, the present stress field is the optimal admissible one that can be developed based upon the single fundamental assumption that in-plane stresses in each ply element are linear functions of the through-thickness direction. Comparisons with the available finite element results (Kuriakose and Talreja, 2004) for laminates of glass/epoxy and graphite/epoxy have shown that the stress components are in very good agreement with the analytical results. It has been shown that Kuriakose and Talreja's model (2004) is a specific case of the current formulation.…”

Section: Introductionsupporting

confidence: 64%

“…This approach derives the work done by transverse cracking in a laminate, using the stress intensity factor for an array of parallel cracks in an infinite transversely isotropic medium. Although simple and generally applicable to symmetric laminates as well as to cracking in multiple layers, the accuracy of this approach remains uncertain (Kuriakose and Talreja, 2004). The errors introduced by the assumption of a homogeneous infinite medium would presumably depend on how different the axial ply properties of the cracked ply are from those of the neighboring plies, as well as on the fact that the laminate thickness is finite and often only a few times greater than the crack length.…”

Section: Introductionmentioning

confidence: 99%

“…Among more advanced and accurate analytical works on bending analysis of laminates with transverse cracks are the stress transfer model of McCartney (McCartney, 2001, 2008McCartney and Bla´zquez, 2009;McCartney and Pierse, 1997) and the variational model developed by Kuriakose and Talreja (2004). The stress transfer model (McCartney and Pierse, 1997) is a two-dimensional analysis, which considers the stress and displacement components based on plane strain assumptions.…”

Section: Introductionmentioning

confidence: 99%

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Variational analysis of cracked general cross-ply laminates under bending and biaxial extension

Hajikazemi

Sadr

Talreja

2014

International Journal of Damage Mechanics

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In the current study, a variational model is developed for predicting stress transfer due to ply cracking in general cross-ply laminates subject to out-of-plane bending and biaxial in-plane loading. The model is valid for multiple ply laminates that can be nonsymmetric. Using the principle of minimum complementary energy, an optimal admissible stress field is derived that satisfies equilibrium, boundary, and traction continuity conditions. Natural boundary conditions are derived from the variational principle to overcome the limitations of the existing variational methods on the analysis of cracked general cross-ply laminates. Comparing laminates of glass/epoxy and graphite/epoxy with the available finite element results shows that stress components are in very good accordance with the analytical results. It is also shown that the existing variational models are specific cases of the current formulation. In the next step, the obtained stress field is used in conjunction with the principle of minimum complementary energy to get the effective stiffness modulus of a cracked general cross-ply laminate. It is indicated that the method provides a lower bound for the stiffness modulus of a cracked laminate.

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Section: Introductionsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational analysis of cracked general cross-ply laminates under bending and biaxial extension

Hajikazemi

Sadr

Talreja

2014

International Journal of Damage Mechanics

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“…In Kuriakose and Talreja (2004), an assumption that the stresses in the uncracked lamina not immediately next to the cracked lamina are not affected by the presence of the cracks in the cracked lamina was introduced to avoid this deficiency. Without supplying an extra boundary condition for an uncracked lamina, the applicability of all existing approaches in the literature, except those displacement-based ones, such as finite strips (Li et al, 1994) and finite elements, will be limited to cases having maximum of two uncracked laminae.…”

Section: Physical Boundary Conditionsmentioning

confidence: 99%

“…The so-called variational approach, as in Hashin (1985), Hu (1992, 1994), Kuriakose and Talreja (2004), as well as the analysis to be presented later in this paper, is a semi-variational approach, in fact, strictly speaking. A variational principle, viz.…”

Section: Introductionmentioning

confidence: 99%

Variation-based cracked laminate analysis revisited and fundamentally extended

Hafeez

2009

International Journal of Solids and Structures

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a b s t r a c tThe analyses of cracked laminates based on a variational principle and related approaches are appraised in this paper. The limitations of the existing methodology on the analyses of more general laminate configurations have been identified. It has been revealed that the limiting factor is the lack of boundary conditions for uncracked laminae. Natural boundary conditions have then been derived from the variational principle to meet the need. Such boundary conditions are mathematically sound but cannot be simply interpreted from the physical construction of the problem intuitively. A well posed boundary value problem has thus been formulated for laminates containing however many cracked and uncracked laminae. Appropriate mathematical tools can then be employed to solve the boundary value problem. The capability of analysing cracked laminates has been enhanced significantly, as a result.

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A variational method for analysis of laminates with parallel arrays of intralaminar cracks

Vinogradov

2019

Numerical Meth Engineering

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This paper presents a robust variational method for prediction of the effective thermoelastic properties of laminates with parallel, but not necessarily coplanar intralaminar cracks. Arbitrary laminate layup, crack patterns, and any in-plane forces and bending moments, and temperature change can be treated simultaneously. The method is based on the principle of minimum complementary energy. The admissible in-plane stress components are assumed to be linear through the ply thickness. Simple matrix expressions are derived for the effective compliance matrix, thermal expansions and curvatures, and specific heat of a cracked laminate. Predictions for the Young's modulus, Poisson's ratio, shear modulus, flexural rigidity, and thermal expansion as functions of crack density for various laminates of symmetric and nonsymmetric layups demonstrated excellent agreement with experimental results of seven independently published studies. Accuracy and robustness of the method are complemented by the fact that no experimentally fitted parameters are required. It is shown that the same formalism can be applied to analysis of closed intralaminar cracks, as well as nonuniform and nonsymmetrical distributions of cracks.

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Variational solutions to stresses in cracked cross-ply laminates under bending

Cited by 18 publications

References 19 publications

Variational analysis of cracked general cross-ply laminates under bending and biaxial extension

Variational analysis of cracked general cross-ply laminates under bending and biaxial extension

Variation-based cracked laminate analysis revisited and fundamentally extended

A variational method for analysis of laminates with parallel arrays of intralaminar cracks

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