An analytical solution for the thermal stresses at the free edges of laminated plates

Webber, J. P. H.; Morton, SK

doi:10.1016/0266-3538(93)90173-e

Cited by 38 publications

(17 citation statements)

References 15 publications

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“…(17) subject to the boundary conditions in (11) and (19). To this end, it is noted that the boundary conditions in (19) will identically be satisfied if the following expressions for the displacement components in (17) are assumed:…”

Section: Case Imentioning

confidence: 99%

Accurate Determination of Interlaminar Stresses in General Cross-Ply Laminates

Tahani

Nosier

2004

Mechanics of Advanced Materials and Structures

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Reddy's layerwise theory is used to investigate analytically the interlaminar stresses near the free edges of general (unsymmetric and symmetric) cross-ply composite laminates with various boundary conditions subjected to mechanical and hygrothermal loadings. Laminates with finite dimensions are considered and full three-dimensional stresses in the interior and the boundary-layer regions are calculated. The results obtained from this theory are compared with those available in the literature. It is found that the theory can predict very accurately the stresses in the interior region and near the free edges of both finite and long laminates.It is well known that a mismatch in elastic properties and thermal and hygroscopic expansion coefficients between adjacent plies of composite laminates causes interlaminar stress concentrations near the edges of a laminate where we have material discontinuity. These stresses, on the other hand, can initiate heterogeneous damage in the forms of delamination and transverse cracking and may cause the damage to propagate to a substantial region of the laminate, resulting in a significant loss of strength and stiffness. Also, in the edge zone of the laminate (also known as the boundary-layer region), it has been shown that the state of stresses is three-dimensional (3D) in nature and the classical lamination theory (CLT), which assumes the plane stress condition, cannot be employed [1,2]. Over the past three decades numerous investigators have used a variety of methods to attempt to calculate these stresses near laminate's free edges ; however, because of inherent complexities involved in the problem, no exact solution is known for elasticity equations. Therefore, various approximate methods for determining the interlaminar stresses are documented in the literature. These methods may, for convenience, be classified as either analytical or numerical. Because of the exceptionally large number of papers on the subject matter, only the pertinent pioneering works are referred here. The interested reader will find sufficient references to cover the literature in more depth in the review article by Kant and Swaminathan [3].

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Section: Case Imentioning

confidence: 99%

Accurate Determination of Interlaminar Stresses in General Cross-Ply Laminates

Tahani

Nosier

2004

Mechanics of Advanced Materials and Structures

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“…Thus, combining Eqs. (1), (6), and (7), one can write the far-field in-plane stress components in the k\h layer as a*> = Af + A? X3 ^ A*' + <> + K O > + A*>> 3 (10) 4« = B*> + Bf * 3 -B*> + < + B«> + B$ X3 (11) = (12) In these expressions, the contribution from the thermal loading has been separated from that of mechanical loading.…”

Section: Mechanical and Thermal Coefficients Of Stressesmentioning

confidence: 99%

“…On the other hand, investigations on thermally induced stresses in composite laminates have revealed that edge effects induced by a uniform temperature change can result in interlaminar stresses of significant amounts. 4 " 6 This suggests that thermal loading, when applied with controlled magnitudes and spatial gradients, has the potential to compensate for the interlaminar stresses that have been caused by mechanical loading. Recently, Kim and Atluri 7 have shown that a thermomechanical control near the free edges with through-thickness temperature variations is indeed an efficient means for this purpose and provided analytical solutions for the optimal temperature distributions.…”

Section: Introductionmentioning

confidence: 99%

Optimal through-thickness temperature gradients for control of interlaminar stresses in composites

Kim

Atluri

1995

AIAA Journal

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Analytical solutions are sought for optimal temperature distributions to control the interlaminar stresses near the free edges of composite laminates subjected to uniaxial loading. Optimal through-thickness temperature gradients are obtained by minimizing appropriate performance indices that are functions of the far-field properties, with respect to the through-thickness temperature differences. Through the application of these temperatures, effects of local mismatches as well as global mismatches in two of the elastic properties, the Poisson's ratio and coefficient of mutual influence, are minimized. Numerical examples are given for several lay-ups made of graphite epoxy. It is shown that for a cross-or angle-ply laminate a uniform temperature rise or drop can completely eliminate all of the interlaminar stresses, whereas for other laminates nonuniform temperature distributions must be applied to minimize the stresses.

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“…In an attempt to efficient analysis of edge-effect problem of symmetric laminates, Kassapoglou and Lagace (1986) obtained a closed-form solution utilizing the force balanced method and the principle of minimum complementary energy. A similar technique to that of Kassapoglou and Lagace (1986) is presented by Webber and Morton (1993) to evaluate thermally induced interlaminar stresses. Based on the firstorder shear deformation theory (FSDT) Rohwer et al (2001) developed a method to compute interlaminar stresses in composite laminates subjected to thermal loading.…”

Section: Introductionmentioning

confidence: 98%

Free-edge stresses in antisymmetric angle-ply laminates in extension and torsion

Nosier

Bahrami

2006

International Journal of Solids and Structures

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The first-order shear deformation theory and the layerwise theory of laminated plates are employed to analyze the edgeeffect problem of an antisymmetric angle-ply laminate subjected to arbitrary combinations of extensional and torsional loads. The first-order theory is used for predicting the unknown constant parameters appearing in the reduced displacement field of elasticity which, on the other hand, signify the global behavior of the laminate. A layerwise theory is then utilized to determine the local interlaminar stresses within the boundary-layer regions of laminates. In order to closely examine the behavioral characteristics of interlaminar stresses, various numerical examples are presented for different antisymmetric angle-ply laminates under an axial force and a torque.

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An analytical solution for the thermal stresses at the free edges of laminated plates

Cited by 38 publications

References 15 publications

Accurate Determination of Interlaminar Stresses in General Cross-Ply Laminates

Accurate Determination of Interlaminar Stresses in General Cross-Ply Laminates

Optimal through-thickness temperature gradients for control of interlaminar stresses in composites

Free-edge stresses in antisymmetric angle-ply laminates in extension and torsion

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