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Free-corner Effects in Cross-ply Laminates: An Approximate Higher-order Theory Solution

mittelstedt{at}imrn30.imr.mb.uni-siegen.de

Wilfried Becker

Department of Mechanical Engineering Institute of Mechanics and Control Engineering Siegen University, Paul-Bonatz-Straße 9–11 D-57068 Siegen, Germany

Like in the well-known free-edge effect situation, stress fields in the vicinity of free corners of layered plates exhibit a distinct three-dimensional and singular behavior and thus represent an important technical situation. Nevertheless, there are only few thorough investigations available concerning stress concentrations near free laminate corners. Since numerical analyses of stress concentration phenomena in composite laminates are computationally expensive, the present contribution is devoted to a simple closed-form higher-order theory approach for the calculation of displacements, strains, and stresses in the vicinity of a rectangular corner of a symmetric cross-ply laminate under thermal load. Appropriate representations for the displacement field in the manner of a single-layer theory with unknown inplane components and assumed trigonometric functions through the thickness yield closed-form expressions for the strains and stresses throughout the whole laminate. The inplane displacement functions are determined by equilibrium considerations in an integrated form with the solution of some resultant characteristic equations. Boundary conditions are fulfilled in an integral sense. The present approach can be applied easily, requires little computational effort and is in good conformity with comparative finite-element calculations and other closed-form analyses.

Key Words: layered plates • composite laminates • free-edge effect • free-corner effect • interlaminar stresses • closed-form analysis • finite elements

Journal of Composite Materials, Vol. 37, No. 22, 2043-2068 (2003)
DOI: 10.1177/0021998303036265


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