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Determining Shear Stress Distribution in a Laminate
 Created: Friday, 01 October 2010
The simplified shear solution does not require solution of a particular boundary value problem.
A “simplified shear solution” method approximates the throughthickness shear stress distribution within a composite laminate based on an extension of laminated beam theory. The method does not consider the solution of a particular boundary value problem; rather, it requires only knowledge of the global shear loading, geometry, and material properties of the laminate or panel. It is thus analogous to lamination theory in that plylevel stresses can be efficiently determined from global load resultants at a given location in a structure and used to evaluate the margin of safety on a plybyply basis. The simplified shear solution stress distribution is zero at free surfaces, continuous at ply boundaries, and integrates to the applied shear load. The method has been incorporated within the HyperSizer® commercial structural sizing software to improve its predictive capability for designing composite structures.
The HyperSizer structural sizing software is used extensively by NASA to design composite structures. In the case of throughthickness shear loading on panels, HyperSizer previously included a basic, industrystandard, method for approximating the resulting shear stress distribution in sandwich panels. However, no such method was employed for solid laminate panels.
The purpose of the innovation is to provide an approximation of the throughthickness shear stresses in a solid laminate given the throughthickness shear loads (Q_{x} and Q_{y}) on the panel. The method was needed for implementation within the HyperSizer structural sizing software so that the approximated plylevel shear stresses could be utilized in a failure theory to assess the adequacy of a panel design.
The simplified shear solution method was developed based on extending and generalizing bimaterial beam theory to platelike structures. It is assumed that the throughthickness shear stresses arise due to local bending of the laminate induced by the throughthickness shear load, and by imposing equilibrium both vertically and horizontally, the throughthickness shear stress distribution can be calculated. The resulting shear stresses integrate to the applied shear load, are continuous at the ply interfaces, and are zero at the laminatefree surfaces. If both Q_{x }and Q_{y} shear loads are present, it is assumed that they act independently and that their effects can be superposed. The calculated shear stresses can be rotated within each ply to the principal material coordinates for use in a plylevel failure criterion.
The novelty of the simplified shear solution method is its simplicity and the fact that it does not require solution of a particular boundary value problem. The advantages of the innovation are that an approximation of the thoughthickness shear stress distribution can be quickly determined for any solid laminate or solid laminate region within a stiffened panel.
This work was done by Brett A. Bednarcyk and Jacob Aboudi of Ohio Aerospace Institute and Phillip W. Yarrington of the Collier Research Corp. for Glenn Research Center. For more information, download the Technical Support Package (free white paper) at www.techbriefs.com/tsp under the Materials category.
Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Innovative Partnerships Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW184411.
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