Edge Stresses in a Laminated Composite Strip Subjected to Axial Temperature Gradients

One of the most severe problems associated with the use of laminated composite structures in thermal environments is the susceptibility to delamination due to the edge effect stresses arising from the thermal expansion mismatch between the constituent laminae. In addition, the problem may be compounded by the introduction of extreme thermal gradient effects as well. Trade studies to develop a satisfactory design for these types of thermal environments have heretofore been rather limited due to the lack of accurate analytical assessments for the edge effects that arise from these thermal loads. The predominant amount of investigation for these types of thermal gradient problems has been restricted to detailed numerical finite element analyses that do not lend to rapid concurrent engineering design processes. No analytical solution has been available to address the thermoelastic edge effects in composite laminates resulting from thermal gradients. In this paper, a combination of Airy stress functions and direct displacement functions is utilized to obtain the plane elasticity solution for the stresses and displacements in a multilayer laminated anisotropic strip subjected to a temperature gradient that is arbitrarily symmetric in the longitudinal direction. The solution cannot be guaranteed to satisfy the free edge normal traction requirement since only resultant force is enforced to zero; however, convergence for enforced zero transverse slope at the strip ends can be established, as the eigenfunctions are orthogonal. Thus the solution is exact for these edge conditions. Numerical results are presented for several examples and compared to those obtained from our own MSC/NASTRAN finite element analyses. The correlation with the finite element numerical results was determined to verify the solution and indicated application of the solution as an approximation to free edge engineering problems is very reasonable for a broad range of practical cases involving temperature gradient effects.