An approximate approach to the calculation of displacements, strains, and stresses near edges and corners in symmetric rectangular layered plates of dissimilar isotropic materials under thermal load is presented. In the thickness direction the plate is discretized into an arbitrary number of sublayers/mathematical layers. A layerwise linear displacement field is formulated such that the terms according to classical laminate plate theory are upgraded with unknown in-plane functions and a linear interpolation scheme through the layer thickness in order to describe edge and corner perturbations. By virtue of the principle of minimum potential energy the governing coupled Euler–Lagrange differential equations are derived, which in the case of free-edge effects allow a closed-form solution for the unknown inplane functions. Free-corner effects are investigated by combining the displacement formulations of the two interacting free-edge effects. Hence, all state variables in the plate are obtained in a closed-form manner. Boundary conditions of traction free plate edges are satisfied in an integral sense. The present methodology is easily applied and requires only reasonable computational expenses.
Thermoelastic Fields in Boundary Layers of Isotropic Laminates
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, November 2, 2003; final revision, June 17, 2004. Associate Editor: D. A. Kouris. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California - Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Mittelstedt, C., and Becker, W. (February 1, 2005). "Thermoelastic Fields in Boundary Layers of Isotropic Laminates ." ASME. J. Appl. Mech. January 2005; 72(1): 86–101. https://doi.org/10.1115/1.1827247
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