Abstract
Recursive formulas are derived for the determination of the curvature and internal stresses in a uniformly heated multilayer strip made of n perfectly bonded isotropic layers in terms of the curvature and stresses in the strip with n − 1 bonded layers. This is accomplished by reducing the problem to solving two linear algebraic equations for two unknowns, the curvature of the strip and the axial force in the layer, from which all other forces, moments, and stresses readily follow. The presented analysis complements the authors’ previous analysis which is based on a developed matrix algorithm for the simultaneous determination of the curvature and stresses in all layers. The derived formulas are applied to trilayer and quadralayer strips. Simple expressions are obtained in the case when all layers have equal thicknesses and equal moduli of elasticity.
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