PIECEWISE-LINEAR WARPING THEORY FOR MULTILAYERED ELASTIC BEAMS

Warping due to transverse shear in multilayered elastic beams is studi ed in this paper. The Betnoulli-Kirchhoff hypothesis that plane sectio ns remain plane after deformations, with independent rotations, is ass umed for each lamina to account for the out-of-plane deformation of th e composite cross section. The effects of shear are included by taking the rotations independent of the transverse deflection, as in Timoshe nko beam theory. The result is a simple piecewise linear warping theor y for layered composite beams. The solution to the governing equations is presented in terms of the eigenvalues and eigenvectors of a genera lized matrix eigenvalue problem associated with the coefficient matric es that appear in the governing equations. The problem of a two-layere d cantilever beam subjected to a uniformly distributed loading is solv ed in detail to show the effects of different elastic moduli on the in terfacial shear stress. Compared with a finite-element solution, the c urrent theory yields significant improvement over elementary beam theo ry (excluding warping) in predicting the interface shear stress.