The warping of unsymmetrically laminated composite is induced by the thermal residual curing stress generated during the fabrication process. Classical lamination theory predicts the cured shapes of cross-ply laminate to be a saddle. Experimental observations, however, indicate some cross-ply laminated composites have cylindrical room-temperature shapes. This anomalous behavior is explained by the extension of classical lamination theory which involves nonlinear strain-displacement relations. Since in-plane residual shear strain exists in most cases of cross-ply laminates, formulating the nonlinear algebraic equations, the analysis including in-plane shear strain for the cross-ply laminates is presented. Present results indicate that thermal residual shear strain is negligible in cases that width-to-thickness ratios are very small or large. However, the significant amount of the shear strain exists in the range of medium width-to-thickness ratios where the bifurcation point occurs. From the displacement functions for the cross-ply laminates, the formulation which treats the curvatures and principal direction of curvature is derived for unsymmetric laminated composites with arbitrary lay-up angles. To allow freedom to the spatial variation of strains, strain and displacement functions are generalized to obtain the governing equation for general laminates with arbitrary lay-up angles. It is shown that principal direction of curvature calculated from classical lamination theory agrees with this analysis in the limited range of length-to-thickness ratios of laminates. Curvatures and principal direction of curvature in unsymmetric laminate depend upon the length-to-thickness, number of layer, lay-up angles, temperature, aspect ratio of the laminates. Curvatures are calculated for square and rectangular laminates as using the nonlinear Newton-Rapson iteration method numerically. It is shown that present numerical results are in good agreement with experimental results.
