Many natural materials, such as bones and trees, indicate non-homogenous anisotropy, and have higher performance than the homogenous one. To exploit those properties for design of artificial engineering structures, laminated composite shells reinforced by curvilinear fibers are analyzed to reveal their vibration and buckling properties. They have local anisotropy due to curved fibers, and show different properties from homogenous one. Projections of contour lines for cubic polynomial surfaces to the horizontal plane represent curvilinear fibers. This make is possible to represent multi-valued function and have large degree of freedom. The natural frequencies and critical buckling loads are calculated by using FEM, where the element coordinate system is translated to the tangential direction of the contour lines in the element centroids at each element. The results are given for a cylindrical shell and a shell with non-uniform curvature. It turns out that the curvilinear fibers have strong possibility to improve vibration and buckling performance of composite shell structures.
