Layer-wise optimization of elliptical laminates with curvilinear fibers

Abstract

The lay-ups of symmetric variable stiffness composite laminated elliptical plates with curvilinear fibers are optimized for the maximum frequencies of the lowest three modes using the layer-wise optimization method. Two design variables and three constraints are considered. The fiber paths are constructed using the method of shifted paths. The laminate is modeled as one curved hierarchical finite element. The formulation is based on the first-order shear deformation theory. The blending function method is used to model accurately the geometry. New results for the optimal lay-ups that maximize the natural frequencies of the lowest three modes are obtained. The method is validated based on convergence test and comparison with published results for symmetric constant stiffness composite laminated elliptical plates with rectilinear fibers. A parametric study is performed showing the effects of aspect ratio, thickness ratio, modulus ratio, number of layers, and boundary constraint on the optimal solutions.

Keywords:

• Optimal lay-up
• maximum natural frequency
• elliptical laminate with curvilinear fibers
• variable stiffness
• curved hierarchical finite element
• layer-wise optimization