A Mathematical Model for the Analysis of Elastic Field in a Stiffened Cantilever of Laminated Composite

A mathematical model is developed for the analytical solution to elastic filed in a deep stiffened cantilever beam of laminated composite under mixed boundary conditions. The two displacement parameters associated with the two-dimensional elasticity problems are defined in terms of a single displacement potential function such that one of the equilibrium equations is satisfied automatically. This reduces the problem to the solution of a single fourth-order partial differential equation, which is solved in terms of Fourier series. To present some numerical results, cantilever beams of glass/epoxy cross-ply and angle-ply laminated composites are considered and different components of stress and displacement at different sections of the beam are presented. The effects of laminate stacking sequence and ply-angle of the cross-ply and angle-ply composite beams, respectively, on the elastic field are analyzed. The numerical results justify that the present mathematical model is simple whereas capable to generate exact results of elastic field in a cantilever beam even at the critical regions of supports and loadings