Three dimensional multilayer composite finite element method for stress analysis of composite laminates

This thesis covers four subjects. These are the formulation of the hybrid variational functional of partial stress finite elements for the stress analysis of laminated composite structures, development of the iso-function method to set up the assumed stress field which is free of spurious kinematic modes in the hybrid finite elements, development of the method of formulating multilayer composite finite element for three dimensional stress analysis of composite laminates and the applications of multilayer composite finite elements for interlaminar stress analysis of several examples.; In order to satisfy the continuous and natural discontinuous conditions in laminated composite structures, the three transverse stresses and the three in-plane strains are taken as basic variables. The basic equations based on the basic variables for stress analysis are given. The variational functional is derived by satisfying these basic equations with the application of the weighted residual method. The iso-function method is developed to set up the partial stress field which is required to form the finite element based on above variational functional. This method gives an easy way to form a stress field and ensures that the stress field is free from zero-energy modes. Three 3-D composite elements are formulated based on the variational functional and by incorporating the iso-function technique. To enforce the satisfaction of the continuity condition at interlaminar surfaces and traction free condition at the upper/lower faces of a laminate, the composite elements are multilayered to formulate a super finite element which is named as multilayer composite element. The continuity of the three transverse stresses across the laminate thickness is assured a priori by introducing a partial stress field vector associated to the lower and upper surfaces of a lamina.; By means of multilayer composite element, stresses in a beam and in a rectangular laminated plate under transverse loading are calculated. Results are compared with Exact elastic theory solutions, classical lamination theory solutions, hybrid finite element solutions and high order shear deformation theory solution. The analysis of straight edge effect problem demonstrates that the stress distributions predicted by the present multilayer composite finite element also satisfy traction-free-edge condition. The present finite element has clear advantage over displacement formulated finite element and computationally more efficient than the conventional hybrid elements.