Static analysis of laminated composite beams based on higher-order shear deformation theory by using mixed-type finite element method

In this paper, mixed finite element (MFEM) equations which are based on a functional are obtained by using the Gâteaux differential (GD) for laminated composite beams. Higher-order shear deformation theory (HOBT) including non-linear distribution of shear stress through thickness of laminated beam is presented. Differential field equations of composite beams are derived from virtual displacement principle. These equations were trans- formed into the operator form and using the mathematical advantages of the proposed the variational method, a functional with geometric and dynamic boundary conditions was obtained after determining that they provide the potential condition with the help of the GD method. Applying MFEM based on this functional, a beam element namely HOBT10 is derived which have 10 degrees of freedoms. There are displacement, rotation, bending and higher-order bending moments, shear force. In addition, Euler-Bernoulli and first order shear deformation beam theories solutions have been made for comparison and better comprehension of solutions and results of static analyses of laminated composite beams. The performance of the element is verified by applying the method to some test problems.