Generalized Differential Quadrature Finite Element Method for Arbitrary Shaped Composite Structures

The basic concept of the Generalized Differential Quadrature Finite Element Method (GDQFEM), for solving composite structures having an arbitrary domain geometry, consists in separating the problem domain into many sub-domains or elements. The mapping technique is used to transform the fundamental system of equations, the compatibility conditions of the adjacent sub-domains and the boundary conditions defined on the physical sub-domain into the regular master element in the computational domain. Pursuing the GDQFEM, the differential problem of an arbitrary shaped composite structure can be converted into an algebraic system. The GDQFEM is hinged upon a different approach compared to the Finite Element Method, where the weak formulation is used. This novel approach is based on the idea of compatibility conditions between two boundaries. In order to capture the discontinuity, without losing accuracy, the compatibility conditions along the element boundaries are correctly applied when the assembly procedure is performed. The strong form of the fundamental equations and of the boundary conditions are used and the order of the problem does not need to be reduced. Also in handling complex physical problems, each discontinuity is treated within a compatibility condition, either between two sub-domains or as a standard boundary condition. The domain relations remain unchanged because each sub-domain is only connected between their boundaries. The convergence of the solution can be achieved usually by either increasing the number of elements or nodes per element. In order to verify the accuracy of GDQFEM, the analytical results concerning particular shape composite structures are compared with the corresponding numerical solutions.