Structural Mechanics Applications using Strong Formulation Finite Element Method

Many practical applications in civil, mechanical and aerospace engineering are difficult to perform and analyze due to the presence of irregular geometries, different or graded materials, as well as cracks, curved boundaries and load discontinuities [1-2]. These problems can be solved by dividing the physical domain into finite elements, as the well-known Finite Element Method (FEM) does. With regard to a new numerical approach, termed Strong Formulation Finite Element Method (SFEM), inside each element a higher order numerical scheme, such as Differential Quadrature (DQ) method, is used for solving the governing equations in their strong form [3-7]. The SFEM approach combines the two DQ and FEM techniques to obtain a hybrid scheme. The former method is used to discretize the differential equations inside each element, the latter for the mapping technique. It should be noted that the SFEM is a numerical procedure that subdivides the domain in several elements and solves the strong form of the differential equations inside each subdomain mapped on the computational element. Several numerical applications are performed to demonstrate convergence, reliability and stability of the SFEM. In particular, both one-dimensional and two-dimensional structural systems are investigated. All the numerical results are compared to analytical and semi-analytical solutions found in literature and to the values obtained through FE modeling.