Strong form finite elements: formulation and applications
It is proven that many practical applications in civil, mechanical and aerospace engineering are difficult to analyze due to irregular geometries, variable materials, cracks, curved boundaries and load discontinuities. These problems can be solved dividing the physical domain into finite elements, similarly to the well-known Finite Element Methods (FEM). 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. This method employs a hybrid structure given by DQ and FEM. The former is used for discretize the differential equations inside each element, the latter for the mapping technique. In other words, 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 semianalytical solutions found in literature and to the values obtained through FE modeling.