Mechanics of Structural Components by Using a Numerical Approach Based on Blending Functions Mapping and a Strong Formulation

Generally, modelling composite materials in engineering design is a complicated subject because inclusions can have an arbitrary shape within a homogeneous matrix. In this matter, several numerical approaches have been introduced to overcome this particular issue. If a standard finite element (FE) model is used, the discretization in such cases must be very refined near the discontinuities due to low order approximating polynomials. This results in heavy numerical models that are complex to solve. Moreover, since the stress jumps among the elements within the mesh are not continuous the approximation of such field is not always accurate. For these reasons, the authors are proposing a new numerical approach based on the strong formulation which needs continuous displacements and stresses among the elements. The present feature gives the possibility of having a complete continuous field in the whole mesh and of presenting more accurate results if compared to classic FE approaches. This important result is achieved due to the strong formulation that solves the partial differential system of equations that govern the physical problem. Moreover, the present paper presents a study wherein blending functions are utilized in the mapping technique to approximate the boundaries of the elements in the given mesh. Such blending functions are taken as NURBS (Not-Uniform Rational B-Splines) from CAD software. This novelty allows a more accurate geometrical approximation of the patches with consequent reduction on the total number of degrees of freedom since less elements are needed for accurately approximates the discontinuities present in the physical problem.