An integrated procedure for three-dimensional structural analysis with the finite cover method

In this paper an integrated procedure for three-dimensional (3D) structural analyses with the finite cover method (FCM) is introduced. In the pre-process of this procedure, the geometry of a structure is modelled by 3D-CAD, followed by digitization to have the corresponding voxel model, and then the structure is covered by a union of mathematical covers, namely a mathematical mesh independently generated for approximation purposes. Since the mesh topology in the FCM does not need to conform to the physical boundaries of the structure, the mesh can be regular and structured. Thus, the numerical analysis procedure is free from the difficulties mesh generation typically poses and, in this sense, enables us to realize the mesh-free analysis. After formulating the FCM with interface elements for the static equilibrium state of a structure, we detail the procedure of the finite cover modelling, including the geometry modelling with 3D-CAD and the identification of the geometry covered by a regular mesh for numerical integration. Prior to full 3D modelling and analysis, we present a simple numerical example to confirm the equivalence of the performance of the FCM and that of the standard finite element method (FEM). Finally, representative numerical examples are presented to demonstrate the capabilities of the proposed analysis procedure.