Geometrically Accurate Infinitesimal-Rotation Spatial Finite Elements

In this paper, a general procedure is used to develop new geometrically accurate infinitesimalrotation finite elements (FE). New spatial beam, plate, and solid elements are developed in terms of constant geometric coefficients obtained using the matrix of position vector gradients. The spatial beam, plate, and solid element shape functions are developed using the displacement field of the absolute nodal coordinate formulation (ANCF). These elements are suited for developing reduced-order models for structural and multibody system (MBS) analyses, particularly when the floating frame of reference (FFR) formulation is used. The initial geometry of the new elements, referred to as the ANCF/FFR elements, is related to B-splines and NURBS (Non-uniform rational B-splines) by a linear mapping, and therefore, their use does not lead to geometry distortion when geometry models are converted to analysis meshes. The main contribution of this technical note is the proposed general procedure for the development of the geometrically accurate spatial ANCF/FFR elements and demonstrating the use of this procedure by developing the ANCF/FFR displacement field of three different spatial elements.