Spline finite elements for thin plates and shells of arbitrary geometry - Luah, Mui Huang. (2009)
The development of plate and shell elements has been a most important topic in the research of finite element method. In the present work, two spline finite elements, namely a thin plate, and a thin shell element applicable to the analysis of arbitrary plate and shell structures are developed. The elements are 9-node, quadrilateral, Kirchhoff-type C elements derived from the conventional displacement approach. Three new features of finite element formulation are included in the development and these are: (i) the use of B3-spline shape functions for the interpolations of both in-plane and out-of-plane displacements of a general thin shell element; (ii) the use of "displacement constraints" and "parameters shifting" to construct a finite element model; and (iii) a proposed modified version of the Koiter's thin shell equations is employed. The resulting elements have advantages such as high accuracy and efficiency, attractive nodal configuration (resembles that of SemiLoof element), insensitive to mesh distortion, etc.