Hanjiang Chang^1,2,*, Qiang Tian¹, Haiyan Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 825-860, 2023, DOI:10.32604/cmes.2023.022774

Abstract To model a multibody system composed of shell components, a geometrically exact Kirchhoff-Love triangular shell element is proposed. The middle surface of the shell element is described by using the DMS-splines, which can exactly represent arbitrary topology piecewise polynomial triangular surfaces. The proposed shell element employs only nodal displacement and can automatically maintain C¹ continuity properties at the element boundaries. A reproducing DMS-spline kernel skill is also introduced to improve computation stability and accuracy. The proposed triangular shell element based on reproducing kernel DMS-splines can achieve an almost optimal convergent rate. Finally, the proposed shell element is validated via three… More > Graphic Abstract

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.3, pp. 249-284, 2010, DOI:10.3970/cmes.2010.066.249

Abstract We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and 1D NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested by enforcing the condition of… More >

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 107-154, 2010, DOI:10.3970/cmes.2010.065.107

Abstract The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries. Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials. There is thus a case for combining these advantages in a so-called hybrid scheme or a 'smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C^p(p ≥ 1) continuity. One such recent attempt, a… More >