Finite Element Analysis of Structures Using C1-Continuous Cubic B-Splines or Equivalent Hermite Elements

Constrained Interpolation via Cubic Hermite Splines

Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation.  It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...

A Higher Order B-Splines 1-D Finite Element Analysis of Lossy Dispersive Inhomogeneous Planar Layers

In this paper we propose an accurate and fast numerical method to obtain scattering fields from lossy dispersive inhomogeneous planar layers for both TE and TM polarizations. A new method is introduced to analyze lossy Inhomogeneous Planar Layers. In this method by applying spline based Galerkin’s method of moment to scalar wave equation and imposing boundary conditions we obtain reflection and...

Bivariate C1 Quadratic Finite Elements and Vertex Splines

Following work of Heindl and of Powell and Sabin, each triangle of an arbitrary (regular) triangulation A of a polygonal region ii in R is subdivided into twelve triangles, using the three medians, yielding the refinement A of A , so that C quadratic finite elements can be constructed. In this paper, we derive the Bézier nets of these elements in terms of the parameters that describe function a...

Geometric Hermite interpolation by cubic G1 splines

In this paper, geometric Hermite interpolation by planar cubic G1 splines is studied. Three data points and three tangent directions are interpolated per each polynomial segment. Sufficient conditions for the existence of such G1 spline are determined that cover most of the cases encountered in practical applications. The existence requirements are based only upon geometric properties of data a...

Finite Element Approximation with Hierarchical B-Splines