Beam theory in spline parametric cooridinate. Part I

Abstract

For defining geometry and displacement of arbitrary curved beam in Euclidean E3 space, using simple and rational basis spline, Bernoulli-Euler beam finite element is defined. Because geometry of line structures is exactly presented with rational basis spline and wanted continuity at the common points between adjacent segments is achieved (C>1), the generalized coordinates for izogeometric finite element are only displacements of control points. The stiffness matrix and equivalent control forces of isogeometric Bernoulli-Euler beam elements are defined under assumption that spline parametric coordinate (beam axis) and principal moments of inertia of cross section have convective character.