A novel method to apply Neumann boundary conditions in the Isogeometric Analysis (IGA) of beam with 1-D formulation

Abstract

Purpose

This paper proposes a novel approach to impose the Neumann boundary condition for isogeometric analysis (IGA) of Euler–Bernoulli beam with 1-D formulation. The proposed method is for only IGA in which it is difficult to handle the Neumann boundary conditions. The control points of B-spline are equivalent to nodes in finite element method. With 1-D formulation, it is not possible to accommodate multiple degrees of freedom in IGA. This case arises in the analysis of beams. The paper aims to propose a way to work around this issue in a simple way.

Design/methodology/approach

Neumann boundary conditions, which are even-order derivatives (example: double derivative) of the primary variable, are inherently satisfied in the weak form. Boundary conditions with an odd number of derivatives (example: slope) are imposed with the introduction of a new penalty matrix.

Findings

The proposed method can impose a slope boundary condition for IGA of a beam using 1-D formulation.

Originality/value

From the literature, it can be observed that the beam is formulated in 1-D by considering it as either a rotation-free element or a 2-D formulation by considering shear strain along with the normal strain. The work represents 1-D formulation of a beam while considering the slope boundary condition, which is easy and effective to formulate, compared with the slope boundary conditions reported in previous works.

Citation

Mondal, S.K., Gondegaon, S. and Voruganti, H.K. (2017), "A novel method to apply Neumann boundary conditions in the Isogeometric Analysis (IGA) of beam with 1-D formulation", World Journal of Engineering, Vol. 14 No. 6, pp. 538-544. https://doi.org/10.1108/WJE-11-2016-0143