A novel method to apply neumann boundary conditions in the isogeometric analysis (IGA) of beam with 1-D formulation

摘要

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.