MATEC Web Conf.
Volume 258, 2019International Conference on Sustainable Civil Engineering Structures and Construction Materials (SCESCM 2018)
|Number of page(s)||7|
|Section||Structural Dynamics and Earthquake Engineering, Structures in Severe Environment, Structural Analysis|
|Published online||25 January 2019|
Two nodes cusp geometry beam element by using condensed IGA
1 Department of Architecture, College of Engineering, Nihon University, Koriyama, Japan
2 Structural and Material Laboratory, Diponegoro University, Tembalang, Semarang, Indonesia
* Corresponding author: email@example.com
A cusp is a curve which is made by projecting a smooth curve in the 3D Euclidean space on a plane. Such a projection results in a curve whose singularities are self-crossing points or ordinary cusps. Self-crossing points created when two different points of the curves have the same projection at a point. Ordinary cusps created when the tangent to the curve is parallel to the direction of projection on a single point. The study of a cusp geometry beam is more complex than that of a straight beam because the structural deformations of the cusp geometry beam depend also on the coupled tangential displacement caused by the singular geometry. The Isogeometric Approach (IGA) is a computational geometry based on a series of polynomial basis functions used to represent the exact geometry. In IGA, the cusp geometry of the beam element can be modeled exactly. A thick cusp geometry beam element can be developed based on the Timoshenko beam theory, which allows the vertical shear deformation and rotatory inertia effects. The shape of the beam geometry and the shape functions formulation of the element can be obtained from IGA. However, in IGA, the number of equations will increase according to the number of degree of freedom (DOF) at the control points. A new condensation method is adopted to reduce the number of equations at the control points so that it becomes a standard two-node 6-DOF beam element. This paper highlights the application of IGA of a cusp geometry Timoshenko beam element in the context of finite element analysis and proposes a new condensation method to eliminate the drawbacks elevated by the conventional IGA. Examples are given to verify the effectiveness of the condensation method in static and free vibration problems.
© The Authors, published by EDP Sciences, 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.