Abstract
The variable-length arbitrary Lagrange–Euler absolute nodal coordinate formulation (ALE-ANCF) finite element, which employs nonrational interpolating polynomials, cannot exactly describe rational cubic Bezier curves such as conic and circular curves. The rational absolute nodal coordinate formulation (RANCF) finite element, whose reference length (undeformed length) is constant, can exactly represent rational cubic Bezier curves. A new variable-length finite element called the ALE-RANCF finite element, which is capable of accurately describing rational cubic Bezier curves, is proposed and was formed by combining the desirable features of the ALE-ANCF and RANCF finite elements. To control the reference length of the ALE-RANCF element within a suitable range, element segmentation and merging schemes are proposed. It is demonstrated that the exact geometry and mechanics are maintained after the ALE-RANCF element is divided into two shorter ones, and compared with the ALE-ANCF elements, there are smaller deviations and oscillations after two ALE-RANCF elements are merged into a longer one. Numerical examples are presented, and the feasibility and advantages of the ALE-RANCF finite element are demonstrated.
Highlights
The sliding joint on a flexible beam [1–4] is widely used in the dynamic modeling of practical engineering systems, such as pantograph/catenary systems [5,6], tethered satellite systems [7,8], and arresting systems [9]
The second aim of this study is to propose an element length-control scheme to control the reference length of the ALE-rational absolute nodal coordinate formulation (RANCF) element within a suitable range
The ALE-RANCF finite element was established by combining the desirable features of the ALE-absolute nodal coordinate formulation (ANCF) and the RANCF finite elements
Summary
The sliding joint on a flexible beam [1–4] is widely used in the dynamic modeling of practical engineering systems, such as pantograph/catenary systems [5,6], tethered satellite systems [7,8], and arresting systems [9]. Nonrational functions cannot be used to exactly represent some geometric shapes such as conic and circular shapes; the ALE-ANCF beam elements that employ nonrational interpolating polynomials cannot exactly describe conic and circular curves. This problem can be solved by substituting the nonrational interpolating polynomials with rational interpolating polynomials, which were used in the rational absolute nodal coordinate formulation (RANCF) finite elements [20–24]. The primary aim of this work is to combine the desirable features of the ALE-ANCF finite elements and the RANCF finite elements to establish a new variable-length ALE-RANCF finite element that could accurately capture rational cubic Bezier geometric shapes.
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