Abstract
A pipe element developed earlier for the analysis of combined large bending and torsional deformations of blood vessels under static loading is extended to model behavior in the presence of large rotations and time-varying external forces. As in the case of the earlier element, the enhanced element supports ovalization and warping of its cross-section. The enhancements presented in this paper are comprised of a mass matrix and gyroscopic effects resulting from fast rotation rates and large deformations. The effectiveness of the element is demonstrated by two examples, which simulate the three-dimensional behavior of a highly flexible pipe under dynamic loading conditions.
Highlights
A straight pipe element that enables the efficient computation of large, three-dimensional deformations in blood vessels with initially circular cross-sections was presented in an earlier study by Jiang and Arabyan [5]
In [5] the variation in the performance of the RC element with grid refinement was shown in comparison to a pipe structure made up of four-node shell elements
It was shown that the stress resultants computed by the RC element converge to “exact” results with a smaller number of degrees of freedom than those obtained using four-node shell elements in ABAQUS [1]
Summary
A straight pipe element that enables the efficient computation of large, three-dimensional deformations in blood vessels with initially circular cross-sections was presented in an earlier study by Jiang and Arabyan [5]. The simplest way to obtain the vector of inertia nodal forces is to take the inner product of a diagonal mass matrix with the nodal acceleration vector This formulation and numerical procedure have been proven to be very effective in most applications. In order to capture all inertia effects and coupling among extension, torsion, and bending deformations, the dynamic formulation of the pipe element must be derived from the full geometrically non-linear shell theory by a consistent formulation. This paper presents a consistent formulation for the dynamic analysis of the three-dimensional pipe elements in which the inertia forces due to large deformations are fully accounted by capturing all the inertia couplings. Jiang / A consistent dynamic finite element formulation for a pipe incremental displacements and rotations are defined in terms of a fixed global co-ordinate system
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