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Use of B-spline surface to model large-deformation continuum plates: procedure and applications

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Abstract

The absolute nodal coordinate formulation (ANCF) has been used in the analysis of large deformation of flexible multibody systems that encompass belt drive, rotor blade, and cable applications. As demonstrated in the literature, the ANCF finite elements are ideal for isogeometric analysis. The purpose of this investigation is to establish a relationship between the B-splines, which are widely used in the geometric modeling, and the ANCF finite elements in order to construct continuum models of large-deformation geometries. This paper proposes a simplified approach to map the B-spline surfaces into ANCF thin plate elements. Matrix representation of the mapping process is established and examined through numerical examples successfully. The matrix representation of the mapping process is used because of its suitability of computer coding and to minimize the calculation time. The error estimation is carried out by analyzing the gap between the points of each ANCF element and the corresponding points of the portion of the B-spline surface. The Hausdorff distance is used to study the effect of the number of control points, the degree of interpolation, and the knot multiplicity on the mapped geometry. It is found that cubic interpolation is recommended for optimizing the accuracy of mapping the B-spline surface to ANCF thin plate elements. It is found that thin plate element in ANCF missing a number of basis functions which considered a source of error between the two surfaces, as well as it does not allow to converting the ANCF thin plate elements model to B-spline surface. In this investigation, an application example of modeling large-size wind turbine blade with uniform structure is illustrated. The use of the continuum plate elements in modeling flexible blades is more efficient because of the relative scale between the plate thickness and its length and width and the high flexibility of its structure. The numerical results are compared with the results of ANSYS code with a good agreement. The dynamic simulation for mapped surface model shows a numerical convergence, which ensures the ability of using the proposed approach for applications of dynamics for design and computer-aided design.

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Acknowledgements

We are grateful to Dynamic Simulation Lab, University of Illinois at Chicago, for generous support of license agreement of SAMS2000 software package and technical support.

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  1. Benha Institute of Technology, Benha University, Benha, 13512, Egypt

    Ayman A. Nada

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  1. Ayman A. Nada
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Correspondence to Ayman A. Nada.

Appendix: Control points

Appendix: Control points

The control points of the numerical example shown in Sect. 4 along x- and y-axes, respectively, to form the shape shown in Fig. 6, are given in Table 4.

Table 4 Control points of Fig. 6
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Nada, A.A. Use of B-spline surface to model large-deformation continuum plates: procedure and applications. Nonlinear Dyn 72, 243–263 (2013). https://doi.org/10.1007/s11071-012-0709-3

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