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Powell-Sabin B-splines and unstructured standard T-splines for the solution of the Kirchhoff-Love plate theory exploiting Bézier extraction

机译:powell-sabin B样条和非结构化标准T样条用于解决Kirchhoff-Love板理论利用Bézier提取

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摘要

The equations that govern Kirchhoff–Love plate theory are solved using quadratic Powell–Sabin B-splines and unstructured standard T-splines. Bézier extraction is exploited to make the formulation computationally efficient. Because quadratic Powell–Sabin B-splines result in inline image-continuous shape functions, they are of sufficiently high continuity to capture Kirchhoff–Love plate theory when cast in a weak form. Unlike non-uniform rational B-splines (NURBS), which are commonly used in isogeometric analysis, Powell–Sabin B-splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T-splines can be modified such that they are inline image-continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T-splines, Powell–Sabin B-splines and NURBS-to-NURPS (non-uniform rational Powell–Sabin B-splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plate
机译:使用二次鲍威尔-萨宾B样条和非结构化标准T样条求解控制基尔霍夫-洛夫板理论的方程。利用贝塞尔(Bézier)提取可提高配方的计算效率。由于二次Powell–Sabin B样条曲线产生连续的图像连续形状函数,因此当以弱形式投射时,它们具有足够高的连续性以捕获Kirchhoff–Love板理论。与等几何分析中通常使用的非均匀有理B样条(NURBS)不同,鲍威尔·萨宾B样条不一定能准确捕获几何图形。但是,将它们定义在三角形而不是四边形上的事实增加了它们在网格划分方面的灵活性,并且可以使它们相对于NURBS具有竞争力,因为不需要用于连接NURBS贴片的弯曲条方法。本文进一步说明了如何修改非结构化T样条,使其在非凡点周围是连续的图像连续的,并且混合功能满足了单位属性的划分。比较了二次NURBS,非结构化T样条,Powell-Sabin B样条和NURBS-to-NURPS(非均匀有理Powell-Sabin B样条的性能),这是通过对NURBS面片进行转换获得的。圆板的研究

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