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B plus plus splines with applications to isogeometric analysis

机译：B加加样条线在等几何分析中的应用

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摘要

A novel spline, named B++ Splines (Boundary Plus Plus Splines), is developed to address the expression of a trimmed NURBS patch in an analytic form, which is a central idea of surface representation. The presented method converts each trimmed NURBS patch into a B++ spline patch that incorporates of specific boundary points as the boundary presentation. Emphasis is placed on the construction of a new analytic formula of a trimmed NURBS patch defined by the boundary points at the trimming curves and a group of enriched control points. B++ spline basis functions are linearly independent, build a partition of unity and satisfy the Kronecker delta property. Each B++ spline basis function is a linear combination of the basis functions of the trimmed NURBS patch. These properties allow imposing the Dirichlet boundary conditions strongly at the boundary of the trimmed patch without the necessity of modifying the basis functions of the trimmed patch. Isogeometric analysis using B++ splines for two-dimensional elastic solids is also proposed. Several numerical examples are used to demonstrate the reliability of the presented method. The numerical example for the patch test illustrates that the B++ spline patch passes the standard patch test. (C) 2016 Elsevier B.V. All rights reserved.
机译：开发了一种名为B ++样条线（Boundary Plus Plus样条线）的新颖样条线，以解析形式表达修剪的NURBS面片，这是表面表示的核心思想。提出的方法将每个修剪的NURBS面片转换为B ++样条面片，该面将特定的边界点合并为边界表示。重点放在构造新的由修剪曲线上的边界点和一组丰富的控制点定义的NURBS面片的解析公式上。 B ++样条基函数是线性独立的，可建立一个单位分区并满足Kronecker delta属性。每个B ++样条基函数是修整后的NURBS贴片的基函数的线性组合。这些特性允许在修整后的斑块的边界处强加Dirichlet边界条件，而无需修改修整后的斑块的基函数。还提出了使用B ++样条对二维弹性实体进行等几何分析的方法。使用几个数值示例来证明所提出方法的可靠性。补丁程序测试的数值示例说明B ++样条补丁程序通过了标准补丁程序测试。 （C）2016 Elsevier B.V.保留所有权利。

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