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On the numerical integration of isogeometric interface elements

机译:关于等几何界面元素的数值积分

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摘要

Zero-thickness interface elements are commonly used in computational mechanics to model material interfaces or to introduce discontinuities. The latter class requires the existence of a non-compliant interface prior to the onset of fracture initiation. This is accomplished by assigning a high dummy stiffness to the interface prior to cracking. This dummy stiffness is known to introduce oscillations in the traction profile when using Gauss quadrature for the interface elements, but these oscillations are removed when resorting to a Newton-Cotes integration scheme 1. The traction oscillations are aggravated for interface elements that use B-splines or non-uniform rational B-splines as basis functions (isogeometric interface elements), and worse, do not disappear when using Newton-Cotes quadrature. An analysis is presented of this phenomenon, including eigenvalue analyses, and it appears that the use of lumped integration (at the control points) is the only way to avoid the oscillations in isogeometric interface elements. New findings have also been obtained for standard interface elements, for example that oscillations occur in the relative displacements at the interface irrespective of the value of the dummy stiffness.
机译:零厚度界面元素通常在计算力学中用于对材料界面建模或引入不连续性。后者要求在开始骨折之前存在不顺应的界面。这是通过在开裂之前为界面分配较高的虚拟刚度来实现的。当使用高斯正交作为接口元素时,这种虚拟刚度会在牵引轮廓中引入振动,但是当采用Newton-Cotes积分方案1时,这些振动会被消除。或非均匀有理B样条曲线作为基本函数(等几何界面元素),更糟的是,使用牛顿-考特斯正交时不会消失。对这种现象进行了分析,包括特征值分析,并且看来(在控制点处)使用集总积分是避免等几何界面元素振荡的唯一方法。对于标准的界面元件也获得了新的发现,例如,不管虚拟刚度的值如何,在界面处的相对位移中都会发生振荡。

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