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Multi-patch NURBS formulation for anisotropic variable angle tow composite plates

机译:各向异性可变角度拖曳复合板的多补丁NURBS配方

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摘要

Conventional methods result in sharp variation of stiffness in analysis of variable angle tow (VAT) composite plates, which can be enhanced using high-order continuity of non-uniform rational B-spline (NURBS). To this end, a Bezier extraction-based isogeometric (IGA) model based on the higher-order shear deformation theory (HSDT) is developed for the parametric instability study of anisotropic VAT composite plates. Bezier extraction-based IGA approach expresses exactly the orientation function of VAT composites for multi-patch geometries, which provides accurate solution for general-shape plates. The accuracy and convergence of the developed framework is compared with recently formulated methods. Primary results shows that the developed concept solves VAT problems with much lower number of equations than variable kinematic models. Further, response characteristics of analyzed anisotropic VAT plates are presented and discussed considering various fiber orientation functions, boundary conditions and multi-patch geometry. Based on results, Bezier control mesh is more accurate than the NURBS-based IGA solution due to considering the continuity of strain field along coupled boundaries. Anisotropic VAT plates have severe deformation couplings and the current concept accurately captures this feature even with courser meshes. The interaction between boundary conditions and fiber orientations along edges affects mainly the dynamic instability regions (DIR) of modeled VAT plates, dislike to straight fiber ones. The dynamic instability opening (DIO) of VAT plates relies on the fiber orientation functions and boundaries. In anisotropic VAT plates, maximum frequency case and maximum buckling force case would not necessarily be the same. Modes shapes are variable of external force intensity and therefore the Rayleigh-Ritz based methods are not appropriate for dynamic stability analysis of VAT plates. It is essential to change the NURBS control mesh to the Bezier type to offer the required accuracy for the multi-patch domains.
机译:传统方法会导致可变角度拖曳(VAT)复合板分析中刚度的急剧变化,可以使用非均匀有理B样条(NURBS)的高阶连续性来增强这种变化。为此,开发了基于高阶剪切变形理论(HSDT)的基于Bezier提取的等几何(IGA)模型,用于各向异性VAT复合板的参数不稳定性研究。基于Bezier提取的IGA方法精确表达了VAT复合材料在多面体几何中的定向功能,从而为一般形状的板材提供了精确的解决方案。所开发框架的准确性和收敛性与最近制定的方法进行了比较。初步结果表明,与可变运动学模型相比,所开发的概念能够以更少的方程式来解决增值税问题。此外,考虑到各种纤维取向函数,边界条件和多面体几何形状,提出并讨论了经过分析的各向异性增值税板的响应特性。基于结果,由于考虑了沿耦合边界的应变场的连续性,因此Bezier控制网格比基于NURBS的IGA解决方案更为精确。各向异性VAT板具有严重的形变耦合,并且即使使用横行网格,当前的概念也可以准确地捕获此特征。边界条件和沿边缘的纤维取向之间的相互作用主要影响建模的VAT板的动态不稳定性区域(DIR),与直纤维板不同。增值税板的动态不稳定性开口(DIO)取决于纤维的定向功能和边界。在各向异性增值税板中,最大频率情况和最大屈曲力情况不一定相同。模式形状是外力强度的变量,因此基于Rayleigh-Ritz的方法不适用于增值税板的动态稳定性分析。必须将NURBS控制网格更改为Bezier类型,以为多面体域提供所需的精度。

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