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NURBS-enriched contact finite elements

机译:富含NURBS的接触有限元

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摘要

A novel enrichment of finite elements for contact computations based on isogeometric analysis is presented. Each body is divided into two parts, an enriched contact surface and the bulk domain together with surfaces that are not in contact. The latter part comprises the large majority of the domain and is treated in the usual manner with standard linear basis function, preserving the efficiency of classical finite element techniques. The enriched contact surface is discretized using NURBS basis functions of at least second order, allowing for a locally differentiable surface representation. This avoids the problem of suddenly changing normal vectors between element boundaries on the contact surface. Following the concept of isogeometric analysis, the smooth basis functions are not only used to describe the surface geometry, but also to approximate the solution on the surface. This leads to higher accuracy in the contact integral evaluation. Numerical results are presented for 2D and 3D contact computations including frictionless sliding, adhesive peeling, and cohesive debonding. The presented contact element enrichment exhibits a major gain in numerical accuracy and stability without loss of efficiency compared to standard linear finite elements. The enrichment technique offers some advantages over Hermite and higher-order Lagrangian contact element enrichment techniques, such as locally differentiable surface representations in 3D, while featuring competitive accuracy and performance.
机译:提出了一种新颖的基于等几何分析的接触计算的有限元富集方法。每个物体都分为两个部分,一个是富集的接触表面,另一个是主体区域,另一个是不接触的表面。后者占该域的绝大部分,并以常规方式使用标准线性基函数进行处理,从而保留了经典有限元技术的效率。使用至少二阶的NURBS基本函数离散化丰富的接触表面,从而实现局部可区分的表面表示。这避免了在接触表面上的元素边界之间突然改变法向矢量的问题。遵循等几何分析的概念,光滑基函数不仅用于描述表面几何形状,而且用于近似表面上的解。这导致接触积分评估的更高准确性。给出了2D和3D接触计算的数值结果,包括无摩擦滑动,胶粘剂剥离和内聚剥离。与标准线性有限元相比,所提出的接触元件富集在数值精度和稳定性方面显示出主要的提高,而没有效率的损失。与Hermite和高阶Lagrangian接触元素富集技术相比,富集技术具有一些优势,例如3D局部可区分的表面表示,同时具有极高的准确性和性能。

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