ABSTRACT

The simulation of large deformation contact problems has been a tough subject due to the existence of multiple nonlinearities, including geometric nonlinearity and contact interface nonlinearity. In this paper, we develop a novel method to compute the large deformation of 2D frictionless contact by employing Nitsche-based isogeometric analysis. The enforcement of contact constraints as one of the main issues in contact simulation is implemented by using Nitsche’s method, and the node-to-segment scheme is applied to the contact interface discretization. We detailedly derive the discrete formulations for 2D large deformation frictionless contact where NURBS is used for geometrical modeling and the Neo-Hookean hyperelastic materials are applied to describe the deformation of the model. The collocation method with Greville points is employed to integrate the contact interface and the classical Legendre–Gauss quadrature rule is used for contact bodies’ integration. The Lagrange multiplier method and penalty method are also implemented for comparison with Nitsche’s method. Several examples are investigated, and the obtained results are compared with that from commercial software ABAQUS to verify the effectiveness and accuracy of the Nitsche-based isogeometric analysis.

中文翻译：

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使用等几何分析和 Nitsche 方法的二维无摩擦大变形接触问题

摘要

由于几何非线性和接触界面非线性等多重非线性的存在，大变形接触问题的模拟一直是一个棘手的课题。在本文中，我们开发了一种新方法，通过采用基于 Nitsche 的等几何分析来计算二维无摩擦接触的大变形。作为接触模拟中主要问题之一的接触约束的执行是通过使用Nitsche的方法来实现的，并且节点到段的方案被应用于接触界面的离散化。我们详细推导了二维大变形无摩擦接触的离散公式，其中 NURBS 用于几何建模，Neo-Hookean 超弹性材料用于描述模型的变形。接触界面积分采用格雷维尔点搭配法，接触体积分采用经典勒让德-高斯求积法则。还实现了拉格朗日乘数法和惩罚法，以便与尼采法进行比较。研究了几个例子，并将获得的结果与商业软件 ABAQUS 的结果进行了比较，以验证基于 Nitsche 的等几何分析的有效性和准确性。