3.1.1静态轮胎分析的对称结果转移
3.1.1 Symmetric results transfer for a static tire analysis
3.1.1静态轮胎分析的对称结果转移
Product: Abaqus/Standard
This example illustrates the u of symmetric results transfer and symmetric model generation to model the static interaction between a tire and a rigid surface.该示例示出了使用对称结果传递和对称模型生成来建模轮胎和刚性表面之间的静态相互作用。
Symmetric model generation (“Symmetric model generation,”Section 10.4.1 of the Abaqus Analysis Ur's Guide) can be ud to create a three-dimensional model by revolving an axisymmetric model about its axis of revolution or by combining two parts of a symmetric model, where one part is the original model and the other part is the original model reflected through a line or a plane. Both model generation techniques are demonstrated in this example.对称模型生成（“对称模型生成”，“Abaqus Analysis用户指南”的10.4.1节）可用
于通过围绕其旋转轴旋转轴对称模型来创建三维模型，或者通过组合对称模型的两个部分，其中一部分是原始模型，另一部分是通过线或平面反射的原始模型。在该示例中示出了两种模型生成技术。
Symmetric results transfer (“Transferring results from a symmetric mesh or a partial three-dimensional mesh to a full three-dimensional mesh,”Section 10.4.2 of the Abaqus Analysis Ur's Guide) allows the ur to transfer the solution obtained from an axisymmetric analysis onto a three-dimensional model with the same geometry. It also allows the transfer of a symmetric three-dimensional solution to a full three-dimensional model. Both the results transfer features are demonstrated in this example. The results transfer capability can significantly reduce the analysis cost of structures that undergo symmetric deformation followed by nonsymmetric deformation later during the loading history.对称结果传输（“将结果从对称网格或部分三维网格传输到完整的三维网格，”Abaqus Analysis用户指南“的10.4.2节）允许用户将从轴对称分析获得的解到具有相同几何形状的三维模型上。它还允许将对称三维解传递到完整的三维模型。这些结果传递特征都在本示例中演示。结果传递能力可以显着降低承受对称变形的结构的分析成本，随
后在加载历史期间随后的非对称变形。
The purpo of this example is to obtain the footprint solution of a 175 SR14 tire in contact with a flat rigid surface, subjected to an inflation pressure and a concentrated load on the axle. Input files modeling a tire in contact with a rigid drum are also included. The footprint solutions are ud as the starting point in “Steady-state rolling analysis of a tire,”Section 3.1.2, where the free rolling state of the tire rolling at 10 km/h is determined and in “Subspace-bad steady-state dynamic tire analysis,”Section 3.1.3, where a frequency respon analysis is performed.本实施例的目的是获得与平坦刚性表面接触的175个SR14轮胎的覆盖区溶液，其受到充气压力和轴上的集中载荷。还包括对与刚性滚筒接触的轮胎建模的输入文件。这些足迹解决方案用作“轮胎的稳态滚动分析”的第3.1.2节，其中确定以10km / h滚动的轮胎的自由滚动状态，并且在“基于子空间的稳定- 状态动态轮胎分析“，第3.1.3节，其中进行频率响应分析。
Problem description问题描述
The different components of the tire are shown in Figure 3.1.1–1. The tread and sidewalls
are made of rubber, and the belts and carcass are constructed from fiber-reinforced rubber composites. The rubber is modeled as an incompressible hyperelastic material, and the fiber reinforcement is modeled as a linear elastic material. A small amount of skew symmetry is prent in the geometry of the tire due to the placement and 20.0° orientation of the reinforcing belts.轮胎的不同部件如图3.1.1-1所示。胎面和侧壁由橡胶制成，并且带和胎体由纤维增强的橡胶复合材料构成。橡胶被模拟为不可压缩的超弹性材料，并且
纤维增强件被建模为线性弹性材料。由于加强带的放置和20.0°取向，在轮胎的几何形状中存在少量的倾斜对称性。
Two simulations are performed in this example. The first simulation exploits the symmetry in the tire model and utilizes the results transfer capability; the cond simulation does not u the results transfer capability. Comparisons between the two methodologies are made for the ca where the tire is in contact with a flat rigid surface. Input files modeling a tire in contact with a rigid drum are also included. The methodology ud in the first ana
lysis is applied in this simulation. Results for this ca are prented in “Steady-state rolling analysis of a tire,”Section 3.1.2.在该示例中执行两个模拟。第一个模拟利用了轮胎模型中的对称性并利用了结果传递能力;第二个模拟不使用结果传递能力。在轮胎与平坦的刚性表面接触的情况下进行两种方法之间的比较。还包括对与刚性滚筒接触的轮胎建模的输入文件。在该模拟中应用在第一分析中使用的方法。这种情况的结果在“轮胎的稳态滚动分析”，第3.1.2节中给出。
The first simulation is broken down into three parate analys. In the first analysis the inflation of the tire by a uniform internal pressure is modeled. Due to the anisotropic nature of the tire construction, the inflation loading gives ri to a circumferential component of deformation. The resulting stress field is fully three-dimensional, but the problem remains axisymmetric in the n that the solution does not vary as a function of position along the circumference. Abaqus provides axisymmetric elements with twist (CGAX) for such situations. The elements are ud to model the inflation loading. Only half the tire cross-ction is needed for the inflation analysis due to a reflection symmetry through the vertical line that pass through the tire axle (e Figure 3.1.1–2). We refer t
o this model as the axisymmetric model.第一个模拟分为三个独立的分析。在第一分析中，通过统一的内部压力对轮胎的充气进行建模。由于轮胎结构的各向异性性质，膨胀负载引起变形的周向分量。所得到的应力场是完全三维的，但是问题保持轴对称的解决方案不作为沿圆周的位置的函数变化的意义。Abaqus为这种情况提供具有扭曲的轴对称元件（CGAX）。这些元素用于模拟充气负荷。由于通过穿过轮胎轴的垂直线的反射对称性，仅需要一半的轮胎横截面用于充气分析（参见图3.1.1-2）。我们将这个模型称为轴对称模型。
The cond part of the simulation entails the computation of the footprint solution, which reprents the static deformed shape of the pressurized tire due to a vertical dead load (modeling the weight of a vehicle). A three-dimensional model is needed for this analysis. The finite element mesh for this model is obtained by revolving the axisymmetric cross-ction about the axis of revolution. A nonuniform discretization along the circumference is ud as shown in Figure 3.1.1–3. In addition, the axisymmetric solution is transferred to the new mesh where it rves as the initial or ba state in the footprint calculations. As with the axisymmetric model, only half of the cross-ction is needed in this simulation,
but skew-symmetric boundary conditions must be applied along the midplane of the cross-ction to account for antisymmetric stress that result from the inflation loading and the concentrated load on the axle. We refer to this model as the partial three-dimensional model.模拟的第二部分需要计算覆盖区解决方案，其表示由于垂直静载荷（建模车辆的重量）导致的加压轮胎的静态变形形状。这个分析需要一个三维模型。该模型的有限元网格是通过围绕旋转轴旋转轴对称横截面而获得的。使用沿着圆周的不均匀离散，如图3.1.1-3所示。此外，轴对称解被传送到新网格，在此处用作覆盖区计算中的初始或基本状态。与轴对称模型一样，在该模拟中仅需要横截面的一半，但是必须沿横截面的中平面应用倾斜对称边界条件以解决由充气加载和集中的负载在轴上。我们将这个模型称为部分三维模型。
