织物成形模拟的有限元方法研究
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摘要
织物变形的模拟问题是从上个世纪80年代中期开始研究的问题，其中有限元方法模拟则开始于上个世纪90年代，距今只有10年左右的历史。国际上这方面的研究方兴未艾，国内研究比较有限，尤其是有限元方法模拟织物变形在国内尚未见到相关文献。迄今为止有限元方法是最有可能全面体现织物材料特性的方法，也是最有希望完全准确反映织物变形的方法，因此本文以织物悬垂的有限元模拟为对象，进行了研究，本文主要有以下几个方面的工作：
(1) 对国内外织物变形研究的历史和现状进行了综合论述，并调查了壳元文献中对有限旋转的表达方法，给以分类。
(2) 提出了一个用相对夹角表达有限旋转的壳元模型，并推导了详尽的算法。在织物的悬垂模拟中有限旋转起着重要作用。作者为此提出了一种有限旋转描述模型，该模型建立各个结点在初始构形上的局部坐标系，使用法线在局部坐标的相对夹角的变化来描述法线的变化。这样的有限旋转描述方法比经典的线性描述准确，比几何精确壳理论的Rodrigues参数表达法要简单。可以说是一种简单而准确的有限旋转表达方法，尤其是该算法的实现比几何精确壳理论要简单。该方法存在不能描述弯矩边界条件的缺点，但对于织物悬垂模拟来说足够可行，因为织物一般不能承受弯矩载荷。
(3) 在上面的有限旋转模型的基础上，按照几何非线性有限元理论，作者详尽地推导了退化曲壳元的T.L.算式。在单元的选用上，通过比较作者选用了9结点的Heterosis单元，最后在计算中应用节减积分技术，由此建立了一套行之有效的有限元算法。
(4) 把织物作为连续介质，探讨了其本构关系的建立问题。假定织物是线弹性的，且是均匀正交异性材料，建立了织物的正交异性本构关系，并讨论了其中的弹性模量的选取问题。指出应该选用织物的弯曲刚度推导出的弹性模量作为本构中的弹性模量，而不是实测的弹性模量。另外讨论了织物的泊松比对其悬垂变形的影响问题，指出正常范围内的泊松比对织物的悬垂变形影响不大。
(5) 按照前述算法编制了有限元程序，模拟了织物的二维和三维悬垂，并给出了织物悬垂的动态过程的图形。这些结果可以应用于纺织界的悬垂预测和评价，也可用于计算机图形学的织物变形模拟，同样也可以用在航空制造的某些特殊工件的加工工序中(如使用碳纤维、玻璃纤维等加工一些工件的工序)，随着织物在航空制造业中越来越广泛的使用，这种模拟技术在航空制造业的重要性也会越来越突出。
The cloth modeling technique is much concerned because of its
extensively application to the textile and apparel industries, human
animation, computer games, virtual reality and so on. Many methods are
suggested for modeling cloth. Among them the finite element method (FEM)
is the most prospective one, by means of which not only the appearance
of cloth deformation can be obtained, but also the physical details can
be attained, although its expression seems rather profound and
complicated. The paper is aimed at the FEM technique in simulating cloth
drape. The following are the major works in the paper.
1. A review of cloth modeling is presented. The parametric
descriptions of the finite rotation are classified based on the study of
papers about shell elements.
2. A new model is proposed that defines the finite rotation by two
relative angles. The finite rotation plays a significant role in the
fabric drape, so that the accuracy of its definition is essential. The
new fini te rotat ion definition is more exact than the classic l inear one,
and is simpler than Rodrigues parametric one in geometric exact shell
theory. In addition, it is easy to implement the computation. The model
is not competent in describing the boundary condition of the bending
moment, but it is not a fatal drawback because fabric cannot generally
stand the bending moment.
3. According to the geometric nonlinear FE theory, a series of total
Lagrangian formulations of degenerated shell element based on the above
finite rotation definition are derived. 9-node heterosis element and a
reduced integration technique are applied to the analysis process for
eliminating the shear locking. Thus a full and efficient algorithm is
proposed.
4. A fabric continuum constitutive equation is proposed. It is
assumed that the fabric is a matter of continuum, homogeneous,
orthogonally anisotropic elastic, and hence the fabric constitutive
equation is formulated. Second, a method of determining the two primary
elastic modules in the constitutive equation from the two respective
primary bending moments instead of the two tensile modules is proposed.
The influence of Poisson's ratio on the drape shape is considered. The
relevant analysis and calculation show that normal Poisson's ratio in
the range of 0.0--0.5 does not show appreciable effect on fabric drape.
5. A computer code is developed to implement the above FE analysis.
By using the code, the fabric static drape examples in 2-D or 3-D and some
dynamic processes of the fabric drape are presented in the paper. The
results show that the FEM proposed in the paper is effective.
(1) 对国内外织物变形研究的历史和现状进行了综合论述，并调查了壳元文献中对有限旋转的表达方法，给以分类。
(2) 提出了一个用相对夹角表达有限旋转的壳元模型，并推导了详尽的算法。在织物的悬垂模拟中有限旋转起着重要作用。作者为此提出了一种有限旋转描述模型，该模型建立各个结点在初始构形上的局部坐标系，使用法线在局部坐标的相对夹角的变化来描述法线的变化。这样的有限旋转描述方法比经典的线性描述准确，比几何精确壳理论的Rodrigues参数表达法要简单。可以说是一种简单而准确的有限旋转表达方法，尤其是该算法的实现比几何精确壳理论要简单。该方法存在不能描述弯矩边界条件的缺点，但对于织物悬垂模拟来说足够可行，因为织物一般不能承受弯矩载荷。
(3) 在上面的有限旋转模型的基础上，按照几何非线性有限元理论，作者详尽地推导了退化曲壳元的T.L.算式。在单元的选用上，通过比较作者选用了9结点的Heterosis单元，最后在计算中应用节减积分技术，由此建立了一套行之有效的有限元算法。
(4) 把织物作为连续介质，探讨了其本构关系的建立问题。假定织物是线弹性的，且是均匀正交异性材料，建立了织物的正交异性本构关系，并讨论了其中的弹性模量的选取问题。指出应该选用织物的弯曲刚度推导出的弹性模量作为本构中的弹性模量，而不是实测的弹性模量。另外讨论了织物的泊松比对其悬垂变形的影响问题，指出正常范围内的泊松比对织物的悬垂变形影响不大。
(5) 按照前述算法编制了有限元程序，模拟了织物的二维和三维悬垂，并给出了织物悬垂的动态过程的图形。这些结果可以应用于纺织界的悬垂预测和评价，也可用于计算机图形学的织物变形模拟，同样也可以用在航空制造的某些特殊工件的加工工序中(如使用碳纤维、玻璃纤维等加工一些工件的工序)，随着织物在航空制造业中越来越广泛的使用，这种模拟技术在航空制造业的重要性也会越来越突出。
The cloth modeling technique is much concerned because of its
extensively application to the textile and apparel industries, human
animation, computer games, virtual reality and so on. Many methods are
suggested for modeling cloth. Among them the finite element method (FEM)
is the most prospective one, by means of which not only the appearance
of cloth deformation can be obtained, but also the physical details can
be attained, although its expression seems rather profound and
complicated. The paper is aimed at the FEM technique in simulating cloth
drape. The following are the major works in the paper.
1. A review of cloth modeling is presented. The parametric
descriptions of the finite rotation are classified based on the study of
papers about shell elements.
2. A new model is proposed that defines the finite rotation by two
relative angles. The finite rotation plays a significant role in the
fabric drape, so that the accuracy of its definition is essential. The
new fini te rotat ion definition is more exact than the classic l inear one,
and is simpler than Rodrigues parametric one in geometric exact shell
theory. In addition, it is easy to implement the computation. The model
is not competent in describing the boundary condition of the bending
moment, but it is not a fatal drawback because fabric cannot generally
stand the bending moment.
3. According to the geometric nonlinear FE theory, a series of total
Lagrangian formulations of degenerated shell element based on the above
finite rotation definition are derived. 9-node heterosis element and a
reduced integration technique are applied to the analysis process for
eliminating the shear locking. Thus a full and efficient algorithm is
proposed.
4. A fabric continuum constitutive equation is proposed. It is
assumed that the fabric is a matter of continuum, homogeneous,
orthogonally anisotropic elastic, and hence the fabric constitutive
equation is formulated. Second, a method of determining the two primary
elastic modules in the constitutive equation from the two respective
primary bending moments instead of the two tensile modules is proposed.
The influence of Poisson's ratio on the drape shape is considered. The
relevant analysis and calculation show that normal Poisson's ratio in
the range of 0.0--0.5 does not show appreciable effect on fabric drape.
5. A computer code is developed to implement the above FE analysis.
By using the code, the fabric static drape examples in 2-D or 3-D and some
dynamic processes of the fabric drape are presented in the paper. The
results show that the FEM proposed in the paper is effective.
引文
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