A computational formulation for constrained solid and liquid membranes considering isogeometric finite elements
A computational formulation for constrained solid and liquid membranes considering isogeometric finite elements
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DOI：
10.1016/j.cma.2013.11.025
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
R. Sauer;T. X. Duong;Callum J. Corbett
中科院分区：
文献类型：
--
作者：
R. Sauer;T. X. Duong;Callum J. Corbett
提出了一种基于曲线坐标和等几何有限元的几何精确膜配方，适用于固体和液体膜。曲线坐标系用于描述膜的理论和有限元方程。在后一种情况下，这避免了在元素级使用局部坐标。因此，不需要导数的变换。该制剂考虑了分裂的平面内和平面外的膜的贡献，这允许建设一个稳定的配方，具有恒定的表面张力的液膜。建议的膜配方是通用的，并占死和活荷载，以及封闭的体积，面积和接触的限制。新的配方说明了几个具有挑战性的例子，考虑线性和二次拉格朗日元素，以及基于二次NURBS和三次T样条等几何元素。可以看出，等几何元素比标准的拉格朗日元素精确得多。对于液膜制剂，增益特别大，因为它明确地取决于表面曲率。
A geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements, and is suitable for both solid and liquid membranes. The curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane. In the latter case this avoids the use of local cartesian coordinates at the element level. Consequently, no transformation of derivatives is required. The formulation considers a split of the in-plane and out-of-plane membrane contributions, which allows the construction of a stable formulation for liquid membranes with constant surface tension. The proposed membrane formulation is general, and accounts for dead and live loading, as well as enclosed volume, area, and contact constraints. The new formulation is illustrated by several challenging examples, considering linear and quadratic Lagrange elements, as well as isogeometric elements based on quadratic NURBS and cubic T-splines. It is seen that the isogeometric elements are much more accurate than standard Lagrange elements. The gain is especially large for the liquid membrane formulation since it depends explicitly on the surface curvature.