hypermesh单元质量参数说明.docVIP

Hypermesh单元质量参数说明网格质量中文名推荐取值物理意义Help原文2D单元质量参数Aspect(ratio)长宽比必须小于5:1单元最长边与最短边（或最短对角节点距离）之比。3D单元的每个面被看做一个2D单元并且计算长宽比。最大的长宽比作为3D单元的长宽比。This is the ratio of the longest edge of an element to either its shortest edge or the shortest distance from a corner node to the opposing edge (height to closest node). HyperMesh uses the same method used for length (min) described below. For 3-D elements, each face of the element is treated as a 2-D element and its aspect ratio determined. The largest aspect ratio among these faces is returned as the 3-D elements aspect ratio.Aspect ratios should rarely exceed 5:1Chord dev弦长偏差圆弧可以大量短直线模拟，弦长偏差是圆弧与直线的垂直距离。Curved surfaces can be approximated by using many short lines instead of a true curve.Chordal deviation is the perpendicular distance between the actual curve and the approximating line segments.Interior Angles内角检查三角形与四边形最大与最小角These maximum and minimum values are evaluated independently for triangles and quadrilaterals.Jacobian雅克比理想值1大于0.7可接受，质量较好， 小于0.5，准确性不能保证jacobian值是衡量网格质量好坏的一个重要指标。数学上Jacobian是进行坐标变换的Jacob矩阵的行列式|J|，它的取值可以在-,+变化。Abs(|J|)1说明面积扩大，abs(|J|)1说明面积缩小。|J|0说明组成微元的两个向量所称的角的sin值发生了符号变化(比如从锐角变成钝角)。HM中所谓的Jacobian并不是上面讲的数学意义上的Jacobian，而是在自然坐标(s,t)中的微元向量dS,dT (在自然坐标中成90度)， 对应在全局坐标中的向量dS, dT所成角度的sin值。 它只体现了变形，而没有体现面积的变化。而实际上单纯面积/体积的变化，对于单元的形状/质量是没有影响的，所以HM用这个sin值来评价单元的质量是有道理的。 这个值应该可以在-1,1变化， 但是由于负值表示单元发生了反转或者穿透(比如TETRA中一个节点运动到了另外三个节点组成三角形的另一侧)，HW认为此时的单元是完全不可用于有限元计算的，所以默认的取值范围是0,1。虽然HM中的Jacobian取值在单元内部各点可能是不同的，但是可以直观地理解为:以QUAD单元为例,如果jacobian=1, 说明该单元的四个角都是直角，单元质量是最好的，也就是所谓的perfect shape;如果jacobian=0, 说明该单元发生了严重的变形，某个内角变为0度或者180度；如果jacobian0, 说明该单元发生了非常严重的变形，某个内角变为负值(反转)或者大于180度。（此段摘自网贴）This measures the deviation of an element from its ideal or perfect shape, such as a triangles deviation from equilateral. The Jacobian value ranges from 0.0 to 1.0, where 1.0 represents a perfectly shaped element. The determinant of the Jacobian relates the local stretching of the parametric space which is required to fit it onto the global coordinate space.HyperMesh evaluates the determinant of the Jacobian matrix at each of the elements integration points (also called Gauss points) or at the elements corner nodes, and reports the ratio between the smallest and the largest. In the case of Jacobian evaluation at the Gauss points, values of 0.7 and above are generally acceptable. You can select which method of evaluation to use (Gauss point or corner node) from the Check Element Settings window.Length(min)最小长度最小长度，计算使用以下两种方式：（1）单元最短变长，对于非四面体网格；（2）从节点到对角边（或面）的最短距离。Minimum element lengths are calculated using one of two methods: The shortest edge of the element. This method is used for non-tetrahedral 3-D elements.The shortest distance from a corner node to its opposing edge (or face, in the case of tetra elements); referred to as height to closest node.You can choose which method to use in the Check Element Settings window. Note that this setting also affects the calculation of Aspect Ratio.Minimum Length / Size 最小单元长度使用两种方法计算最小单元长度：（1）最短边长；（2）节点到对边的高度。HyperMesh uses 2 methods to calculate the minimum element size: the shortest edge (in which the length of the shortest edge of each element is used) and the height to closest node (which is more accurate, but more complex). Height to Closest Node (HCN) is calculated differently for different element types. For triangular elements:For each corner node (i) HyperMesh calculates the closest (perpendicular) distance to the ray including the opposite leg of the triangle, h(i). HCN = min(hi) * 2/sqrt(3.0). The scaling factor 2/sqrt(3.0) ensures that for equilateral triangles, the HCN is the length of the minimum side. For quadrilateral elements:For each corner node, HM calculates the closest (perpendicular) distances to the rays containing the legs of the quadrilateral that do not include this node. The figure above depicts these lengths as red lines. Height to Closest Node is taken to be the minimum of all eight lines and the four edge lengths (thus, the minimum of 12 possible lengths).skew面扭曲三角单元的扭曲度计算方式如下：从每个节点到对边中点的矢量以及两相邻边中点矢量的最小夹角Skew of triangular elements is calculated by finding the minimum angle between the vector from each node to the opposing mid-side, and the vector between the two adjacent mid-sides at each node of the element. The minimum angle found is subtracted from ninety degrees and reported as the elements skew.Taper锥度四边形对角节点连线分割成两个三角形。锥度等于1减去最小三角形面积除以四边形一半面积的比值。Taper ratio for the quadrilateral element is defined by first finding the area of the triangle formed at each corner grid point:These areas are then compared to one half of the area of the quadrilateral.HyperMesh then finds the smallest ratio of each of these triangular areas to the quad elements total area (in the diagram above, a is smallest). The resulting value is subtracted from 1, and the result reported as the element taper. This means that as the taper approaches 0, the shape approaches a rectangle. Triangles are assigned a value of 0, in order to prevent HyperMesh from mistaking them for highly-tapered quadrilaterals and reporting them as failed.Warpage翘曲度小于5度依次沿对角线将四边形分为两个三角形，寻找这两个三角形所在面构成夹角的最大夹角，该角即为Warp Angle。This is the amount by which an element (or in the case of solid elements, an element face) deviates from being planar. Since three points define a plane, this check only applies to quads. The quad is divided into two trias along its diagonal, and the angle between the trias normals is measured.Warpage of up to five degrees is generally acceptable.3D网格质量检查补充参数Minimum Length / Size 最短边长使用两种方法计算：（1）最短变长（2）节点到对面最短距离。HyperMesh uses 2 methods to calculate the minimum element size: the shortest edge (in which the length of the shortest edge of each element is used) and the height to closest node (which is more accurate, but more complex). In the height to closest node method, HyperMesh calculates the closest (perpendicular) distances to the planes formed by the opposite faces for each corner node. The resulting minimum length/size is the minimum of all such measured distances.Tetra collapse网格塌陷理想值1；网格塌陷时逼近0；不小于0.5四面体网格高度根据四个节点到对面的距离计算，除以面积平方根。最小的值除以1.24。网格塌陷，这个值逼近0。理想的四面体该数值为1。非四面体单元统一赋值为1，以免Hypermesh误以为质量差的四面体单元。The height of the tetra element is measured from each of the four nodes to its opposite face, and then divided by the square root of the faces area. The minimum of the four resulting values (one per node) is then normalized by dividing it by 1.24. As the tetra collapses, the value approaches 0.0, while a perfect tetra has a value of 1.0. Non-tetrahedral elements are given values of 1 so that HyperMesh wont mistake them for bad tetra elements.Vol. Aspect Ratio体长宽比取四面体网格最长边除以最短变长HyperMesh evaluates Tetrahedral elements by finding the longest edge length and dividing it by the shortest