hypermesh单元质量参数说明.doc

Hypermesh单元质量参数说明
网格质量
中文名
推荐取值
物理意义
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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单元得每个面被瞧做一个2D单元并且计算长宽比。最大得长宽比作为3D单元得长宽比。
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 3D elements, each face of the element is treated as a 2D element and its aspect ratio determined、  The largest aspect ratio among these faces is returned as the 3D element’s aspect ratio、
Aspect ratios should rarely exceed 5:1
Chord dev
弦长偏差
—
圆弧可以大量短直线模拟,弦长偏差就是圆弧与直线得垂直距离。
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值就是衡量网格质量好坏得一个重要指标。数学上Jacobian就是进行坐标变换得Jacob矩阵得行列式|J|,它得取值可以在[∞,+∞]变化。Abs(|J|)>1说明面积扩大,abs(|J|)<1说明面积缩小。|J|<0说明组成微元得两个向量所称得角得sin值发生了符号变化(比如从锐角变成钝角)。
HM中所谓得Jacobian并不就是上面讲得数学意义上得Jacobian,而就是在自然坐标(s,t)中得微元向量dS,dT (在自然坐标中成90度), 对应在全局坐标中得向量dS’, dT’所成角度得sin值。 它只体现了’变形’,而没有体现面积得变化。而实际上单纯面积/体积得变化,对于单元得形状/质量就是没有影响得,所以HM用这个sin值来评价单元得质量就是有道理得。 这个值应该可以在[1,1]变化, 但就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得另一侧),HW认为此时得单元就是完全不可用于有限元计算得,所以默认得取值范围就是[0,1]。
虽然HM中得’Jacobian’取值在单元内部各点可能就是不同得,但就是可以直观地理解为:
以QUAD单元为例,如果jacobian=1, 说明该单元得四个角都就是直角,单元质量就是最好得,也就就是所谓得’perfect shape’;如果jacobian=0, 说明该单元发生了严重得变形,某个内角变为0度或者180度;如果jacobian<0, 说明该单元发生了非常严重得变形,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 triangle’s 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 element’s integration points (also called Gauss points) or at the element’s 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)得最短距离。
Minimum element lengths are calculated using one of two methods:
•
The shortest edge of the element、  This method is used for nontetrahedral 3D 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)节点到对边得高度。
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 plex)、
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

三角单元得扭曲度计算方式如下:从每个节点到对边中点得矢量以及两相邻边中点矢量得最小夹角
Skew of triangular elements is calculated by finding the minimum angle between the vector from each node to the opposing midside, and the vector between the two adjacent midsides at each node of the element、

The minimum angle found is subtracted from ninety degrees and reported as the element’s 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得比值。

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 pared to one half of the area of the quadrilateral、
HyperMesh then finds the smallest ratio of each of these triangular areas to ½ the quad element’s 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 highlytapered 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得最大夹角,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 plex)、
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得距离计算,除以面积平方根。最小得值除以1、24。网格塌陷,这个值逼近0。理想得四面体该数值为1。非四面体单元统一赋值为1,以免Hypermesh误以为质量差得四面体单元。
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 face’s 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、  Nontetrahedral elements are given values of 1 so that HyperMesh won’t 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 height (measured from a node to its opposing face)、  Other 3D elements, such as hex elements, are evaluated based on the ratio of their longest edge to their shortest edge、
Volume Skew

体扭曲度
0最优
1最差
仅检查四面体单元。其她单元都被赋值为零。体扭曲度等于四面体单元体积除以理想四面体体积。
This check applies only to tetrahedral elements; all others are assigned values of zero、 Volume Skew is defined as 1shape factor, so a skew of 0 is perfect and a skew of 1 is the worst possible value、
The shape factor for a tetrahedral element is determined by dividing the element’s volume by the volume of an ideal (equilateral) tetrahedron of the same circumradius、  In the case of tetrahedral elements, the circumradius is the radius of a sphere passing through the four vertices of the tetrahedron、

Vol AR
高度与底面积比值