Hypermesh單元質(zhì)量參數(shù)說明網(wǎng)格質(zhì)量中文名推薦取值物理意義Help原文2D單元質(zhì)量參數(shù)Aspect(ratio)長寬比必須小于5:1單元最長邊與最短邊（或最短對角節(jié)點距離）之比。3D單元的每個面被看做一個2D單元并且計算長寬比。最大的長寬比作為3D單元的長寬比。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弦長偏差圓弧可以大量短直線模擬，弦長偏差是圓弧與直線的垂直距離。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內(nèi)角檢查三角形與四邊形最大與最小角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，質(zhì)量較好， 小于0.5，準確性不能保證jacobian值是衡量網(wǎng)格質(zhì)量好壞的一個重要指標。數(shù)學(xué)上Jacobian是進行坐標變換的Jacob矩陣的行列式|J|，它的取值可以在-,+變化。Abs(|J|)1說明面積擴大，abs(|J|)1說明面積縮小。|J|0說明組成微元的兩個向量所稱的角的sin值發(fā)生了符號變化(比如從銳角變成鈍角)。HM中所謂的Jacobian并不是上面講的數(shù)學(xué)意義上的Jacobian，而是在自然坐標(s,t)中的微元向量dS,dT (在自然坐標中成90度)， 對應(yīng)在全局坐標中的向量dS, dT所成角度的sin值。 它只體現(xiàn)了變形，而沒有體現(xiàn)面積的變化。而實際上單純面積/體積的變化，對于單元的形狀/質(zhì)量是沒有影響的，所以HM用這個sin值來評價單元的質(zhì)量是有道理的。 這個值應(yīng)該可以在-1,1變化， 但是由于負值表示單元發(fā)生了反轉(zhuǎn)或者穿透(比如TETRA中一個節(jié)點運動到了另外三個節(jié)點組成三角形的另一側(cè))，HW認為此時的單元是完全不可用于有限元計算的，所以默認的取值范圍是0,1。雖然HM中的Jacobian取值在單元內(nèi)部各點可能是不同的，但是可以直觀地理解為:以QUAD單元為例,如果jacobian=1, 說明該單元的四個角都是直角，單元質(zhì)量是最好的，也就是所謂的perfect shape;如果jacobian=0, 說明該單元發(fā)生了嚴重的變形，某個內(nèi)角變?yōu)?度或者180度；如果jacobian0, 說明該單元發(fā)生了非常嚴重的變形，某個內(nèi)角變?yōu)樨撝?反轉(zhuǎn))或者大于180度。（此段摘自網(wǎng)貼）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)最小長度最小長度，計算使用以下兩種方式：（1）單元最短變長，對于非四面體網(wǎng)格；（2）從節(jié)點到對角邊（或面）的最短距離。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 最小單元長度使用兩種方法計算最小單元長度：（1）最短邊長；（2）節(jié)點到對邊的高度。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面扭曲三角單元的扭曲度計算方式如下：從每個節(jié)點到對邊中點的矢量以及兩相鄰邊中點矢量的最小夾角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錐度四邊形對角節(jié)點連線分割成兩個三角形。錐度等于1減去最小三角形面積除以四邊形一半面積的比值。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翹曲度小于5度依次沿對角線將四邊形分為兩個三角形，尋找這兩個三角形所在面構(gòu)成夾角的最大夾角，該角即為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網(wǎng)格質(zhì)量檢查補充參數(shù)Minimum Length / Size 最短邊長使用兩種方法計算：（1）最短變長（2）節(jié)點到對面最短距離。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網(wǎng)格塌陷理想值1；網(wǎng)格塌陷時逼近0；不小于0.5四面體網(wǎng)格高度根據(jù)四個節(jié)點到對面的距離計算，除以面積平方根。最小的值除以1.24。網(wǎng)格塌陷，這個值逼近0。理想的四面體該數(shù)值為1。非四面體單元統(tǒng)一賦值為1，以免Hypermesh誤以為質(zhì)量差的四面體單元。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體長寬比取四面體網(wǎng)格最長邊除以最短變長HyperMesh evaluates Tetrahedral elements by finding the longest edge length and dividing it by the shortest