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hypermesh单元质量参数说明

作者:高考题库网
来源:https://www.bjmy2z.cn/gaokao
2021-02-01 21:31
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2021年2月1日发(作者:档次)


Hypermesh


单元质量参数说明



网格质量



中文名



推荐取值



物理意义



2D


单元质量参数



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 (


Help


原文



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< /p>


单元的每个面被


看做一个


2D

< p>
单元并且计算长宽比。


最大的长宽比作为


3D


单元的长宽


比。



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 element’s aspect ratio.



Aspect ratios should rarely exceed 5:1


Curved surfaces can be approximated by using many


short lines instead of a true curve.


Chord dev


弦长偏






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。




Chordal deviation is the perpendicular distance


between the actual curve and the approximating line


segments.


These maximum and minimum values are


InteriorAngle


s


内角





检查三角形与四边形最大与最小角



evaluated independently for triangles and


quadrilaterals.



Jacobian


雅克比



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|



理想值

1









[ -


∞,+∞]




大于


0.7


Abs(|J|)> 1


说明面积扩大,


abs(|J|)<1


可接受,


说明面积缩小。


|J|<0


说明组成微元的


质量较


两个向量所称的角的

sin


值发生了符


好,



号变化


(


比如从锐角变成钝角

< br>)




小于

0.5



HM


中所谓的

< p>
Jacobian


并不是上面讲



确性



的数学意义上的


Jac obian


,而是在自


能保证



然坐标


(s,t)


中的微元向量


dS,dT (


在自


然坐标中成

90



)


,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


This measures the deviation of an element from its


ideal or


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

< br>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

< br>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



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]


< p>


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


:



QUAD


单元为例

< br>,


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


jacob ian<0,



明该单元发生了非常严重的变形,

< p>


个内角变为负值


(


反转


)


或者大于


180

度。


(此段摘自网贴)



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.


Minimum element lengths are calculated using


one of two methods:



?



?



non-tetrahedral 3-D elements.


The shortest edge of the element.


This method is


The shortest distance from a corner node to its opp


Length(min)


最小长






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。



the case of tetra elements); referred to as


You can choose which method to use in the Check


Element Settings window.


Note that this setting


also affects the calculation of Aspect Ratio.



HyperMesh uses 2 methods to calculate the


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。



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 of triangular elements is calculated by


skew


面扭曲




三 角单元的扭曲度计算方式如下:



finding the minimum angle between the vector


每个节点到对边中点的矢量以及两


from each node to the opposing mid-side, and the


相邻边中点矢量的最小夹角



vector between the two adjacent mid- sides at each


node of the element.


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