FEM_Result_Averaging

1、Washing machine DivisionWGG, HAIER Electronics张强2012.11.28CAE/CATCook: 计算出的应力通常在单元内部是最精确的，而不是在单元边界上。这是令人遗憾的，因为我们对边界上的应力最感兴趣。因此，应力可以在单元内部的一些点上计算，然后外推（extrapolate）到单元边界上，或是用跨越单元的一个“分片”进行平滑处理来得到应力。 一般地，相邻单元在他们共有的节点处有不同的应力状态。由于不知道这些应力状态中哪个是最准确的，故任意单元节点的平均应力比隶属于此节点处的应力更值得相信。有代表性的软件计算的都是节点的平均应力，并用它们绘制应力带（

2、或应力等值线）。这些带是单元间连续的，比不连续的一个单元接一个单元的应力带更好看一些。但是，由于明显的应力不连续告诉我们，网格太粗糙得不到可靠的结果，一个接一个的单元应力带对分析者还是有用的。 在节点处的应力通常比高斯点处的应力更受到关注，主要有两个原因。第一，节点在表面上，应力通常比内部的应力要大。第二，共享一个节点的单元通常不会在共享节点处预报出相同的应力值，因此这个差异可以用于误差测量。 在一个四节点矩形（和一个8节点的矩形六面体）中，直接在一节点处计算的应力与4（或8）个高斯点处外推到节点的应力是一致的。对一般形状单元他们不一致，几何形状越不规则，差异越大。（Cook, P200）40

3、.5 Selecting result optionsAbaqus/CAE offers several methods for you to display field output results stored in the output database. Some of these methods require that field output data originally saved to the output database at element centroid or integration point locations be calculated at nodal l

4、ocations. Such calculations apply to line and banded-type contour plots, probing at nodal locations, forming a display group or color coding based on result values, and extracting element-based XY data along a path. You can control some of the options related to these computations, such as how eleme

5、nt-based results are averaged.In addition, you can choose to apply coordinate system transformations to your field output results; you can choose from several display forms for complex results: the magnitude, phase angle, real component, imaginary component, or value at a specified angle; and you ca

6、n choose whether or not to cache results in memory to improve performance.Select Result Options to locate the options that control the result calculations, result transformations, display of complex results, and result caching. This section discusses the result computations and the options that affe

7、ct these computations.40.5.1 Understanding how results are computedThe computations necessary to display results stored in the output database depend on whether the results are for a node-based quantity, such as displacement or velocity, or for an element-based quantity, such as stress or strain.How

8、 node-based field output results are computedNode-based field output variables are written to the output database at each node, along with any nodal transformations applied during model creation. For the display of nodal field output variables, Abaqus/CAE reads the required values from the output da

9、tabase for each node included in the plot. By default, these values are displayed in the global coordinate system; you can choose to apply the nodal transformations to the results or to apply a user-specified coordinate system transformation. The final values are then used to produce contours, nodal

10、 probe values, display groups or color coding based on results, or XY data along a path.How element-based field output results are computedElement-based field output variables are written to the output database at the integration points, the element centroid, or the element nodes, depending on the v

11、ariable. For the display of element based field output variables, Abaqus/CAE reads values from the output database for all elements connected to all nodes included in the plot. Computations are then applied to these values to produce contours, nodal probe results, display groups or color coding base

12、d on results, or XY data along a path.For results saved to the output database at the integration points or at the element centroid, the first computation applied is extrapolation. (Results saved at the element nodes do not require extrapolation.) For contour plots only, you can choose quilt-type ex

13、trapolation, in which case the remaining computations discussed below do not apply. To learn more about quilt-type extrapolation, see “Understanding how contour values are computed,” Section 42.1.1. For all other methods of results display, Abaqus/CAE extrapolates results to the nodes using weightin

14、g appropriate for the element type and shape.Extrapolated values are generally not as accurate as the values calculated at the integration points. Therefore, adequately detailed meshing is recommended around nodes where accurate nodal values of such element results are needed. You should be particul

15、arly careful interpreting output variables extrapolated to the nodes for second-order elements with midside nodes outside the quarter-point region, such as when one edge is collapsed in two dimensions or one face is collapsed in three dimensions.Extrapolation of element tensor quantities is performe

16、d on the individual tensor components in the local material coordinate system. Nodes common to two or more elements receive extrapolated values from all contributing elements. Depending on the characteristics of your model, these contributions may originate from more than one result region. If all c

17、ontributions at a node originate from a single result region, the values are combined as necessary in further computations. If contributions are received from more than one result region, you can choose to respect the region boundary and keep the contributions separate in further computations or to

18、ignore the region boundary and combine the values. The default result regions in an output database duplicate the regions that were used to assign section properties to the model prior to analysis. Alternatively, you can select element sets or display groups to use as result regions. For more inform

19、ation, see“Controlling computations at region boundaries,” Section 40.5.7, in the online HTML version of this manual.If invariants or components are requested, you can specify whether Abaqus/CAE should use the extrapolated data from each element or the combined data from all contributing elements to

20、 compute the invariants. By default, invariants are computed before the extrapolated results are combined (averaged). Contour plots of invariants or components may be affected by the order in which Abaqus performs the computations. For example, values for the von Mises stress may exceed the yield st

21、ress of inelastic materials; in addition, the invariant results may not take into account situations where the material orientations vary within a finite element in a non-isoparametric fashion. If invariants are computed after averaging, Abaqus determines the orientations at a node by averaging the

22、contributing element orientations; component values will be affected if the orientations differ between contributing elements.If you select element sets to define the result regions and invariants will be computed after averaging, the element sets that you select must contain compatible elements. Co

23、mpatible elements share the same basic element type (continuum, shell, beam, etc.), use interpolation functions of the same order (first-order elements versus second-order elements), and have the same integration scheme (reduced integration, full integration, etc.).Finally, computations depend on wh

24、ether you choose to display the field output values or discontinuities; discontinuities are the differences in field output values between adjacent elements (应力梯度：相邻区域的应力变化程度). Field Output: For the display of field output values, the calculated invariants or components at nodes common to two or mor

25、e elements are averaged conditionally, depending on the compatibility of contributing result regions and on options you select. For more information, see “Understanding result value averaging,” Section 40.5.2. Discontinuities: For the display of discontinuities, the calculated invariants or componen

26、ts at nodes common to two or more elements are compared to determine the greatest difference, depending on the compatibility of contributing result regions and on options you select. Nodes associated with only one element and nodes receiving equivalent values from all contributing elements will show

27、 a value of zero in a plot of putationExtrapolating (from element centroid or integration point to Node)Averaging (average the extrapolated results from all contributing elements)InvariantExtrapolatingAveragingInvariantAveragingExtrapolatingInvariantDiscontinuityExtrapolatingthe greatest differencec

28、ompareInvariant40.5.2 Understanding result value averagingResult value averaging is applicable to the display of element-based field output variables using any of the following methods: line- or banded-type contours, probing at nodal locations, forming a display group or color coding based on result

29、 values extracting XY data along a path, or generating reports for field data.The display of node-based field output variables, quilt contour plots, and plots of discontinuities doesnot involve value averaging.Extrapolated output database values at nodes common to two or more elements are averaged c

30、onditionally. You can use the following options to control the extent to which Abaqus/CAE averages the values at the nodes: Select result regions and choose whether averaging takes place across region boundaries. Choose whether shell and membrane feature edges are treated as region boundaries for av

31、eraging. Include or exclude contributions from elements that are not displayed. Choose whether invariants are computed and components are extracted before or after averaging. Select a threshold value to control averaging based on the difference between the contributing element values (this option is

32、 available only if you choose to calculate invariants before averaging). Figure 402 Contour plots using region boundaries and averaging across region boundaries.Abaqus/CAE averages values at nodes common to two or more elements when the contributing elements lie in the same result region. The defaul

33、t result regions are the same regions defined when you assign sections to your model; you can also define custom result regions using saved element sets or display groups. You can choose whether or not Abaqus/CAE averages values at nodes common to two or more result regions. You can suppress averagi

34、ng across regions (use the region boundaries) to emphasize any discontinuities at region boundaries, or you can request averaging across regions (ignore region boundaries) to produce a more continuous effect. For example, Figure 402 shows a contour plot using region boundaries on the left and averag

35、ing across region boundaries on the right.XXYYZZXYYZZXVon-MisesElement 1 node i3.931-3.77610.638.286-1.179-1.402 19.28Element 2 node i-4.883-10.71-1.9344.0500.6537-0.1754 10.51Element 3 node i-1.23-2.8152.3613.678-0.10930.6115 7.927Element 4 node i-1.297-6.4191.5766.2271.4810.1554 13.12node i12.71XXYYZZXYYZZXVon-MisesElement 1 node i3.931-3.77610.638.286-1.179-1.402Element 2 node i-4.883-10.71-1.9344.0500.6537-0.1754Element 3 node i-1.23-2.8152.3613.678-0.10930.6115Element 4 node i-1.297-6.4191.5766.2271.4810.1554node i-0.869