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From version < 36.1 >
edited by Fredrik Lagerström
on 2020/03/27 05:50
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edited by Fredrik Lagerström
on 2020/03/27 05:57
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1 +Finite Element Mesh
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1 +Manuals.User Manual.WebHome
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1 +{{box cssClass="floatinginfobox" title="**Contents**"}}
2 +{{toc/}}
3 +{{/box}}
4 +
5 +Finite Element Method is used in calculation engine as it is also visible in the name of program (__F__inite __E__lement __M__ethod = FEM). This chapter introduces the main concepts, features and functions of the built-in finite element method.
6 +
7 += Element Types =
8 +
9 +Depending on the applied FEM-Design module, the engine uses the following line and 2D (rectangular and triangular) finite elements.
10 +
11 +(% border="1" %)
12 +|= |=(% colspan="6" rowspan="1" style="text-align: center;" %)**Finite Elements**
13 +| |(% colspan="2" rowspan="1" style="text-align:center" %)**Line element**|(% colspan="2" rowspan="1" style="text-align:center" %)**2D element**|(% colspan="2" rowspan="1" style="text-align:center" %)**3D element**
14 +|**FEM-Design Module**|(% style="text-align:center" %)**“Standard”**|(% style="text-align:center" %)**“Accurate”**|(% style="text-align:center" %)**“Standard”**|(% style="text-align:center" %)**“Accurate”**|(% style="text-align:center" %)**“Standard”**|(% style="text-align:center" %)**“Accurate”**
15 +|(% style="text-align:center" %)[[image:1585283936395-928.png]] [[image:1585284003385-882.png]]|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %) |(% style="text-align:center" %)[[image:1585284338571-882.png]] [[image:1585284345045-753.png]]
16 +8-node  6-node|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %)
17 +|(% style="text-align:center" %)[[image:1585284331773-415.png]]|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="text-align:center" %)[[image:1585284378769-839.png]]
18 +Beam|(% style="background-color:#c0c0c0; text-align:center" %) |(((
19 +(% style="text-align: center;" %)
20 +[[image:1585284634926-866.png]] [[image:1585284640430-195.png]]
21 +
22 +(% style="text-align: center;" %)
23 +9-node  6-node
24 +)))|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %)
25 +|(% style="text-align:center" %)[[image:1585284404468-380.png]]|(((
26 +(% style="text-align: center;" %)
27 +[[image:1585284513216-336.png]]
28 +
29 +(% style="text-align: center;" %)
30 +Truss
31 +)))|(((
32 +(% style="text-align: center;" %)
33 +[[image:1585284519249-788.png]]
34 +
35 +(% style="text-align: center;" %)
36 +Beam
37 +)))|(((
38 +(% style="text-align: center;" %)
39 +[[image:1585284553890-705.png]] [[image:1585284561776-271.png]]
40 +
41 +(% style="text-align: center;" %)
42 +4-node  3-node
43 +)))|(((
44 +(% style="text-align: center;" %)
45 +[[image:1585284567449-345.png]] [[image:1585284573884-853.png]]
46 +
47 +(% style="text-align: center;" %)
48 +9-node  6-node
49 +)))|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %)
50 +|(% style="text-align:center" %)[[image:1585284419793-514.png]]|(((
51 +(% style="text-align: center;" %)
52 +[[image:1585284513216-336.png]]
53 +
54 +(% style="text-align: center;" %)
55 +Truss
56 +)))|(((
57 +(% style="text-align: center;" %)
58 +[[image:1585284519249-788.png]]
59 +
60 +(% style="text-align: center;" %)
61 +Beam
62 +)))|(((
63 +(% style="text-align: center;" %)
64 +[[image:1585284555924-547.png]] [[image:1585284563294-388.png]]
65 +
66 +(% style="text-align: center;" %)
67 +4-node  3-node
68 +)))|(((
69 +(% style="text-align: center;" %)
70 +[[image:1585284568864-479.png]] [[image:1585284575335-532.png]]
71 +
72 +(% style="text-align: center;" %)
73 +9-node  6-node
74 +)))|(% style="text-align:center" %)[[image:1585284431164-331.png]][[image:1585284436735-255.png]][[image:1585284454407-999.png]]
75 +4-, 6-, 8 - nodes|(% style="text-align:center" %)[[image:1585284442074-438.png]][[image:1585284447150-457.png]][[image:1585284460408-988.png]]
76 +10-, 17-, 27 nodes
77 +
78 +Table: Finite element types by FEM-Design modules
79 +
80 +In the 3D modules, you can choose between “standard” and “accurate” 2D element types. With standard elements you can run 4-times faster but less accurate analysis than with the fine elements. In case of bar elements, the program assigns 2-node line elements to each beam and column element by default:
81 +
82 +* 1 piece when choosing “standard” elements, and
83 +* 2 pieces when choosing “accurate” mode.
84 +
85 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.wmz||alt="MCj04113200000%5b1%5d"]] **The program divides curved beam objects by several line elements in number depends on the central angle of the arc.
86 +
87 +The element type “standard” or “accurate” can be set in the calculation dialog (//Analysis > Calculate > Analysis > Finite element types//).
88 +
89 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png]]
90 +
91 +Figure: Finite element types by FEM-Design modules
92 +
93 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.wmz||alt="MCj04113200000%5b1%5d"]] **Modification on the geometry of a structural object causes the deletion of its finite elements.
94 +
95 +=== Mesh Generation ===
96 +
97 +FEM-Design offers a fully automatic finite element mesh generation by using optimized (factory default) or custom mesh settings. Of course, the generated mesh can be modified with special easy-to-use [[**edit and modify function**>>path:#_Edit_and_Modify]]**//s//**.
98 +
99 +Fully automatism means that the program generates the mesh with elements having average element size optimized for the structure and its environment (supports and loads). The process can contain automatic element refinement and [[**peak smoothing**>>path:#_Peak_Smoothing]] algorithm according to the settings.
100 +
101 +Automatic mesh generation can be done according to the [[**mesh settings**>>path:#_Mesh_Settings]]:
102 +
103 +* **Before calculations**
104 +
105 +Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png||alt="icon_prepare.png"]] //Prepare //in the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png||alt="icon_finiteelementtab.png"]] tabmenu. You can see and check the finite element suggested. The mesh will be visible by activating the //Surface elements// layer automatically. If you do not edit the mesh and modify the structural model, the later calculations will use the mesh generated by //Prepare//, so no further mesh generation will be done.
106 +
107 +* **As the result of calculations**
108 +
109 +If the program does not find previously generated finite element mesh, running calculations (analysis or design) by [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png||alt="icon_calculate.png"]] //Calculate// generates it automatically. The mesh can be displayed by activating the //Surface elements// layer in the current structural or result view mode or just by returning to [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png||alt="icon_finiteelementtab.png"]] mode.
110 +
111 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image007.png||alt="mesh_generation.png"]]
112 +
113 +Figure: Automatic finite element mesh generation
114 +
115 +==== Mesh Settings ====
116 +
117 +The settings of the automatic mesh generation are available only in [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png||alt="icon_finiteelementtab.png"]] mode and at //Settings> All...> FEM// //> Mesh// and //Calculation//.
118 +
119 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image008.png]]
120 +
121 +Figure: Settings affect automatic mesh generation (Prepare)
122 +
123 +**“General” settings**
124 +
125 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image009.png||alt="mesh_generalset.png"]]
126 +
127 +* **Merge objects**
128 +
129 +The program merges [[**fixed points**>>path:#FEM_fixed_point_chapter]], [[**fixed lines**>>path:#FEM_fixed_line_chapter]], [[**supports**>>path:#_Supports]], [[**beams**>>path:#_Beam]], [[**columns**>>path:#_Column]] and [[**walls**>>path:#_Wall]] (only in the //Plate// module) to [[**plate**>>path:#_Plate]] and/or [[**wall**>>path:#_Wall]] regions (the border of the regions). It is decided randomly which objects will be let in their place or removed. The objects shorter than a merging //distance// will be deleted. The objects being at the same place (covering) and having same properties will be deleted except one.
130 +
131 +The program also merges columns and/or beams together. It is decided randomly which line elements will be let in their place or removed. The bars shorter than the merging distance will be deleted. After that, the supports fit to the bars. The objects being at the same place (covering) and having same properties will be deleted except one.
132 +
133 +The program merges the loads to the geometry created in the first step. Those loads that have not been merged by the previous way will be merged together. It is decided randomly which ones will be let in their place or removed. Line loads shorter than the merging distance will be deleted. If the //Avoid load multiplication// option (see later) is active, the loads having the same position and same properties will be deleted except one.
134 +
135 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.wmz||alt="MCj04113200000%5b1%5d"]] **The merge process may modify the original shape of the objects to a simpler geometry; but a simple figure cannot be changed for a more complicated one. For example the program does not fit a line load having straight action line to a curved edge although merging distance requires that.
136 +
137 +This version of object merge cannot merge the plate or wall regions to themselves or to each other. The user has to pay attention to the correctness of these objects.
138 +
139 +Using //Auto merge objects// (recommended) corrects structural object misplacements. If the option is inactive, geometric anomalies cause too long mesh generation process or generation failure.
140 +
141 +Using //Inform about volume of merged objects// option together with object merge sends information about the quantity of corrections.
142 +
143 +//Distance// sets the maximal investigation zone between elements, so if the objects are closer than the defined distance, they will be merged. The suggested distance value is 3 to 5cm for engineering problems.
144 +
145 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image010.png||alt="mesh_objectmerge copy.PNG"]]
146 +
147 +Figure: Correction of misplaced elements (Object merge)
148 +
149 +Activating //Merge peak smoothing region// and //Merge load// allows the object merge to work for peak smoothing regions and loads.
150 +
151 +Using //Avoid load multiplication// deletes the loads having the same position, geometry and properties (load case host and value) by keeping only one copy.
152 +
153 +* **Load handling**
154 +
155 +By default, load positions are independent from the finite element mesh; so for example, it is not necessary to place point loads into finite element nodes and vice versa. Although it is recommended to place loads (especially the concentrated loads with high value) into nodes, it is not necessary. //Adjust mesh to load positions// automatically places finite element nodes in the action points, on the action line and region border of the loads depending on their types (point, line and surface load), so the mesh follows the load position and geometry.
156 +
157 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image011.png||alt="mesh_loadadjust.png"]]
158 +
159 +Figure: Load handling in mesh generation
160 +
161 +* **Auto peak smoothing region around...**
162 +
163 +To solve the result [[**singularity problems**>>path:#_Peak_Smoothing]] above supports and other critical points, the program may run [[**peak smoothing algorithm**>>path:#FEM_peak_smoothing_alg_chapter]] around the listed elements. Activating an element in the list, the program automatically creates [[**peak smoothing region**>>path:#FEM_peak_smoothing_region_chapter]] around it.
164 +
165 +**“Elements” settings**
166 +
167 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image012.png||alt="mesh_elemset.png"]]**
168 +
169 +* **Calculated average element size**
170 +
171 +By default, the program automatically calculates the optimal average size of the 2D finite elements considering the size, the geometry, the environment etc. of the structural elements. So, you do not need to give an initial value for it. The automatic calculation and the element size depend on the following settings options.
172 +
173 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.wmz||alt="MCj04113200000%5b1%5d"]] **Element sizes can be set manually for all model regions or by regions with the [[**Average element size**>>path:#FEM_av_element_size_chapter]]**// //**command. If you modify the default “Automatic” value for a planar structural element (wall or plate) to a given value, the automatic element size calculation will be skipped for that region, and the given size will be used for that.
174 +
175 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image013.png||alt="mesh_setaverage.png"]]
176 +
177 +Figure: The Average element size command and the “Automatic” option
178 +
179 +Using //Region by region//, the program optimizes the element size by model regions. In this case, the regions will contain meshes generated by different average element sizes. This option is recommended to use in case regions (e.g. having openings and holes) need to be refined (more dense mesh).
180 +
181 +Using //Consider all regions together//, the one optimal average element size will be determined for all model regions having “[[**Automatic**>>path:#FEM_av_element_size_chapter]]” size setting. This option is suggested for structural models contain regions with nearly same geometry and size parameters.
182 +
183 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image014.png||alt="mesh_averageelementtz.png"]]
184 +
185 +Figure: Calculation modes of average size of 2D elements
186 +
187 +In the //Scale// figure, the optimal average element size can be reduced or increased with a given ratio set by the scroll button. The grey mesh shows the recommended optimal size, whilst the blue one shows the modified custom size. Double clicking the //Scale// figure resets the element size to the optimal average element size (1:1 ratio).
188 +
189 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image015.png||alt="mesh_setaveragescroll.png"]]
190 +
191 +Figure: The average element size will be four times bigger than the optimal size
192 +
193 +The //Correct according to the minimum division numbers// option modifies the average element size of the 2D elements, if the minimum division number ([[**automatic**>>path:#FEM_division_number_chapter]] or [[**custom**>>path:#FEM_division_number_chapter]]) of the boundary lines and edges requires that. This option is recommended for generating uniform finite element meshes. Skipping this option causes dense mesh near edges where the minimum division numbers are predefined.
194 +
195 +Using the //According to the peak smoothing regions// option considers the [[**peak smoothing**>>path:#_Peak_Smoothing]] settings of model elements in the calculation of the average element size.
196 +
197 +* **Line element parameters**
198 +
199 +The default minimum number of the line elements can be set here for the bar elements. The meaning of the default division number depends on the applied element type: [[**standard or accurate**.>>path:#_Element_Types_1]] For example n=2 value sets (minimum) 2 finite elements for a whole bar (if neighboring elements connect to it only in its endpoints) or a continuous part of it (in case of joined or intersected neighbors) in case //standard// element type and 4 elements at //accurate// element type.
200 +
201 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image016.png||alt="mesh_lineelementnumber copy.png"]]
202 +
203 +Figure: Meaning of Division number in case of Standard and Accurate element types
204 +
205 +At curved beams, alpha parameter sets the minimum division number:
206 +
207 + minimum division number = central angle of the curved beam / alpha .
208 +
209 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.wmz||alt="MCj04113200000%5b1%5d"]] **Division number can be set manually for all bar elements or by line elements with the [[**Division number**>>path:#FEM_division_number_chapter]]**// //**command.
210 +
211 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image017.wmz||alt="MCj02990090000%5b1%5d"]] **For imperfection (of steel bars), stability and dynamic calculations, it is suggested to set the default //n// value to more than 1; 4-5 division number is the recommended minimum for //n//.
212 +
213 +
214 +
215 +**“Functions” settings**
216 +
217 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image018.png||alt="mesh_funcset.png"]]**
218 +
219 +* **Automatic refinement in surface mesh (Generate surface mesh)**
220 +
221 +The //Refine locally where needed// option – as an iteration process - eliminates distorted elements, which may normally be derived from accidental geometric errors (if [[**object merge**>>path:#FEM_object_merge_chapter]] is not used). So, the option makes the finite element mesh denser at the locations where needed. (Deactivation of this option can be used in case of searching geometric errors.) The //Max. step// (recommended value is 6) defines the number of the iteration step of refining. The iteration will end when generated elements have the required side-ratio or the steps of the iteration reach their maximal value. If //Max. step// is not enough for the optimal refining, a warning message informs you the number of iteration steps is not enough and there are critical geometry errors (if the //Warn about reaching max. step// option is active).
222 +
223 +The automatic refinement may cause too dense mesh at special geometries (e.g. at highly depressed regions), so in that case, it would be more practical to reduce the average element size with the //Reduce average element size if necessary// option.
224 +
225 +* **Smooth surface mesh**
226 +
227 +Smooth procedure calculates the optimal coordinates of the corner nodes of elements. It is recommended after splitting or merging elements. The best mesh can be achieved with the iterative use of the [[**Rebuild**>>path:#FEM_rebuild_chapter]] and the [[**Smooth**>>path:#FEM_smooth_chapter]]**// //**commands. Smoothing of a mesh is executed with iteration technique: the procedure places the nodes of the triangle elements in such a way, that the area of the triangles will be balanced. The number of the smoothing steps can be set in the //Steps// field.
228 +
229 +* **Check surface mesh**
230 +
231 +The //Check surface mesh //option lets the program to check the geometry of the mesh after automatic mesh generation. The mesh can be controlled with respect to unsuitable geometry, overlaps and topology. This means that mesh errors, produced by an automatic or manual mesh generation can be easily found. If the program finds defective geometric elements in the model, it sends a warning message (error list) and displays the position of the mesh errors.
232 +
233 +The //Geometry// tool checks the geometry of finite elements, such as the angles of the elements and the ratio of the largest and smallest sides (//Max. side ratio//).
234 +
235 +The //Overlap & cut// tool checks overlapping and intersecting finite elements, which can be caused for example by copying or moving regions together with their finite element meshes.
236 +
237 +The //Topology & gap// tool checks the topology of the finite elements and finds possible gaps. A typical topological error, when for example a corner node of an element lies on a side edge of another element. This problem can easily arise manually by using the [[**Split**>>path:#FEM_splitting_elements_chapter]] command incorrectly.
238 +
239 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image019.png||alt="mesh_topologerror.png"]]
240 +
241 +Figure: Topologic errors (unconnected nodes)
242 +
243 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image017.wmz||alt="MCj02990090000%5b1%5d"]] **Topological errors can be easily solved by the [[**Rebuild**>>path:#FEM_rebuild_chapter]] and [[**Smooth**>>path:#FEM_smooth_chapter]] commands and quick algorithms.
244 +
245 +**“Prepare” settings**
246 +
247 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image020.png||alt="mesh_prepareset.png"]]
248 +
249 +* **Regenerate surface mesh automatically on the changed regions**
250 +
251 +Using this option, the program will regenerate the mesh at any geometrical changes of region elements and will generate mesh on the regions having no mesh.
252 +
253 +If you switch off the //Regenerate surface mesh automatically//... option, the program will not generate mesh on the regions modified geometrically and will send an error message. In this case you cannot start calculation until you generate mesh on those regions. And, if you would like to generate mesh manually with the [[**edit functions**>>path:#_Edit_Functions]], also inactivate this option.
254 +
255 +From the element list, you can choose element types for automatic mesh refinement around them.
256 +
257 +The //Optimal rebuild surface mesh after refine// option rebuilds the mesh automatically after refine. It is recommended to use this option, because elements having non-optimal side-ratio (after refining) will be removed. This procedure will also create more optimal quadrates from the triangles.
258 +
259 +If you have objects to refine, the //Smooth surface mesh after refine// option will smooth the mesh after generation, refine and rebuild procedures.
260 +
261 +* **Check the surface mesh**
262 +
263 +If this option is activated, the program will automatically check the mesh on regions having valid mesh and are not necessary to be regenerated. The mesh of a region is valid, if the geometry of the region has not been modified since the last generation.
264 +
265 +==== Peak Smoothing ====
266 +
267 +**Singularity problem**
268 +
269 +As an effect of the mesh refinement the calculated results are converging to the theoretical solution. The problem is that at certain places we get infinite inner forces according to the theory, so the inner forces increase each time by refining the mesh. These places could be: point supports, end points of edge supports,
270 +
271 +vertices of surface supports, end points of beams and columns, end points of intersection lines of adjoining surfaces, point loads, end points of line loads, vertices of surface loads etc.
272 +
273 +In practice, usually, the singularity problem occurs at supports because they heavily influence the inner forces (e.g. negative moments) in ratio.
274 +
275 +**Possible solutions**
276 +
277 +There are three known possibilities to solve the above-mentioned problem:
278 +
279 +* **Choosing optimal finite element size at singularity places**
280 +
281 +FEM-Design aids that with several built-in tools such as automatic element size adjustment, automations in mesh generation, automatic local densification etc. It is evident, that choosing optimal element size cannot be perfect, because we should have to know the appropriate values to which we adjust the average element size in advance. The functions used today for automatic element size calculation and generation are providing values with adequate precision in most cases, but it is obvious that they cannot guarantee that in any case.
282 +
283 +* **More realistic and precise model definition**
284 +
285 +Point and line loads/supports with action surface (only action points and lines) do not exist in real life. So, if you model all point/line loads and supports as surface loads/supports, then you can cease the problem derived from the singularity. This opportunity is available in FEM-Design, because the user can apply [[**surface supports**>>path:#_Supports]] and [[**loads**>>path:#_Load_Types]] with any directions and any geometry of action surface.
286 +
287 +* **Peak smoothing**
288 +
289 +Singularities always cause only local disturbance in the inner forces, they do not influence the inner forces at adequately short distance from the location of singularities. The “adequately short distance” is defined by the national standards. In the zones causing substantial changes three solutions can occur according to the codes: the peak can be cut (1), or it can be approached with a linear or higher order function (2), or a constant value may be set above the substantial area (3). In the last solution, the capacity of the inner force figure above the area may become equal with the capacity of the original figure. The last solution is the safest one, so it is accepted by every standard.
290 +
291 +The peak smoothing algorithm is available (**for internal forces and stresses in planar elements**) in every FEM-Design modules work with planar objects.
292 +
293 +**Peak smoothing region**
294 +
295 +The program defines peak smoothing regions to solve the possible singularity problems. Basically, these regions are the active zones in the environment of the singularity, where the inner forces change substantially as a result of mesh refinement.
296 +
297 +Peak smoothing regions can be generated automatically by the mesh generator or calculation processes. Automatic generation always results circular peak smoothing regions with centre points placed in the location of the singularity. The radius of a circular smoothing region depends on the geometry of singularity locations.
298 +
299 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image017.wmz||alt="MCj02990090000%5b1%5d"]] **Peak smoothing regions with any arbitrary shape can be defined manually with the [[**Peak smoothing region**>>path:#FEM_peak_smoothing_chapter]] command. That command is able to edit predefined (automatically or manually) peak smoothing regions.
300 +
301 +Automatic generation of peak smoothing regions can be set and controlled at the [[**General**>>path:#_Mesh_Settings]] settings of mesh generation (//Settings> All…> FEM> Mesh> General//). At //Peak smoothing region around...// option you can set the places (depending on the current module) where you want the program to create circular peak smoothing regions. The radius of the circular regions is calculated from the following formula:
302 +
303 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image021.png]]
304 +
305 +Figure: Settings of automatic peak smoothing generation
306 +
307 +//r = t / 2 + f * v//,
308 +
309 +where:
310 +
311 +//t// is the characteristic geometric parameter of the object that causes singularity:
312 +
313 +* 0 value in case of supports (point, line and surface),
314 +* the diameter of circle circumscribed of a cross-section, if bar elements connect to planar elements,
315 +* the thickness of the plate or wall, if the peak smoothing region generated in plate/wall connection;
316 +
317 +//v// is the thickness of the planar element (plate, wall) in the considered place;
318 +
319 +//f //is a factor can be set manually. The default value is 0.5, which means 45 degrees angle of projection starts from the connection (singularity cause) and ends in the calculation plane of the related planar element (see the figure before).
320 +
321 +
322 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image022.png||alt="mesh_peak.png"]]
323 +
324 +Figure: Examples for peak smoothing regions by different element-plate connection
325 +
326 +**Peak smoothing algorithm**
327 +
328 +The steps of the peak smoothing algorithm are the followings during calculations (inner forces):
329 +
330 +1. Select the peak smoothing method for moments, normal and shear forces under Settings/Calculation/Peak smoothing/Method
331 +
332 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image023.png]]
333 +
334 +1. The program creates peak smoothing regions and/or checks the predefined active zones.
335 +
336 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image024.png]]
337 +
338 +Figure: Generation of peak smoothing region at column-plate/wall connections
339 +
340 +1. Allow peak smoothing algorithm for internal force and stress calculations. It is not enough to generate peak smoothing regions, so you have to confirm the smoothing process in the //Calculate// dialog before starting any analysis (and design) calculations.
341 +
342 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image025.png]]
343 +
344 +Figure: Peak smoothing algorithm set for analysis calculations
345 +
346 +1. The program calculates a constant value for cutting the peaks according to volume calculations of inner diagrams above the peak smoothing regions. That means, the volume at the final constant result value (//Volume (smooth)//) is equal with the volume derived from the peak (singularity) value (//Volume (peak)//) above the same peak smoothing region. Let’s see the next figure.
347 +
348 +
349 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image026.png||alt="mesh_peak2.png"]]
350 +
351 +Figure: Peak smoothing algorithm (modified inner force diagram)
352 +
353 +
354 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image027.png||alt="mesh_peak6.png"]]
355 +
356 +Figure: Internal force “graph” and “section” diagrams after using peak smoothing algorithm
357 +
358 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image017.wmz||alt="MCj02990090000%5b1%5d"]] **Although peak smoothing is available for internal and stress calculations of planar elements, you can solve the singularity peak problem of line reactions and line connection forces. The program calculates the average value of the reaction and connection forces by finite element. That means, line reactions and connection forces can be displayed with constant (average) value by element ([[**Distribution > Constant by element**>>path:#DispRes_distribution]]). In this case, you can easily place [[**numeric values**>>path:#_Numeric_Values]] onto the steps of a figure (//Numeric value> Find all local maximum/minimum//).
359 +
360 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image028.png||alt="23_average_theory"]]
361 +
362 +Figure: Singularity of line reaction force solved by simple display technique
363 +
364 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image017.wmz||alt="MCj02990090000%5b1%5d"]] **It is important to select the correct peak smoothing method cause it has big effect to the results.
365 +
366 +|**Don’t smooth**|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image029.png]]|
367 +|**Use constant shape function**|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image030.png]]|
368 +|**Use higher order shape functions**|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image031.png]]|
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