<
From version < 38.1 >
edited by Fredrik Lagerström
on 2020/03/27 06:03
To version < 39.1 >
edited by Fredrik Lagerström
on 2020/03/27 06:08
>
Change comment: There is no comment for this version

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9 9  Depending on the applied FEM-Design module, the engine uses the following line and 2D (rectangular and triangular) finite elements.
10 10  
11 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”**
12 +|=(% colspan="1" rowspan="3" style="text-align: center;" %)**FEM-Design Module**|=(% 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 +|(% 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 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 16  8-node  6-node|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %)
17 17  |(% style="text-align:center" %)[[image:1585284331773-415.png]]|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="text-align:center" %)[[image:1585284378769-839.png]]
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23 23  9-node  6-node
24 24  )))|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %)
25 25  |(% style="text-align:center" %)[[image:1585284404468-380.png]]|(((
26 -(% style="text-align: center;" %)
26 +(% style="text-align:center" %)
27 27  [[image:1585284513216-336.png]]
28 28  
29 29  (% style="text-align: center;" %)
30 30  Truss
31 31  )))|(((
32 -(% style="text-align: center;" %)
32 +(% style="text-align:center" %)
33 33  [[image:1585284519249-788.png]]
34 34  
35 35  (% style="text-align: center;" %)
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48 48  9-node  6-node
49 49  )))|(% style="background-color:#c0c0c0; text-align:center" %) |(% style="background-color:#c0c0c0; text-align:center" %)
50 50  |(% style="text-align:center" %)[[image:1585284419793-514.png]]|(((
51 -(% style="text-align: center;" %)
51 +(% style="text-align:center" %)
52 52  [[image:1585284513216-336.png]]
53 53  
54 54  (% style="text-align: center;" %)
55 55  Truss
56 56  )))|(((
57 -(% style="text-align: center;" %)
57 +(% style="text-align:center" %)
58 58  [[image:1585284519249-788.png]]
59 59  
60 60  (% style="text-align: center;" %)
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92 92  
93 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 94  
95 -=== Mesh Generation ===
95 += Mesh Generation =
96 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//**.
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//s//**.
98 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.
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** algorithm according to the settings.
100 100  
101 -Automatic mesh generation can be done according to the [[**mesh settings**>>path:#_Mesh_Settings]]:
101 +Automatic mesh generation can be done according to the **mesh settings**:
102 102  
103 103  * **Before calculations**
104 104  
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126 126  
127 127  * **Merge objects**
128 128  
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.
129 +The program merges **fixed points**, **fixed lines**, **supports**, **beams**, **columns** and **walls** (only in the //Plate// module) to **plate** and/or **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.
130 130  
131 131  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.
132 132  
... ... @@ -160,7 +160,7 @@
160 160  
161 161  * **Auto peak smoothing region around...**
162 162  
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.
163 +To solve the result **singularity problems** above supports and other critical points, the program may run **peak smoothing algorithm** around the listed elements. Activating an element in the list, the program automatically creates **peak smoothing region** around it.
164 164  
165 165  **“Elements” settings**
166 166  
... ... @@ -170,7 +170,7 @@
170 170  
171 171  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.
172 172  
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.
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// //**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.
174 174  
175 175  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image013.png||alt="mesh_setaverage.png"]]
176 176  
... ... @@ -178,7 +178,7 @@
178 178  
179 179  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).
180 180  
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.
181 +Using //Consider all regions together//, the one optimal average element size will be determined for all model regions having “**Automatic**” size setting. This option is suggested for structural models contain regions with nearly same geometry and size parameters.
182 182  
183 183  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image014.png||alt="mesh_averageelementtz.png"]]
184 184  
... ... @@ -190,13 +190,13 @@
190 190  
191 191  Figure: The average element size will be four times bigger than the optimal size
192 192  
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.
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** or **custom**) 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.
194 194  
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.
195 +Using the //According to the peak smoothing regions// option considers the **peak smoothing** settings of model elements in the calculation of the average element size.
196 196  
197 197  * **Line element parameters**
198 198  
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.
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**. 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.
200 200  
201 201  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image016.png||alt="mesh_lineelementnumber copy.png"]]
202 202  
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206 206  
207 207   minimum division number = central angle of the curved beam / alpha .
208 208  
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.
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// //**command.
210 210  
211 211  **[[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//.
212 212  
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218 218  
219 219  * **Automatic refinement in surface mesh (Generate surface mesh)**
220 220  
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).
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** 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).
222 222  
223 223  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.
224 224  
225 225  * **Smooth surface mesh**
226 226  
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.
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** and the **Smooth// //**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.
228 228  
229 229  * **Check surface mesh**
230 230  
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234 234  
235 235  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.
236 236  
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.
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** command incorrectly.
238 238  
239 239  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image019.png||alt="mesh_topologerror.png"]]
240 240  
241 241  Figure: Topologic errors (unconnected nodes)
242 242  
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.
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** and **Smooth** commands and quick algorithms.
244 244  
245 245  **“Prepare” settings**
246 246  
... ... @@ -250,7 +250,7 @@
250 250  
251 251  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.
252 252  
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.
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**, also inactivate this option.
254 254  
255 255  From the element list, you can choose element types for automatic mesh refinement around them.
256 256  
... ... @@ -282,7 +282,7 @@
282 282  
283 283  * **More realistic and precise model definition**
284 284  
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.
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** and **loads** with any directions and any geometry of action surface.
286 286  
287 287  * **Peak smoothing**
288 288  
... ... @@ -296,9 +296,9 @@
296 296  
297 297  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.
298 298  
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.
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** command. That command is able to edit predefined (automatically or manually) peak smoothing regions.
300 300  
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:
301 +Automatic generation of peak smoothing regions can be set and controlled at the **General** 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:
302 302  
303 303  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image021.png]]
304 304  
... ... @@ -345,7 +345,6 @@
345 345  
346 346  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.
347 347  
348 -
349 349  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image026.png||alt="mesh_peak2.png"]]
350 350  
351 351  Figure: Peak smoothing algorithm (modified inner force diagram)
... ... @@ -355,7 +355,7 @@
355 355  
356 356  Figure: Internal force “graph” and “section” diagrams after using peak smoothing algorithm
357 357  
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//).
357 +**[[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**). In this case, you can easily place **numeric values** onto the steps of a figure (//Numeric value> Find all local maximum/minimum//).
359 359  
360 360  [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image028.png||alt="23_average_theory"]]
361 361  
... ... @@ -366,3 +366,261 @@
366 366  |**Don’t smooth**|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image029.png]]|
367 367  |**Use constant shape function**|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image030.png]]|
368 368  |**Use higher order shape functions**|[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image031.png]]|
368 +
369 += Edit Functions =
370 +
371 +There are numerous tools in the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png||alt="icon_finiteelementtab.png"]] tabmenu allow you to edit the finite element mesh generated automatically.
372 +
373 +A short summary of the edit functions:
374 +
375 +* adding additional nodes to the mesh (**Fixed point**),
376 +* fixing lines inside the mesh (**Fixed line**),
377 +* editing peak smoothing regions or definition of new ones (**Peak smoothing region**),
378 +* fixing the node numbers on fixed lines (**Division number**),
379 +* modifying the element number on bar elements (**Division number**),
380 +* modifying the average element size of 2D finite elements (**Average element size**),
381 +* refining mesh manually (**Refine**),
382 +* splitting elements to modify finite element geometries (**Split**),
383 +* modifying node positions (**Move node**),
384 +* deletion of mesh regions (**Delete**).
385 +
386 +After editing finite element mesh, you can do automatic mesh **object merge**, **rebuild**, **smooth**, **check// //**etc. processes with special tools of the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png||alt="icon_finiteelementtab.png"]] tabmenu. Mesh generation can be done by planar regions with the **Generate** tool.
387 +
388 +**Adding nodes to mesh**
389 +
390 +With [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png]] //Fixed point//, nodes can be manually added to a predefined mesh in given points.
391 +
392 +Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png||alt="icon_prepare.png"]] //Prepare //to update the mesh according to the new nodes. Depending on **mesh settings**, the program automatically does refine, smooth and check processes to create an optimal mesh, if it is possible.
393 +
394 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png||alt="mesh_fixedpointd.png"]]
395 +
396 +Figure: Adding nodes to a mesh
397 +
398 +Fixed points defined in the model can be displayed with the //Geometrical system// object layer.
399 +
400 +**Fixing lines of mesh**
401 +
402 +With [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png]] //Fixed line//, lines (straight and curved) can be fixed in a mesh to generate nodes on it.
403 +
404 +Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image007.png]] //Prepare //to update the mesh according to the new nodes. The program defines nodes in the line endpoints and some points on the lines. Depending on **mesh settings**, the program automatically does refine, smooth and check processes to create an optimal mesh, if it is possible. Further node distribution of the fixed line element can be influenced by the **Division number** command.
405 +
406 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image008.png]]
407 +
408 +Figure: Adding lines to a mesh
409 +
410 +Fixed points defined in the model can be displayed with the //Geometrical system// object layer. In brackets, the number of line elements can be seen defined by the **Division number** command. If “-“ is displayed, there is no restriction on the element number.
411 +
412 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image009.wmz||alt="MCj02990090000%5b1%5d"]] **//Fixed lines// display the intersection lines of structural regions (e.g. intersections of slabs and walls) too. This is very useful for defining holes/openings that connect accurately to finite element meshes (see the next figure).
413 +
414 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image010.png]]
415 +
416 +Figure: Fixed lines used for editing regions
417 +
418 +**Editing peak smoothing regions**
419 +
420 +With [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image011.png]] //Peak smoothing region//, the predefined peak smoothing regions can be edited (status, shape and size modification), or new ones can be defined manually.
421 +
422 +The following functions can be done with the //Peak smoothing region// command:
423 +
424 +* **Modifying the geometry of predefined peak smoothing region**
425 +
426 +**Automatic generation** of peak smoothing region always results circular geometry of regions. If you would like to create regions with custom shape, draw a new one with the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image012.png||alt="icon_define.png"]] //Define// tool and the different shape tools. If the new region covers an automatic one (and it is active, see later), the program will use the new region instead of the automatic one for solving the singularity.
427 +
428 +
429 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image013.png]]
430 +
431 +Figure: Manually drawn peak smoothing regions with custom shape
432 +
433 +Sometimes, you need to correct the geometry of automatic regions to avoid the creation of incorrect or too dense finite element mesh (nodes are generated in the intersections and on the edges of peak smoothing regions).
434 +
435 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image014.png]]
436 +
437 +Figure: Geometry modification effect on finite element mesh generation
438 +
439 +* **Creation of new peak smoothing regions manually**
440 +
441 +With the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image015.png]] //Define// tool, totally new peak smoothing regions can be drawn with custom shapes, too.
442 +
443 +* **Modifying the status of a predefined peak smoothing region**
444 +
445 +Apply the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image016.png]] //Properties// tool and the //[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image017.png||alt="icon_peak_inactive.png"]] // //Inactive// option for peak smoothing regions to modify their status from active to inactive. Inactive region will not be considered in mesh generations and in calculations too. To reset an inactive status of a region to an active one, apply the //Properties// tool together with the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image018.png||alt="icon_peak_active.png"]] //Active// option for the region.
446 +
447 +
448 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image019.png||alt="mesh_peaktool copy.PNG"]]
449 +
450 +Figure: Difference between active and inactive peak smoothing regions
451 +
452 +Peak smoothing regions defined in the model are stored in the //Peak smoothing regions// object layer.
453 +
454 +Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image007.png]] //Prepare //to update the mesh according to the new and modified peak smoothing regions. Depending on **mesh settings**, the program automatically does refine, smooth and check processes to create an optimal mesh, if it is possible.
455 +
456 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image020.wmz||alt="MCj04113200000%5b1%5d"]] **It is not enough to generate/define peak smoothing regions, so you have to confirm the smoothing process in the //Calculate// dialog before starting any analysis (and design) calculations.
457 +
458 +**Division number**
459 +
460 +Division number sets:
461 +
462 +* the number of line finite elements of bar elements (columns and beams),
463 +* the number of 2D element-edges on **fixed lines** and structural region edges.
464 +
465 +In case of bar elements, the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image021.png]] //Division number //command can modify their default element number (value in brackets) set at **“Elements” setting**.
466 +
467 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image020.wmz||alt="MCj04113200000%5b1%5d"]] **In 3D modules, the meaning of division number depends on the element type sets at calculations. For example division number 2 sets 2 line elements for //standard// element type and 4 line elements for //accurate// element type. The line elements together with their node numbers can only be displayed after analysis (or design) calculations (see **display settings**).
468 +
469 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image022.png||alt="mesh_divisionnumber.PNG"]]
470 +
471 +Figure: The meaning of division number for bar elements
472 +
473 +In case of fixed lines and structural region edges, the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image021.png]] //Division number //command can fix the **minimum number **of 2D elements (sides) will be connected to the lines/edges by the mesh generator. “//-//” label in brackets shows no number-restriction for lines/edges.
474 +
475 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image023.png||alt="mesh_divisionnumber2.png"]]
476 +
477 +Figure: The meaning of division number for fixed lines and edges
478 +
479 +Defined division numbers together with fixed lines, edges and structural lines of bar elements are displayed with the //Geometrical system// object layer (red by default).
480 +
481 +**Modifying average element size**
482 +
483 +The [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image024.png]] //Average element size// command modifies the optimized element size(s) of 2D elements calculated by the program according to **mesh settings**.
484 +
485 +Applying the command for a structural region (wall, plate etc.), a dialog shows with “//Automatic//” label, that the optimal element size calculation is the active by default for the region. Typing an arbitrary element size (in //a// field) overwrites the usage of the optimal size. Of course, the final average element size generates by the mixture of the value set by //Average element size// and the effect of **mesh settings**. Inactivating all mesh generation automatism (refine, smooth and check processes together with “//Elements//” settings), the //a// value will be the average element size for the related structural regions.
486 +
487 +Clicking //Calculate automatically// button shows the optimized average element size used when “//Automatic//” is set for the related object region(s).
488 +
489 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image025.png||alt="mesh_averageelement.png"]]
490 +
491 +Figure: “Automatic” and custom average element size
492 +
493 +Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image007.png]] //Prepare //or [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image026.png]] //Generate// (for the region only) to update the mesh according to the average element size setting.
494 +
495 +**Refine mesh manually**
496 +
497 +A predefined finite element mesh can be refined manually. Apply the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image027.png]] //Refine// command to refine mesh parts by picking structural objects connect to the meshed region or by clicking directly finite elements.
498 +
499 +* **Refine mesh around objects**
500 +
501 +Activate first the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image028.png||alt="icon_refine_mark.png"]] //Mark element mode//. Pick the checkbox of object types (e.g. //Region border//), which you would like to allow refining the mesh around. Select objects (e.g. Walls) assigned to allowed object types on the drawing area with [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image029.png||alt="icon_refine_pickobject.png"]] //Pick object//, or click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image030.png||alt="icon_refine_selectall.png"]] //Mark elements around all objects// to refine mesh around all objects belongs to the checked object types. Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image031.png||alt="icon_Enter"]] to start the refine process.
502 +
503 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image032.png||alt="mesh_refineobject.png"]]
504 +
505 +Figure: Refined finite element mesh around columns
506 +
507 +* **Refine 2D elements**
508 +
509 +Activate first the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image028.png||alt="icon_refine_mark.png"]] //Mark element mode//. Select elements of a mesh on the drawing area with [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image033.png||alt="icon_refine_pickelement.png"]] //Pick element//, or click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image030.png||alt="icon_refine_selectall.png"]] //Mark all elements// to refine all finite elements of the project. Click [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image031.png||alt="icon_Enter"]] to start the refine process.
510 +
511 +
512 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image034.png||alt="mesh_refineelement.png"]]
513 +
514 +Figure: Refined finite elements (element-selection)
515 +
516 +To deselect previously selected elements (before clicking [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image031.png||alt="icon_Enter"]] to start refine), switch to [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image035.png||alt="icon_refine_unmark.png"]] //Unmark element mode// and do the same steps mentioned for selection.
517 +
518 +**Splitting elements**
519 +
520 +2D finite elements can be refined according to splitting patterns, too. Start the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image036.png]] //Split// command, then chose a cut pattern, and finally select an element which you would like to apply the selected cut mode. Each pattern has a short description about its usage for rectangular and triangular 2D finite elements. At some splitting patterns, red “+” shows the click position in an element to get the requested splitting shapes.
521 +
522 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image037.png]]
523 +
524 +Figure: Element refinement manually with Split
525 +
526 +**Modifying node positions**
527 +
528 +The position of mesh nodes can be modified with the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image038.png]] //Move node// command. Select node(s) you would like to move, and define the displacement vector with a start- and endpoint. The program sends an error message, if it finds nodes being out of legal moving range.
529 +
530 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image039.png||alt="mesh_movenode.PNG"]]
531 +
532 +Figure: Modifying node positions
533 +
534 +**Deletion of mesh regions**
535 +
536 +With the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image040.png]] //Delete// command, predefined mesh of selected planar object (regions) can be deleted. Just select the required region(s) and the program erases the mesh.
537 +
538 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image020.wmz||alt="MCj04113200000%5b1%5d"]] **If you modify the geometry of an object region (e.g. by inserting a hole, by stretching one of region corners etc.), mesh assigned to it will be automatically deleted.
539 +
540 +
541 +
542 +**Object merge**
543 +
544 +The **object merge process** can be run any time you want by clicking the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image041.png]] //Object merge// command button.
545 +
546 +**Rebuild**
547 +
548 +After using manual tools (mentioned before) to edit the mesh generated automatically before, it is recommended to rebuild the mesh. The process rebuilds the current mesh of selected object regions according to the global optimum without the movement of mesh nodes.
549 +
550 +The steps of the rebuild process are:
551 +
552 +1. The program builds a mesh from triangular elements using the principles of Delaunay triangular technique.
553 +1. It converts these triangles to quadrates corresponding to the global optimum of the mesh.
554 +
555 +If the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image042.png]] //Rebuild// command results drastic changes in the mesh, **smoothing** algorithm is also recommended. The best, the most optimal finite element meshes can be achieved with the iterative usage of the two commands.
556 +
557 +**Smooth**
558 +
559 +Smooth process calculates the optimal coordinates of the corner element nodes. Smoothing the mesh is highly recommended after **splitting** or **merging** elements. If the mesh is modified drastically after **rebuild**, use smoothing for the model. The best, the most optimal finite element meshes can be achieved with the iterative use of the **//rebuild//** and the smoothing.
560 +
561 +Just apply the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image043.png||alt="icon_smooth.png"]] //Smooth// command for selected mesh regions. Mesh smoothing is executed with iteration technique: the procedure places the nodes of the triangular elements in such a way, that the area of the triangles will be balanced. The number of the smoothing iteration steps can be set at **“Functions > Smooth surface mesh” settings**.
562 +
563 +**[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image020.wmz||alt="MCj04113200000%5b1%5d"]] **//Undo// cannot restore the mesh state before using //Smooth//.
564 +
565 +**Check**
566 +
567 +After using manual tools (mentioned before) to edit the mesh generated automatically before, it is recommended to check the mesh. It can be done according to **“Functions > Check surface mesh” settings** any time you want by clicking the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image044.png||alt="icon_check.png"]] //Check// command button.
568 +
569 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image045.png||alt="mesh_check.png"]]
570 +
571 +Figure: Topological errors found by Check
572 +
573 +**Generate (vs. Prepare)**
574 +
575 +Automatic mesh generation can be done by planar object region with the [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image026.png]] //Generate// command. (**Prepare** runs automatic mesh generation for the entire structural model.) //Generate //takes into consideration the manual editing functions (such as **Fixed point**, **Fixed line**, **Peak smoothing**, **Division number** and **Average element size**) and the **Mesh settings** excluding the **Check**, the **Smooth** and the **Prepare** settings. //Generate// is also recommended to find defective geometric finite elements by checking (generating mesh) regions by regions.
576 +
577 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image046.png]]
578 +
579 +Figure: Mesh generation by regions (Generate)
580 +
581 +Mesh generation is an iteration process, of which goal is to generate optimal and eurhythmic mesh by the given or automatically calculated average element size. The main and general steps of the generation process are the following:
582 +
583 +1. Defining the node positions of elements.
584 +1. Creating triangle elements by nodes.
585 +1. Converting triangle elements to mixed quadrate mesh where it is possible.
586 +1. Optimization of node coordinates (e.g. smoothing the mesh).
587 +1. Definition of middle points on element sides.
588 +
589 += Renumbering and Display Settings =
590 +
591 +**Renumbering**
592 +
593 +Mesh generator automatically add numbers for finite elements and nodes. If you edit the mesh (e.g. adding new nodes and elements, mesh refinement etc.), you can rerun the renumbering process with the //Refresh numbering// command of the //Tools// menu.
594 +
595 +**Display settings**
596 +
597 +The display style of node symbols and **peak smoothing** **regions**, the numbering of nodes and finite elements can be set at //Settings > All... > Display > Mesh//.
598 +
599 + [[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png]]
600 +
601 +Figure: Display settings of mesh items
602 +
603 +* **2D finite elements**
604 +
605 +Although 2D finite elements are displayed automatically after mesh generation (if the //Surface elements// object layer is active), the element numbers (//Number//) can be displayed only after **analysis// //**or **design** calculations. The nodes can be displayed with circle or cross symbols any time, but with numbers (//Number//) after analysis and design calculations.
606 +
607 +[[image:file:///C:/Users/Fredrik/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png]]
608 +
609 +Figure: Finite elements displayed with numbers and nodes
610 +
611 +* **Line finite elements**
612 +
613 +Line finite elements together with their numbers (//Number//) can be displayed only after **analysis// //**or **design** calculations, if the //Line elements// object layer is active. The nodes can be displayed with circle, cross symbols or with numbers (//Number//).
614 +
615 +The color of the elements, nodes and peak smoothing regions depends on the color of their own object layer.
616 +
617 += Error Handling =
618 +
619 +Warning and error messages assist you when problems appear in mesh creation functions, during analysis or design calculations.**cracked** But, how you can find the position of these cautions to solve them later?
620 +
621 +The program points the geometrical and mesh errors, the load misplacements and any other problems in the model, and it collects their coordinates (in the //Global coordinate-system//) in an error/warning dialog.
622 +
623 +[[image:1585285418327-736.png]]
624 +
625 +Figure: Geometrical errors detected by the average element size calculation
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