Example: beam02
We build the model based a few parameters as follows.
1 # initialize a system model
2 SpanLengths = [ 8.0 * 12, 10.0 * 12, 8.0 * 12 ]
3 Nelems = 2 # number of elements
4 params = {'E': 29000., 'A': 5, 'I':50}
5
6 # define load
7 w = -1.00
SpanLengths is a list of span lengths for a series of spans on a continuous beam. Each span will be modeled by Nelems elements. This list serves of a wrapper around input similar to :doc:../beam01/beam01.rst. The loop is emphasized in the next code segment (yellow line).
All mesh creation is based solely on the above parameters to allow for easy manipulation of the model.
The actual model is built by the block below.
8 model = System()
9
10 # meshing parameters
11 Xnode = 0.0
12 Ynode = 0.0
13 Offset = 0.0
14
15 # create left node
16 nd0 = Node(Xnode, Ynode)
17 nd0.fixDOF('ux', 'uy') # pin support left end
18 model += nd0
19
20 # initialization for node and element creation
21 ndi = nd0
22
23 for SpanLength in SpanLengths:
24
25 Le = SpanLength / Nelems
26
27 for e in range(Nelems):
28 # create next node
29 Xnode += Le
30 ndj = Node(Xnode, Ynode)
31 model += ndj
32
33 # create elements
34 elem = Beam2D(ndi, ndj, ElasticSection(params))
35 model += elem
36
37 # load the element with a uniform load
38 elem.setDistLoad(w)
39
40 # shift one node to the right
41 ndi = ndj
42
43 # define support(s)
44 ndj.fixDOF('uy') # roller support right end
45
46 # move on to the next span
47 Offset = Xnode
48
49 # done building the model
Line 8 instantiates one model space.
Lines 16, 28-30 create the nodes, and lines 18 and 31 add them to the model space.
Lines 34-35 create the elements and add them to the model space. You only need to create variables for Node and Element objects, respectively, if you need to either add or retrieve information from that object later.
A uniform load w (positive is up) is applied directly to the beam elements in line 38.
The support conditions are defined by providing the respective information directly to the supported nodes. Line 17 adds a pin support on the first node and line 44 adds a roller on the last one.
The system equations are solved by a single call to the solver:
50 # analyze the model
51 model.solve()
You can obtain a debug-style report on the state of the system:
52 # write out report
53 model.report()
Resulting in an output like (may change as the code evolves).
System Analysis Report ======================= Nodes: --------------------- Node 0: {'uy': 0, 'rz': 1} x:[0. 0.], fix:['ux', 'uy'], P:[0. 0.], u:[ 0. -0.0123663] Node 1: {'uy': 0, 'rz': 1} x:[48. 0.], fix:[], P:[0. 0.], u:[-0.292646 0.00326429] Node 2: {'uy': 0, 'rz': 1} x:[96. 0.], fix:['uy'], P:[0. 0.], u:[ 0. -0.00069085] Node 3: {'uy': 0, 'rz': 1} x:[156. 0.], fix:[], P:[0. 0.], u:[-3.93139430e-01 -4.24063967e-19] Node 4: {'uy': 0, 'rz': 1} x:[216. 0.], fix:['uy'], P:[0. 0.], u:[0. 0.00069085] Node 5: {'uy': 0, 'rz': 1} x:[264. 0.], fix:[], P:[0. 0.], u:[-0.292646 -0.00326429] Node 6: {'uy': 0, 'rz': 1} x:[312. 0.], fix:['uy'], P:[0. 0.], u:[0. 0.0123663] Elements: --------------------- Beam2D: node 0 to node 1: material ElasticSection properties: {'E': 29000.0, 'A': 5, 'I': 50, 'nu': 0.0, 'fy': 1e+30} strain:{'axial': 0.0, 'flexure': 0.0} stress:{'axial': 0.0, 'flexure': 0.0} nodal forces: Vi:11.673913043478258 Mi:-191.99999999999994 Vj:-11.673913043478258 Mj:752.3478260869563 Beam2D: node 1 to node 2: material ElasticSection properties: {'E': 29000.0, 'A': 5, 'I': 50, 'nu': 0.0, 'fy': 1e+30} strain:{'axial': 0.0, 'flexure': 0.0} stress:{'axial': 0.0, 'flexure': 0.0} nodal forces: Vi:-36.32608695652172 Mi:-752.347826086956 Vj:36.32608695652172 Mj:-991.3043478260865 Beam2D: node 2 to node 3: material ElasticSection properties: {'E': 29000.0, 'A': 5, 'I': 50, 'nu': 0.0, 'fy': 1e+30} strain:{'axial': 0.0, 'flexure': 0.0} stress:{'axial': 0.0, 'flexure': 0.0} nodal forces: Vi:29.999999999999993 Mi:883.3043478260867 Vj:-29.999999999999993 Mj:916.6956521739128 Beam2D: node 3 to node 4: material ElasticSection properties: {'E': 29000.0, 'A': 5, 'I': 50, 'nu': 0.0, 'fy': 1e+30} strain:{'axial': 0.0, 'flexure': 0.0} stress:{'axial': 0.0, 'flexure': 0.0} nodal forces: Vi:-29.99999999999999 Mi:-916.6956521739127 Vj:29.99999999999999 Mj:-883.3043478260865 Beam2D: node 4 to node 5: material ElasticSection properties: {'E': 29000.0, 'A': 5, 'I': 50, 'nu': 0.0, 'fy': 1e+30} strain:{'axial': 0.0, 'flexure': 0.0} stress:{'axial': 0.0, 'flexure': 0.0} nodal forces: Vi:36.32608695652173 Mi:991.3043478260865 Vj:-36.32608695652173 Mj:752.347826086956 Beam2D: node 5 to node 6: material ElasticSection properties: {'E': 29000.0, 'A': 5, 'I': 50, 'nu': 0.0, 'fy': 1e+30} strain:{'axial': 0.0, 'flexure': 0.0} stress:{'axial': 0.0, 'flexure': 0.0} nodal forces: Vi:-11.673913043478258 Mi:-752.347826086956 Vj:11.673913043478258 Mj:192.0
An easier way to look at the simulation results are plots. A deformed system plot is obtained using the model.plot() directive. If a filename is given, the plot will be saved to the harddrive using that file name. An internal force plot is created equally simple.
54 # create plots
55 model.plot(factor=100., filename="beam02_deformed.png")
56
57 model.beamValuePlot('V', filename="beam02_shear.png")
58 model.beamValuePlot('M', filename="beam02_moment.png")
Showing file beam02_deformed.png
Showing file beam02_shear.png
Showing file beam02_moment.png
Importing the example
from femedu.examples.beams.beam02 import *
# load the example
ex = Examplebeam02()
More beam examples: Beam Examples