As we know, the results obtained by the finite element method are nodal solutions, such as displacements, internal forces, stresses, etc. at nodes, while the results at any point inside an element are obtained through assumed shape functions interpolation. However, when we build finite element models, what we are most concerned about are the structural characteristics and boundary conditions, which belong to the pre-processing module and often do not consider the extraction of the structure. This leads to the problem that if we need to extract results at certain points, lines or surfaces in the model, but these points, lines, and surfaces do not coincide with the nodal positions or the centroids and integration points of the elements, what should we do?
This is where our Path Mapping technology comes in.
The so-called Path Mapping is actually a post-processing technology based on interpolation operations, which can virtually map any result data onto any path of the model. When using it, we can set the path, map the results of interest onto the path, and then perform some mathematical operations on the path to obtain more meaningful results. Its features are as follows:
- Multiple paths can be set simultaneously, and the results on a path are actually a column of data. Multiple paths form a matrix that can be subject to multiple matrix operations.
- After mapping the results, they can be viewed or saved in graphical, list, or file formats.
The steps of Path Mapping operation are as follows:
Step1: Define the path
Defining the path includes two aspects, one is to define the result coordinate system (the specific concept can refer to the chapter of ANSYS coordinate explanation in my beginner tutorial), and the other is to define the specific path. The main command flow is as follows:
PATH, Name, nPts, nSets, nDiv
PPATH, POINT, NODE, X, Y, X, CS
/PBC, PATH, 1
Step2: Map the path results
ANSYS can virtually map any result data onto any path of the model, such as raw data (DOF nodal solutions), derived data (stress, flux, gradient, etc.), element data tables, etc. The mapping process is to specify a certain path as the current path, specify the result coordinate system for this mapping, and map the result.
Common command flow is as follows:
PDEF, Lab, Item, Comp, Avglab
Step3: Observe the path
After mapping the results, we can directly observe the distribution of the results along the path. We can specify a coordinate component of the path point as the X-axis, and when the path is a spatial curve, what is displayed is the result after stretching. PLPATH and PRPATH can be used to display multiple variable curves in one graph by appending. Common command flow is as follows:
! Select the X coordinate of the path point as the X-axis
! Display the UZ-X curve
! Display the SZ-X and SX-X curves
PLPATH, SZ, SX
Step4. Perform mathematical operations on the path
The path result can be regarded as a column vector, which can be subject to various mathematical operations, such as simple arithmetic operations, power and calculus.
Step5. Save data to an array
If we want to export data and perform operations using third-party software such as MATLAB, we need to save the path result to an array. The command flow is as follows:
PAGET, PATHR2, Tabl
Here is an example.
There is a reinforced concrete cantilever beam with a cross-section size of 250×500, C30 grade, and a length of 2000. The top of the beam was subjected to a uniformly distributed load of 2KN/m. To analyze the elasticity of the beam, solid element 186 was employed.
To fulfill the requirements, we need to draw the centerline of the top and bottom and plot the relationship curve of the principal stress in the Z-direction coordinate.
Here’s the APDL code:
Finish /clear /prep7 Et,1,solid186 Mp,ex,1,3.0e4 Mp,dens,1,2500e-12 Mp,prxy,1,0.2 Blc4,,,250,500,2000 Asel,s,loc,y,500 Sfa,all,1,pres,2e3/250 Allsel,all Esize,50 Vmesh,all /solu Asel,s,loc,z,0 Da,all,all,all Allsel,all Acel,,9800 Solve !================ /post1 Path,dibu,5 Ppath,1,,125,,0 Ppath,2,,125,,500 Ppath,3,,125,,1000 Ppath,4,,125,,1500 Ppath,5,,125,,2000 Path,dingbu,5 Ppath,1,,125,500,0 Ppath,2,,125,500,500 Ppath,3,,125,500,1000 Ppath,4,,125,500,1500 Ppath,5,,125,500,2000
!================== Path,dibu Pdef,yingli1,s,1 Pdef, yingli2,s,2 Pdef, yingli3,s,3 Pdef, dengxiao,s,eqv Prange,1,,,ZG Plpath,yingli1,yingli2,yingli3,dengxiao
!============== Path,dingbu Pdef,yingli1,s,1 Pdef, yingli2,s,2 Pdef, yingli3,s,3 Pdef, dengxiao,s,eqv Prange,1,,,ZG Plpath,yingli1,yingli2,yingli3,dengxiao
The mises stress of the whole structure is as follows: