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walkthrough [2017/10/12 14:22]
marijn.nijenhuis [Node properties] 		walkthrough [2017/10/18 10:51] (current)
marijn.nijenhuis [Element properties]
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 ====== Problem description ====== ====== Problem description ======
-Let's consider a parallel flexure guide consisting of two parallel leafsprings and an intermediate rigid body. For this problem, we consider L=100mm and W=50mm. Furthermore, we consider steel leafsprings with a width of 50mm and a thickness of 0.5mm. The rigid intermediate body is made from aluminium and has a cross-section of 50x50mm. A schematic overview is given in the figure below.+Let's consider a parallel flexure guide consisting of two parallel leafsprings and an intermediate rigid body. For this problem, we consider L=100mm and W=50mm. Furthermore, we consider steel leafsprings with a width of 50mm and a thickness of 0.5mm. The rigid intermediate body is made from aluminium and has a cross-section of 50x25mm. A schematic overview is given in the figure below.
  
 {{:parallel_flexure_guide.jpg?direct&350 |}} {{:parallel_flexure_guide.jpg?direct&350 |}}
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 We start by defining the positions of the nodes where we place the origin at node 1. ''nodes'' is an n<sub>n</sub>×3 matrix for //defining the positions of the nodes//. Each row represents a node (there are n<sub>n</sub> nodes). The row number determines the number a node gets. The first column contains the ''x''-coordinate of the node position, the second column the ''y''-coordinate, and the third column the ''z''-coordinate. We start by defining the positions of the nodes where we place the origin at node 1. ''nodes'' is an n<sub>n</sub>×3 matrix for //defining the positions of the nodes//. Each row represents a node (there are n<sub>n</sub> nodes). The row number determines the number a node gets. The first column contains the ''x''-coordinate of the node position, the second column the ''y''-coordinate, and the third column the ''z''-coordinate.
 <code matlab> <code matlab>
-clc    %clear command window +clear   %clear workspace 
-clear  %clear workspace+clc     %clear command window
  
-%% NODE POSITIONS+% addpath('spacar') %have this point to the folder where spacar is located 
 + 
 +%some dimensions
 L = 0.1;    %[m] L = 0.1;    %[m]
 W = 0.05;   %[m] W = 0.05;   %[m]
 + 
 %% NODE POSITIONS %% NODE POSITIONS
 nodes = [0 0 0;     %node 1 nodes = [0 0 0;     %node 1
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            3 4];    %leafspring between node 3 and 4             3 4];    %leafspring between node 3 and 4 
 </code> </code>
- 
 ===== Node properties ===== ===== Node properties =====
 Node properties are defined by a structure array to assign properties to nodes, such as boundary conditions, applied loads, and inertia. The usage is ''nprops(i).field = value;'' to assign property ''field'' with value ''value'' to node ''i''. For a full syntax list with all possible inputs, see [[full_syntax#3. Node properties|SPACAR Light syntax]]. Node properties are defined by a structure array to assign properties to nodes, such as boundary conditions, applied loads, and inertia. The usage is ''nprops(i).field = value;'' to assign property ''field'' with value ''value'' to node ''i''. For a full syntax list with all possible inputs, see [[full_syntax#3. Node properties|SPACAR Light syntax]].
  
 First of all, node 1 and 4 are fixed: First of all, node 1 and 4 are fixed:
-<code>+<code matlab>
 %% NODE PROPERTIES %% NODE PROPERTIES
 nprops(1).fix = true;       %fix node 1 nprops(1).fix = true;       %fix node 1
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 Furthermore, we would like for the parallel flexure guide to start 10mm deflected to the left and let it move 20mm to the right. For this purpose, we pre-describe the position of node 2 in x-direction: Furthermore, we would like for the parallel flexure guide to start 10mm deflected to the left and let it move 20mm to the right. For this purpose, we pre-describe the position of node 2 in x-direction:
 <code matlab> <code matlab>
-nprops(2).displ_initial_x =-0.01; %start with node 2 displaced 10mm to the left +nprops(2).displ_initial_x =-0.01; %start with node 2 displaced 10 mm to the left 
-nprops(2).displ_x =         0.02; %displace node 2 20mm to the right+nprops(2).displ_x =         0.02; %displace node 2 20 mm to the right
 </code> </code>
 At last we apply a load of 5N in Z-direction on node 2 and 3 At last we apply a load of 5N in Z-direction on node 2 and 3
 <code matlab> <code matlab>
-nprops(2).force_initial = [0 0 5]; %initial load of 5N i z-direction  +nprops(2).force_initial = [0 0 5]; %initial load of 5N in z-direction on node 2 
-nprops(3).force_initial = [0 0 5]; %initial load of 5N i z-direction +nprops(3).force_initial = [0 0 5]; %initial load of 5N in z-direction on node 3
 </code> </code>
  
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 <code matlab> <code matlab>
 %% ELEMENT PROPERTIES %% ELEMENT PROPERTIES
- 
 %first element property set %first element property set
-eprops(1).elems = [1 3];        %assing property set 1 to element 1 and 3+eprops(1).elems = [1 3];        %assing property set 1 to elements 1 and 3
 eprops(1).emod = 210e9;         %E-modulus [Pa] eprops(1).emod = 210e9;         %E-modulus [Pa]
-eprops(1).smod = 70e9;          %G-modulus [Pa]+eprops(1).smod = 70e9;          %shear modulus [Pa]
 eprops(1).dens = 7800;          %density   [kg/m^3] eprops(1).dens = 7800;          %density   [kg/m^3]
-eprops(1).dim = [0.05 0.0005];  %crossectional dimension [w t] in [mm] +eprops(1).dim = [0.05 0.0005];  %cross-sectional dimension (width and thickness, resp.) [m] 
-eprops(1).cshape = 'rect';      %crossectional shape rectangular +eprops(1).cshape = 'rect';      %rectangular cross-sectional shape  
-eprops(1).flex = [2 3 4];       %torsional (2) and out-of-plane bending (3,4) deformations are flexible+eprops(1).flex = [2 3 4];       %flexible deformations: torsion (2) and out-of-plane bending (3,4) 
 eprops(1).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction eprops(1).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction
-eprops(1).nbeams = 2;           %Leafspring simulated with 2 spacar-beams for increased accuracy. +eprops(1).color = [0.8549    0.8588    0.8667]; %color in rgb values between 0 and 1
 </code> </code>
  
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 eprops(2).elems = [2];          %assing property set 2 to element 2 eprops(2).elems = [2];          %assing property set 2 to element 2
 eprops(2).dens = 2700;          %density   [kg/m^3] eprops(2).dens = 2700;          %density   [kg/m^3]
-eprops(2).dim = [0.05 0.05];    %crossectional dimension [w t] in [mm] +eprops(2).dim = [0.05 0.025];   %cross-sectional dimension (width and thickness, resp.) [m] 
-eprops(2).cshape = 'rect';      %crossectional shape rectangular+eprops(2).cshape = 'rect';      %rectangular cross-sectional shape
 eprops(2).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction eprops(2).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction
 +eprops(2).color = [0.1686    0.3922    0.6627]; %color in rgb values between 0 and 1
 </code> </code>
  
-====== Resolve overconstraints ====== +====== Run simulation ====== 
-At this moment we have defined the basic configuration for our simulation and we can analyze the overconstraints in our model. For an initial suggestion for the releases to resolve the overconstraints, we can call ''spacarlight'' with+When all input seems complete, a call to ''spacarlight'' can be invoked:
 <code matlab> <code matlab>
  out = spacarlight(nodes,elements,nprops,eprops);  out = spacarlight(nodes,elements,nprops,eprops);
 </code> </code>
-or alternatively +If the model works, ''spacarlight'' automatically runs the static simulation and produces a visualization of the model.
-<code matlab> +
- rlse = []; +
- out = spacarlight(nodes,elements,nprops,eprops,rlse); +
-</code> +
-When the system is properly defined, the number of overconstraints and the suggestion for released deformation modes is provided in the command window like below: +
-<code> +
-Warning: System is overconstrained; releases are required in order to run static simulation. +
-A suggestion for possible releases is given in the table below. +
- +
-  +
-Number of overconstraints: 7 +
- +
-    Element    def_1    def_2    def_3    def_4    def_5    def_6 +
-    _______    _____    _____    _____    _____    _____    _____ +
- +
-    1          1        1        1        1        1        1     +
-    2          1        1        1        1        1        1     +
-    3          1        1        1        1        1        1     +
-</code> +
-It appears this problem contains 7 overconstraints and a suggestion is provided. Now we can add a single released deformation mode with the help of table and redo the overconstrained analyses. Therefore, we define the ''rls'' structure array which assigns 'released' deformation modes. The usage is ''rls(i).def = value;'' to assign the released deformations modes ''value'' to element ''i''. More information on using the ''rls'' structure is provided at [[full_syntax#5. Releases|SPACAR Light syntax]]. +
- +
-To release the second deformation mode of element two, we use: +
-<code matlab> +
-%% RELEASES +
-rls(1).def = [2]; +
-</code> +
-If we now redo the overconstrained analyses (call ''out = spacarlight(nodes,elements,nprops,eprops,rlse);''), it will show 6 overconstraints and an updated release table. By repeating this process six more times and by adding a single released deformation at each step, a full set of releases can be obtained (multiple solutions/combinations are possible): +
-<code matlab> +
-%% RELEASES +
-rls(1).def = [1 2 3 4 5 6]; +
-rls(3).def = [3]; +
-</code> +
- +
-====== Run simulation ====== +
-When an exact constrained model is obtained, ''spacarlight'' automatically runs the static simulation when it is called an a visualization of the model will appear. For more information on the visualization GUI, see ????. +
- +
-Furthermore, simulation results are stored in the output argument ''out''. +
  
 +Also, simulation results are stored in the MATLAB workspace in the structure ''out''.
  
 ====== Example script ====== ====== Example script ======
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 clc clc
  
 +% addpath('spacar') %have this point to the folder where spacar is located
 +
 +%some dimensions
 L = 0.1;    %[m] L = 0.1;    %[m]
 W = 0.05;   %[m] W = 0.05;   %[m]
 + 
 %% NODE POSITIONS %% NODE POSITIONS
 nodes = [0 0 0;     %node 1 nodes = [0 0 0;     %node 1
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          W L 0;     %node 3          W L 0;     %node 3
          W 0 0];    %node 4          W 0 0];    %node 4
-      +  
 + 
 %% ELEMENT CONNECTIVITY %% ELEMENT CONNECTIVITY
 elements= [1 2;     %leafspring between node 1 and 2  elements= [1 2;     %leafspring between node 1 and 2 
            2 3;     %intermediate body            2 3;     %intermediate body
            3 4];    %leafspring between node 3 and 4             3 4];    %leafspring between node 3 and 4 
- +  
- +  
- + %% NODE PROPERTIES
-%% NODE PROPERTIES+
 nprops(1).fix = true;       %fix node 1 nprops(1).fix = true;       %fix node 1
-nprops(4).fix = true;   %fix node 4 +nprops(4).fix = true;       %fix node 4 
- +  
-nprops(2).displ_initial_x =-0.01; %start with node 2 displaced 10mm to the left +nprops(2).displ_initial_x =-0.01; %start with node 2 displaced 10 mm to the left 
-nprops(2).displ_x =         0.02; %displace node 2 20mm to the right +nprops(2).displ_x =         0.02; %displace node 2 20 mm to the right 
- +  
-nprops(2).force_initial = [0 0 5]; %initial load of 5N in z-direction  +nprops(2).force_initial = [0 0 5]; %initial load of 5N in z-direction on node 2 
-nprops(3).force_initial = [0 0 5]; %initial load of 5N in z-direction  +nprops(3).force_initial = [0 0 5]; %initial load of 5N in z-direction on node 3 
- +  
 + 
 %% ELEMENT PROPERTIES %% ELEMENT PROPERTIES
- 
 %first element property set %first element property set
-eprops(1).elems = [1 3];        %assing property set 1 to element 1 and 3+eprops(1).elems = [1 3];        %assing property set 1 to elements 1 and 3
 eprops(1).emod = 210e9;         %E-modulus [Pa] eprops(1).emod = 210e9;         %E-modulus [Pa]
-eprops(1).smod = 70e9;          %G-modulus [Pa]+eprops(1).smod = 70e9;          %shear modulus [Pa]
 eprops(1).dens = 7800;          %density   [kg/m^3] eprops(1).dens = 7800;          %density   [kg/m^3]
-eprops(1).dim = [0.05 0.0005];  %crossectional dimension [w t] in [mm] +eprops(1).dim = [0.05 0.0005];  %cross-sectional dimension (width and thickness, resp.) [m] 
-eprops(1).cshape = 'rect';      %crossectional shape rectangular +eprops(1).cshape = 'rect';      %rectangular cross-sectional shape  
-eprops(1).flex = [2 3 4];       %torsional (2) and out-of-plane bending (3,4) deformations are flexible+eprops(1).flex = [2 3 4];       %flexible deformations: torsion (2) and out-of-plane bending (3,4) 
 eprops(1).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction eprops(1).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction
-eprops(1).nbeams = 2;           %Leafspring simulated with 2 spacar-beams for increased accuracy.  +eprops(1).color = [0.8549    0.8588    0.8667]; %color in rgb values between 0 and 1 
 + 
 %second element property set %second element property set
 eprops(2).elems = [2];          %assing property set 2 to element 2 eprops(2).elems = [2];          %assing property set 2 to element 2
 eprops(2).dens = 2700;          %density   [kg/m^3] eprops(2).dens = 2700;          %density   [kg/m^3]
-eprops(2).dim = [0.05 0.05];    %crossectional dimension [w t] in [mm] +eprops(2).dim = [0.05 0.025];   %cross-sectional dimension (width and thickness, resp.) [m] 
-eprops(2).cshape = 'rect';      %crossectional shape rectangular+eprops(2).cshape = 'rect';      %rectangular cross-sectional shape
 eprops(2).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction eprops(2).orien = [0 0 1];      %width-direction of leafspring oriented in z-direction
- +eprops(2).color = [0.1686    0.3922    0.6627]; %color in rgb values between 0 and 1 
- + 
-%% RELEASES +
-rls(1).def = [1 2 3 4 5 6]; +
-rls(3).def = [3]; +
  
 %% DO SIMULATION %% DO SIMULATION
-out = spacarlight(nodes,elements,nprops,eprops,rls);+out = spacarlight(nodes,elements,nprops,eprops);
 </code> </code>
walkthrough.1507810952.txt.gz · Last modified: 2017/10/12 14:22 by marijn.nijenhuis

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