This is an old revision of the document!
This example shows a rudimentary script for the simulation of contact. It can definitely be enhanced and we are open to specific improvements.
Here, we're using a beam that is clamped on one side. The beam is largely rigid, but near the clamping, it is flexible. The flexible part acts like a hinge. We're using an actuation force of 1 N in x
-direction on node 3. Without any contact, the tip of the beam would displace 0.0311 m.
We're imagining a line at x=0.025
, representing a contact surface that cannot be crossed. To simulate this, we're creating a custom force on the node of contact (node number 4), whenever it crosses the position of x=0.025
. We choose the value of this force to be -stiffn*(pos-x0)
. This creates a fictitious force that acts like a spring with stiffness stiffn
and stress-free reference position of x0=0.025
. Variable pos
is the current value of the suspected node of contact.
This simulation is tricky because it involves iterations to get the system in the right state. We currently have no clear rationale for picking the values of stiffn
of the fictitious force (or the precise mathematical form of this force, for that matter). Also, it's best to do these iterations within one single Spacar call, seeing as each new SPACAR Light call would make the system start from the undeformed configuration again. The current interface for doing a custom force within Spacar is by means of the usersig interface. This interface hasn't been implemented in SPACAR Light properly, but here are some pointers to get a simulation up and running.
opt.customdyn
field. See the development branch on GitHub.opt.customdyn = 'usersig PUSHSIG';
to have Spacar call the m-file PUSHSIG.m (all of this is case-sensitive)opt.loadsteps
. This file contains a function with very specific input and output requirements. Within this function, you'll have available the x
-vector, which contains the current positions of the nodes. Unfortunately, the node numbering in Spacar (full) is different from SPACAR Light. This is actually by design, and something you usually shouldn't have to come across. Here, you do, though. The conversion is simple and detailed in the file. Note that this simple conversion may not work whenever you use multiple elements per beam with eprops(i).nbeams
> 1. (The .dat-file actually shows you what the conversion should be in all cases.)function [time,sig,f] = PUSHSIG(t,ne,le,e,ep,nx,lnp,x,xp) x0 = 0.025; %defines contact line stiffn = 300; spalightnode = 4; %conversion between SPACAR Light node and Spacar (full) node. %(for each SPACAR Light node, there are 2 nodes in Spacar full. %They are numbered consecutively. First one is the translation node, %second one is the rotation node. Here, we're taking just the translation node.) spanode = (spalightnode-1)*2+1; %get current position pos = x(lnp(spanode,1:3)); %contains x,y,z coordinate of spalightnode %define a custom force node = spanode; %node number (according to Spacar full numbering) dir = 1; %direction of force: 1 for x, 2 for y, 3 for z debug_info = 1; %print out some debug info during simulation if debug_info fprintf('Current position: %f\n',pos(1)) end if pos(1) > x0 %if within (forbidden) contact region val = -stiffn*(pos(1)-x0); %define force to push it back deriv = stiffn; f = [node dir val deriv 0]; %apply force if debug_info fprintf('Within contact region. Applying force: %f\n',val) end else f = []; %if not within contact region, don't apply contact force if debug_info fprintf('Not within contact region.\n') end end sig = []; %can be left empty (is used for specifying generalized stresses) time = t; %this line needs to be there; don't modify. end
The script with the SPACAR Light model looks like this.
% EXAMPLE SCRIPT FOR RUNNING SPACAR LIGHT % This example simulates a simple cross flexure rotating due to an applied moment clear clc close all % addpath('spacar') %Specify location of spacar folder, if not current %% NODE POSITIONS % x y z nodes = [ 0 0 0; %node 1 0 -0.02 0; %node 2 0 -0.04 0; %node 3 0 -0.06 0]; %node 4 %% ELEMENT CONNECTIVITY % p q elements = [ 1 2; %element 1 2 3; %element 2 3 4]; %element 3 %% NODE PROPERTIES %node 1 nprops(1).fix = true; %Fix node 1 nprops(3).force = [1 0 0]; %% ELEMENT PROPERTIES eprops(1).elems = [1]; %Add this set of properties to elements 1 and 3 eprops(1).emod = 2e9; %E-modulus [Pa] eprops(1).smod = 68.9e6; %G-modulus [Pa] eprops(1).dens = 1150; %Density [kg/m^3] eprops(1).cshape = 'rect'; %Rectangular cross-section eprops(1).dim = [5e-3 1e-3]; %Width: 50 mm, thickness: 0.2 mm eprops(1).orien = [0 0 1]; %Orientation of the cross-section as a vector pointing along "width-direction" eprops(1).nbeams = 1; %Number of beams used to model this element eprops(1).flex = 1:6; %Model out-of-plane bending (modes 3 and 4) as flexible eprops(1).color = 'grey'; %Color eprops(2).elems = [2 3]; %Add this set of properties to elements 1 and 3 eprops(2).emod = 2e9; %E-modulus [Pa] eprops(2).smod = 68.9e6; %G-modulus [Pa] eprops(2).dens = 1150; %Density [kg/m^3] eprops(2).cshape = 'rect'; %Rectangular cross-section eprops(2).dim = [5e-3 5e-3]; %Width: 50 mm, thickness: 0.2 mm eprops(2).orien = [0 0 1]; %Orientation of the cross-section as a vector pointing along "width-direction" eprops(2).nbeams = 1; %Number of beams used to model this element eprops(2).flex = 1:6; %Model out-of-plane bending (modes 3 and 4) as flexible eprops(2).color = 'grey'; %Color %% OPTIONAL ARGUMENTS opt.filename = 'contact'; %Filename opt.loadsteps = 20; opt.customdyn = {'usersig PUSHSIG'}; %Unfortunately, this is case-sensitive ... %% CALL SPACAR_LIGHT out = spacarlight(nodes, elements, nprops, eprops, opt); pos = out.node(4).p(1,:); figure plot(pos)
Some more notes:
opt.customdyn
line, whereas the actuation force is applied using the nprops(3).force
line. Note the differences between nprops.force
and nprops.force_initial
. The latter probably won't work because SPACAR Light will ignore the opt.loadsteps
(which you do need when using usersig
) when there is no nprops.force
present, it seems.spacar(-10,'contact')
.