added flexure specification sim

flexure/CMD

+python flexure_stiffness.py -Q -M simulate -f 15 -flexure_type cyclic -w .0007 -t .0015 -l .010

flexure/flexure_stiffness.py

+#!/usr/bin/env python
+from __future__ import division
+from numpy import *
+import argparse
+from pyframe3dd.frame3dd import write_frame3dd_file, read_lowest_mode, read_frame3dd_displacements, compute_mass
+from pyframe3dd.util import magnitudes, close
+import subprocess
+
+def plot_connections(nodes,beamsets):
+    #for debug only, this is slow!
+    import matplotlib as mpl
+    from mpl_toolkits.mplot3d import Axes3D
+    import numpy as np
+    import matplotlib.pyplot as plt
+    fig = plt.figure()
+    cmap = plt.cm.get_cmap('Dark2', len(beamsets)+1)
+    ax = fig.gca(projection='3d')
+    for i,beamset in enumerate(beamsets):
+	    for seg in beamset:
+	        ax.plot(nodes[seg,0], nodes[seg,1], nodes[seg,2], c=cmap(i))
+    plt.show()
+
+def run_frame3dd(args,nodes,global_args,beam_sets,constraints,loads):
+	write_frame3dd_file(nodes,global_args,beam_sets,constraints,loads)
+	cmd = ["frame3dd", "-i",global_args['frame3dd_filename']+'.csv']
+	if args.quiet: cmd.append("-q")
+	print ' '.join(cmd)
+	subprocess.call(cmd)
+
+def clean_up_frame3dd(filename):
+	#Delete files generated by frame3dd
+	files = [filename+end for end in ["_out.csv",".csv.out",".csv.plt",".csv.if01",".csv"]]
+	subprocess.call(["rm"]+files)
+
+def build(args):
+	#return nodes,rods as numpy arrays
+	dxy = args.attach_radius/sqrt(2)
+
+	if args.flexure_type == 'mirrored':
+		nodes = args.l*array([[0,0,0],[0,1,0],[-1,1,0],[1,0,0],[1,-1,0]]) #one side of flexure plate
+		beams = array([[0,1],[1,2],[0,3],[3,4]])
+		nodes += array([dxy,dxy,0]) #offset by attachment radius
+
+	elif args.flexure_type == 'cyclic':
+		nodes = args.l*array([[0,0,0],[0,1,0],[-1,1,0]]) + array([dxy,dxy,0])
+		beams = array([[0,1],[1,2],[3,4]])
+		nodes = vstack((nodes, args.l*array([[1,1,0],[1,0,0]]) + array([dxy,-dxy,0])))
+
+	nodes = vstack((nodes,array([[-n[0],-n[1],0] for n in nodes]))) #append reflection
+	beams = vstack((beams, beams + 5))
+	z_os = array([0,0,.5*args.sep])
+	nodes = vstack((nodes + z_os, nodes - z_os))
+	beams = vstack((beams, beams + 10))
+
+	solid_nodes = array([ [dxy,-dxy,.5*args.sep],[-dxy,dxy,.5*args.sep],[dxy,-dxy,-.5*args.sep],[-dxy,dxy,-.5*args.sep] ])
+	nodes = vstack((nodes, solid_nodes))
+	solid_beams = array([
+		[0,5],[0,10],[5,15],[10,15],#[0,15],[5,10],
+		[0,20],[0,21],[5,20],[5,21],[20,21],
+		[10,22],[10,23],[15,22],[15,23],[22,23],
+		[20,22],[21,23],#[20,23],[21,22],
+		[0,22],[0,23],[5,22],[5,23],
+		[10,20],[10,21],[15,20],[15,21]
+		])
+	if args.flexure_type == 'cyclic':
+		beams = vstack((beams, array([[4,20],[9,21],[14,22],[19,23]])))
+	return nodes, beams, solid_beams
+
+def run_simulation(args):
+	#set up simulation
+	nodes,beams,solid_beams = build(args)
+	global_args = {
+		'n_modes':args.n_modes,'length_scaling':args.length_scaling,'exagerration':10,
+		'node_radius':zeros(shape(nodes)[0]),'frame3dd_filename':args.base_filename+"_frame3dd"
+	}
+	clean_up_frame3dd(global_args['frame3dd_filename'])
+	beam_sets = [
+	(beams,{'E':args.E,'nu':args.nu,'rho':args.rho,'cross_section':'rectangular','d2':args.w,'d1':args.t,'roll':0.,'loads':[],'beam_divisions':args.bd,'prestresses':[]}),
+	(solid_beams,{'E':10*args.E,'nu':args.nu,'rho':args.rho,'cross_section':'rectangular','d1':args.w,'d2':args.t,'roll':0.,'loads':[],'beam_divisions':args.bd,'prestresses':[]})
+	]
+	if args.flexure_type == 'mirrored':
+		fixed_nodes = [2,4,7,9,12,14,17,19]
+	elif args.flexure_type == 'cyclic':
+		fixed_nodes = [2,3,7,8,12,13,17,18]
+	constraints = [{'node':node,'DOF':dof,'value':0} for dof in [0,1,2,3,4,5] for node in fixed_nodes]
+
+	
+	for force_dof in [0,1,2]:
+		loaded_nodes = [0,5,10,15]
+		loads = [{'node':n,'DOF':force_dof,'value':args.force/len(loaded_nodes)} for n in loaded_nodes]
+
+		run_frame3dd(args,nodes,global_args,beam_sets,constraints,loads)
+		results = {}
+		results['beam_mass'] = compute_mass(nodes,beam_sets)
+		disps = read_frame3dd_displacements(global_args['frame3dd_filename'])
+		force_disp = average(disps[loaded_nodes,force_dof])
+		print "Degree of freedom: %d"%force_dof
+		print "Force applied: %.1f N"%(args.force)
+		print "Calculated displacement: %.1f microns"%(force_disp*1e6)
+
+	#todo: read average displacement of loaded nodes
+	#todo: plot displacements vs. design parameters
+
+
+	#results['fundamental_frequency'] = read_lowest_mode(global_args['frame3dd_filename']+'.csv')
+	return results
+
+def find_stability_threshold(args):
+	#out loop of simulations to determine the buckling load
+	lower = 0 #lower bound
+	upper = 10*args.force_res #initial upper bound before bracketing
+	bracketed=False
+	#actually not necessary, but fun to have the unloaded frequency
+	args.force = lower
+	res = run_simulation(args)	
+	freqs = [res['fundamental_frequency']]
+	forces = [args.force]
+
+	i = 0
+	while not bracketed:
+		print lower,upper,bracketed,res['fundamental_frequency']
+		args.force = upper
+		res = run_simulation(args); i += 1
+		if res['fundamental_frequency']<0:
+			bracketed=True
+		else:
+			freqs.append(res['fundamental_frequency'])
+			forces.append(args.force)
+			lower = upper
+			upper = 2*upper
+	while (upper-lower > args.force_res):
+		print lower,upper,bracketed
+		args.force = .5*(upper+lower)
+		res = run_simulation(args); i += 1
+		if res['fundamental_frequency']>0:
+			freqs.append(res['fundamental_frequency'])
+			forces.append(args.force)
+			lower = .5*(upper+lower)
+		else:
+			upper = .5*(upper+lower)
+	return forces,freqs,res
+
+
+if __name__ == '__main__':
+	parser = argparse.ArgumentParser()
+	parser.add_argument('-M','--mode',choices=('simulate','search', 'visualize'), required=True)
+	parser.add_argument('-flexure_type','--flexure_type',choices=('cyclic','mirrored'), required=True)
+	parser.add_argument('-Q','--quiet',action='store_true',help='Whether to suppress frame3dd output')
+	parser.add_argument("-f","--force",  type=double, default=.1, help="force to apply")
+	#parser.add_argument("-fr","--force_res", type=double, default=.01, help="Final resolution of force for search mode")
+
+	parser.add_argument("-w","--w", type=double, default=.0005, help="width of flexure (m)")
+	parser.add_argument("-t","--t", type=double, default=.0023, help="thickness of flexure material (m)")
+	parser.add_argument("-l","--l", type=double, default=.0068, help="length of flexure segment (m)")
+	parser.add_argument("-attach_radius","--attach_radius", type=double, default=.0043, help="distance from z axis to flexure attachment (m)")
+	parser.add_argument("-sep","--sep", type=double, default=.025, help="flexure plate z separation (m)")
+
+	parser.add_argument("-bd","--bd", type=int, default=1, help='how many divisions for each rod, useful in buckling analysis')
+	parser.add_argument("-E","--E", type=double, default=70e9, help="Young's Modulus of laminate")
+	parser.add_argument("-nu","--nu", type=double, default=.33, help="Poisson Ratio")
+	parser.add_argument("-base_filename","--base_filename", default='buckle', help="Base filename for segments and frame3dd")
+	parser.add_argument("-rho","--rho",type=double,default=2700.,help='density of beam material, kg/m^3')
+	parser.add_argument("-n_modes","--n_modes",type=int,default=0,help='number of dynamic modes to compute')
+	parser.add_argument("-ls","--length_scaling", type=double, default=1., help="Scale factor to keep numbers commesurate")
+	args = parser.parse_args()
+
+	if args.mode=='search':
+		forces,freqs,last_res = find_stability_threshold(args)
+		print "Fundamental frequency: %.3f Hz"%(freqs[-1])
+		print "Critical force: %.3f N"%(forces[-1])
+		print "Critical stress: %.3f MPa"%(last_res['stress']/1e6)
+	elif args.mode=='simulate':
+		res = run_simulation(args)
+		#print "Fundamental frequency: %.3f Hz"%res['fundamental_frequency']
+		#print "Stress: %.3f MPa"%(res['stress']/1e6)
+	elif args.mode=='visualize':
+		nodes,rods,solid_beams = build(args)
+		plot_connections(nodes,[rods,solid_beams])
+	else:
+		assert(0) #should not be here
+
+
+