Datasets:
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Other
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json
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10K - 100K
Tags:
agentfem
soft-robotics
programmable-matter
structural-mechanics
inverse-design
scientific-machine-learning
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File size: 4,060 Bytes
07af0b5 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | """Independent checks, mandatory before data publication."""
import sys,json
from pathlib import Path
sys.path.insert(0,str(Path(__file__).resolve().parents[1]/'src'))
from rod import Rod,Controls
import numpy as np
from scipy.integrate import solve_bvp
from scipy.optimize import brentq
def run():
checks={}
r=Rod(24); c=Controls(chi=.004,fx=.005,fy=.002,h=.001,k1=.3,k2=-.2,k3=.6)
z=.4*np.sin(np.linspace(0,np.pi/2,r.d)); e,g,K=r.terms(z,c)
eps=1e-6; eye=np.eye(r.d)
gn=np.array([(r.terms(z+eps*v,c)[0]-r.terms(z-eps*v,c)[0])/(2*eps) for v in eye])
Kn=np.column_stack([(r.terms(z+eps*v,c)[1]-r.terms(z-eps*v,c)[1])/(2*eps) for v in eye])
checks['gradient_fd_max_abs']=float(np.max(np.abs(g-gn)))
checks['hessian_fd_max_abs']=float(np.max(np.abs(K-Kn)))
assert checks['gradient_fd_max_abs']<1e-8 and checks['hessian_fd_max_abs']<1e-8
axial=r.solve(Controls(fx=.03))
checks['axial_tip_error']=float(np.linalg.norm(axial['tip']-[1.03,0]))
assert checks['axial_tip_error']<1e-12
circular=[]
for n in [24,48,96]:
rr=Rod(n); cc=Controls(k1=1.2,k2=1.2,k3=1.2)
ans=rr.solve(cc,np.linspace(0,1.2,n+1)[1:])
exact=np.array([np.sin(1.2)/1.2,(1-np.cos(1.2))/1.2])
circular.append(float(np.linalg.norm(ans['tip']-exact)))
checks['circular_tip_errors_n24_48_96']=circular
assert circular[2]<circular[1]<circular[0] and circular[-1]<1e-5
rr=Rod(96); cc=Controls(chi=1e-4,h=.01,delta=.1)
pc=(-1+np.sqrt(1+16*cc.h*cc.delta-np.pi**2*cc.chi))/2-2*cc.h
def eig(p):
cc.fx=p
return rr.solve(cc)['lambda_min_over_chi']
pn=brentq(eig,pc-.001,pc+.001,xtol=1e-13)
checks['critical_load_analytic']=pc; checks['critical_load_discrete_rod96']=pn
checks['critical_load_error']=abs(pc-pn)
assert abs(pc-pn)<1e-7
# Independent solve_bvp of paper Eqs.52-53, negative branch. Not our FE energy.
errors=[]; chain_errors=[]
for p in [-.017159,-.016428,-.016316]:
chi,h,d=1e-4,.01,.1; a=p+2*h
s=np.linspace(0,1,101)
def fun(s,y):
th=y[0]; stretch=1+a*np.cos(th)
return np.vstack([y[1],(a*stretch-4*h*d)*np.sin(th)/chi,stretch*np.cos(th),stretch*np.sin(th)])
def bc(l,r): return [l[0],r[1],l[2],l[3]]
candidates=[]
for amp in [-.3,-1.,-2.]:
y=np.vstack([amp*np.sin(np.pi*s/2),amp*np.pi/2*np.cos(np.pi*s/2),s,amp*s*s/2])
b=solve_bvp(fun,bc,s,y,tol=1e-9,max_nodes=10000)
if b.success and b.y[3,-1]<-1e-3: candidates.append(b)
assert candidates
b=min(candidates,key=lambda b:abs(b.y[0,-1]))
target=b.sol(np.linspace(0,1,65))[2:4].T
c=Controls(chi=chi,h=h,delta=d,fx=p)
arod=Rod(96); out=arod.solve(c,b.sol(np.linspace(0,1,97))[0,1:])
assert out['accepted'] and out['tip'][1]<0 and out['stability']=='stable'
errors.append(float(np.sqrt(np.mean(np.sum((out['centerline']-target)**2,axis=1)))))
one=[]
for n in [15,30,60,120]:
rc=Rod(n,'chain'); v=rc.solve(c,b.sol(np.arange(1,n)/n)[0])
assert v['accepted'] and v['tip'][1]<0
one.append(float(np.linalg.norm(v['tip']-target[-1])))
assert one[-1]<one[0]
chain_errors.append(one)
checks['fig9_rod96_centerline_rmse_over_L']=errors
checks['fig9_chain_tip_errors_n15_30_60_120']=chain_errors
assert max(errors)<.001
# Exact chain linear critical load verifies the independently assembled hinge boundary.
rc=Rod(15,'chain'); c=Controls(chi=1e-4,h=.01)
omega2=4*np.sin(np.pi/(2*(2*15-1)))**2
expected=(-1+np.sqrt(1-4*c.chi*15**2*omega2+16*c.h*c.delta))/2-2*c.h
c.fx=expected; v=rc.solve(c)
checks['chain_critical_eigenvalue']=v['lambda_min_over_chi']
assert abs(v['lambda_min_over_chi'])<1e-8
checks['passed']=True
return checks
if __name__=='__main__':
checks=run()
p=Path(__file__).resolve().parents[1]/'reports/validation.json'
p.write_text(json.dumps(checks,indent=2))
print(json.dumps(checks,indent=2))
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