def rhombus_3x2_crane_y_fixed(n_steps = 10, dx = 0.5):
"""
This example shows a 3x2 rhombus creasepattern.
"""
cpr = YoshimuraCreasePattern(n_steps = n_steps,
L_x = 3,
L_y = 2,
n_x = 3,
n_y = 4,
MAX_ITER = 5000)
cp = Lifting(n_steps = n_steps, MAX_ITER = 500)
caf = CnstrTargetFace(F = [r_, s_, 4 * 0.4 * t_ * r_ * (1 - r_ / 3) + 0.25])
n_arr = np.hstack([cpr.N_h[:, :].flatten(),
#cpr.N_v[:, :].flatten(),
cpr.N_i[:, :].flatten()
])
cp.init_tf_lst = [(caf, n_arr)]
cp.cp_geo(cpr)
grab_nodes = [[0.5, 0.333, 0],
[0.5, 0.667, 0],
[0.5, 1.333, 0],
[0.5, 1.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[1.5, 1.333, 0],
[1.5, 1.667, 0],
[2.5, 0.333, 0],
[2.5, 0.667, 0],
[2.5, 1.333, 0],
[2.5, 1.667, 0]]#33
crane_nodes = [#crane
[0, 0, 1], #34
[0.7, 0, 1],
[1.5, 0, 1],
[2.3, 0, 1],
[3, 0, 1],
[0, 2, 1.],
[0.7, 2, 1.], #40
[1.5, 2, 1.],
[2.3, 2, 1.],
[3, 2, 1.],
[0, 0.5, 1.],
[3, 0.5, 1.], #45
[0, 1.5, 1.],
[3, 1.5, 1.],
[0.7, 0.4, 1.],
[0.7, 0.6, 1.],
[1.5, 0.4, 1.], #50
[1.5, 0.6, 1.],
[2.3, 0.4, 1.],
[2.3, 0.6, 1.],
[0.7, 1.4, 1.],
[0.7, 1.6, 1.], #55
[1.5, 1.4, 1.],
[1.5, 1.6, 1.],
[2.3, 1.4, 1.],
[2.3, 1.6, 1.],
[0.74, 0.4131, 1.2], #60
[0.74, 0.5866, 1.2],
[1.5, 0.4131, 1.2],
[1.5, 0.5866, 1.2],
[2.26, 0.4131, 1.2],
[2.26, 0.5866, 1.2], #65
[0.74, 1.4131, 1.2],
[0.74, 1.5866, 1.2],
[1.5, 1.4131, 1.2],
[1.5, 1.5866, 1.2],
[2.26, 1.4131, 1.2], #70
[2.26, 1.5866, 1.2],
]
cp.N = np.vstack([cp.N, grab_nodes])
cp.N = np.vstack([cp.N, crane_nodes])
crane_cl = [#crane
[34, 35], #49
[35, 36],
[36, 37],
[37, 38],
[39, 40],
[40, 41],
[41, 42], #55
[42, 43],
[34, 44],
[35, 48],
[36, 50],
[37, 52], #60
[38, 45],
[12, 44],
[13, 46],
[14, 45],
[15, 47], #65
[22, 60],
[23, 61],
[24, 66],
[25, 67],
[26, 62], #70
[27, 63],
[28, 68],
[29, 69],
[30, 64],
[31, 65], #75
[32, 70],
[33, 71],
[44, 46],
[46, 39],
[47, 43],
[45, 47],
[48, 49],
[49, 54],
[54, 55],
[55, 40],
[50, 51],
[51, 56],
[56, 57],
[57, 41],
[52, 53],
[53, 58],
[58, 59],
[59, 42]
]
cp.L = np.vstack([cp.L, crane_cl])
cp.GP = [[22, 0],
[23, 14],
[26, 2],
[27, 16],
[30, 4],
[31, 18],
[24, 1],
[25, 15],
[28, 3],
[29, 17],
[32, 5],
[33, 19]
]
cp.LP = [#[44, 57],
#[46, 57],
#[45, 61],
#[47, 61],
#[48, 58],
#[49, 58],
#[54, 58],
#[55, 58],
#[50, 59],
#[51, 59],
#[56, 59],
#[57, 59],
#[52, 60],
#[53, 60],
#[58, 60],
#[59, 60],
[48, 66],
[49, 67],
[54, 68],
[55, 69],
[50, 70],
[51, 71],
[56, 72],
[57, 73],
[52, 74],
[53, 75],
[58, 76],
[59, 77]
]
return cp
def rhombus_3x3_crane_fixed_sticks(n_steps = 10, dx = 0.5):
"""
This example shows a 3x2 rhombus creasepattern.
"""
cpr = YoshimuraCreasePattern(n_steps = n_steps,
L_x = 3,
L_y = 3,
n_x = 3,
n_y = 6,
MAX_ITER = 5000)
cp = Lifting(n_steps = n_steps, MAX_ITER = 500)
caf = CnstrTargetFace(F = [r_, s_, 4 * 0.4 * t_ * r_ * (1 - r_ / 3) + 0.25])
n_arr = np.hstack([cpr.N_h[:, :].flatten(),
#cpr.N_v[:, :].flatten(),
cpr.N_i[:, :].flatten()
])
cp.init_tf_lst = [(caf, n_arr)]
cp.cp_geo(cpr)
grab_nodes = [[0.5, 0.333, 0], #31
[0.5, 0.667, 0],
[0.5, 1.333, 0],
[0.5, 1.667, 0],
[0.5, 2.333, 0], #35
[0.5, 2.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[1.5, 1.333, 0],
[1.5, 1.667, 0],
[1.5, 2.333, 0],
[1.5, 2.667, 0],
[2.5, 0.333, 0],
[2.5, 0.667, 0],
[2.5, 1.333, 0], #45
[2.5, 1.667, 0],
[2.5, 2.333, 0],
[2.5, 2.667, 0]]#48
crane_nodes = [#crane
[0, 0, 1], #49
[0.5, 0, 1],
[1.5, 0, 1],
[2.5, 0, 1],
[3, 0, 1],
[0, 3, 1.01],
[0.5, 3, 1.], #55
[1.5, 3, 1.],
[2.5, 3, 1.],
[3, 3, 1.],
[0, 0.5, 1.],
[3, 0.5, 1.], #60
[0, 1.5, 1.],
[3, 1.5, 1.],
[0, 2.5, 1],
[3, 2.5, 1],
[0.5, 0.333, 1.], #65
[0.5, 0.667, 1.],
[1.5, 0.333, 1.],
[1.5, 0.667, 1.],
[2.5, 0.333, 1.],
[2.5, 0.667, 1.], #70
[0.5, 1.333, 1.],
[0.5, 1.667, 1.],
[1.5, 1.333, 1.],
[1.5, 1.667, 1.],
[2.5, 1.333, 1.], #75
[2.5, 1.667, 1.],
[0.5, 2.333, 1.],
[0.5, 2.667, 1.],
[1.5, 2.333, 1.],
[1.5, 2.667, 1.], #80
[2.5, 2.333, 1.],
[2.5, 2.667, 1.],
[0.5, 0.333, 1.2],
[0.5, 0.667, 1.2],
[1.5, 0.333, 1.2], #85
[1.5, 0.667, 1.2],
[2.5, 0.333, 1.2],
[2.5, 0.667, 1.2],
[0.5, 1.333, 1.2],
[0.5, 1.667, 1.2], #90
[1.5, 1.333, 1.2],
[1.5, 1.667, 1.2],
[2.5, 1.333, 1.2],
[2.5, 1.667, 1.2],
[0.5, 2.333, 1.2], #95
[0.5, 2.667, 1.2],
[1.5, 2.333, 1.2],
[1.5, 2.667, 1.2],
[2.5, 2.333, 1.2],
[2.5, 2.667, 1.2], #100
]
cp.N = np.vstack([cp.N, grab_nodes])
cp.N = np.vstack([cp.N, crane_nodes])
crane_cl = [#crane
[49, 50], #72
[50, 51],
[51, 52],
[52, 53], #75
[54, 55],
[55, 56],
[56, 57],
[57, 58],
[49, 59], #80
[59, 61],
[61, 63],
[63, 54],
[53, 60],
[60, 62], #85
[62, 64],
[64, 58],
[50, 55],
[51, 56],
[52, 57], #90
[83, 31],
[84, 32],
[89, 33],
[90, 34],
[95, 35], #95
[96, 36],
[85, 37],
[86, 38],
[91, 39],
[92, 40], #100
[97, 41],
[98, 42],
[87, 43],
[88, 44],
[93, 45], #105
[94, 46],
[99, 47],
[100, 48],
[59, 16],
[61, 17], #110
[63, 18],
[60, 19],
[62, 20],
[64, 21]
]
cp.L = np.vstack([cp.L, crane_cl])
cp.GP = [[31, 0],
[32, 21],
[33, 1],
[34, 22],
[35, 2],
[36, 23],
[37, 3],
[38, 24],
[39, 4],
[40, 25],
[41, 5],
[42, 26],
[43, 6],
[44, 27],
[45, 7],
[46, 28],
[47, 8],
[48, 29]
]
cp.LP = [[65, 88],
[66, 88],
[71, 88],
[72, 88],
[77, 88],
[78, 88],
[67, 89],
[68, 89],
[73, 89],
[74, 89],
[79, 89],
[80, 89],
[69, 90],
[70, 90],
[75, 90],
[76, 90],
[81, 90],
[82, 90],
[65, 91],
[66, 92],
[71, 93],
[72, 94],
[77, 95],
[78, 96],
[67, 97],
[68, 98],
[73, 99],
[74, 100],
[79, 101],
[80, 102],
[69, 103],
[70, 104],
[75, 105],
[76, 106],
[81, 107],
[82, 108],
]
return cp
def rhombus_3x1_crane(n_steps = 10, dx = 1.5):
cp = Lifting(n_steps = n_steps, MAX_ITER = 5000)
cp.N = [[0, 0, 0], #0
[0, 1, 0],
[1, 0, 0],
[1, 1, 0],
[2, 0, 0],
[2, 1, 0], #5
[3, 0, 0],
[3, 1, 0],
[0, 0.5, 0],
[3, 0.5, 0],
[0.5, 0.5, 0], #10
[1.5, 0.5, 0],
[2.5, 0.5, 0],
[0.5, 0.333, 0], #13
[0.5, 0.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[2.5, 0.333, 0],
[2.5, 0.666, 0],
#crane
[0, 0, 1], #19
[0.5, 0, 1],
[1.5, 0, 1],
[2.5, 0, 1],
[3, 0, 1],
[0, 1, 1.01],
[0.5, 1, 1.], #25
[1.5, 1, 1.],
[2.5, 1, 1.],
[3, 1, 1.],
[0, 0.5, 1.],
[3, 0.5, 1.], #30
[0.5, 0.333, 1.],
[0.5, 0.667, 1.],
[1.5, 0.333, 1.],
[1.5, 0.667, 1.],
[2.5, 0.333, 1.], #35
[2.5, 0.667, 1.],
[0.5, 0.333, 1.2],
[0.5, 0.667, 1.2],
[1.5, 0.333, 1.2],
[1.5, 0.667, 1.2], #40
[2.5, 0.333, 1.2],
[2.5, 0.667, 1.2],
]
cp.L = [[0, 2], #0
[0, 8],
[0, 10],
[1, 3],
[1, 8],
[1, 10],
[2, 4],
[2, 10],
[2, 11],
[3, 5],
[3, 10], #10
[3, 11],
[4, 6],
[4, 11],
[4, 12],
[5, 7],
[5, 11],
[5, 12],
[6, 9],
[6, 12],
[7, 9], #20
[7, 12],
[8, 10],
[9, 12],
[10, 11],
[11, 12],
#crane
[19, 20],
[20, 21],
[21, 22],
[22, 23],
[24, 25], #30
[25, 26],
[26, 27],
[27, 28],
[19, 29],
[29, 24],
[20, 25],
[21, 26],
[22, 27],
[23, 30],
[30, 28], #40
[29, 8],
[30, 9],
[37, 13],
[38, 14],
[39, 15], #45
[40, 16],
[41, 17],
[42, 18]
]
cp.F = [[0, 2, 10],
[2, 4, 11],
[4, 6, 12],
[2, 11, 10],
[4, 11, 12],
[0, 8, 10],
[6, 9, 12],
[1, 3, 10],
[3, 5, 11],
[5, 7, 12],
[3, 10, 11],
[5, 11, 12],
[1, 8, 10],
[7, 9, 12]
]
cp.LP = [[31, 36],
[32, 36],
[33, 37],
[34, 37],
[35, 38],
[36, 38],
[31, 43],
[32, 44],
[33, 45],
[34, 46],
[35, 47],
[36, 48], ]
cp.GP = [[13, 0],
[14, 7],
[15, 1],
[16, 8],
[17, 2],
[18, 9]
]
cp.cnstr_lhs = [[(39, 2, 1.0)],
[(39, 2, 1.0), (40, 2, -1.0)],
[(19, 2, 1.0)],
[(19, 2, 1.0), (20, 2, -1.0)],
[(20, 2, 1.0), (21, 2, -1.0)],
[(21, 2, 1.0), (22, 2, -1.0)],
[(22, 2, 1.0), (23, 2, -1.0)],
[(19, 2, 1.0), (29, 2, -1.0)],
[(29, 2, 1.0), (24, 2, -1.0)],
[(24, 2, 1.0), (25, 2, -1.0)],
[(25, 2, 1.0), (26, 2, -1.0)],
[(26, 2, 1.0), (27, 2, -1.0)],
[(27, 2, 1.0), (28, 2, -1.0)],
[(28, 2, 1.0), (30, 2, -1.0)],
[(19, 1, 1.0)],
[(19, 1, 1.0), (20, 1, -1.0)],
[(20, 1, 1.0), (21, 1, -1.0)],
[(21, 1, 1.0), (22, 1, -1.0)],
[(22, 1, 1.0), (23, 1, -1.0)],
[(19, 0, 1.0)],
[(19, 0, 1.0), (24, 0, -1.0)],
[(23, 0, 1.0), (30, 0, -1.0)],
[(19, 0, 1.0), (29, 0, -1.0)],
[(13, 1, 1.0), (37, 1, -1.0)],
[(14, 1, 1.0), (38, 1, -1.0)],
[(15, 1, 1.0), (39, 1, -1.0)],
[(16, 1, 1.0), (40, 1, -1.0)],
[(17, 1, 1.0), (41, 1, -1.0)],
[(18, 1, 1.0), (42, 1, -1.0)],
[(31, 1, 1.0), (33, 1, -1.0)],
[(33, 1, 1.0), (35, 1, -1.0)],
[(32, 1, 1.0), (34, 1, -1.0)],
#[(34, 1, 1.0), (36, 1, -1.0)],
[(32, 1, 1.0), (31, 1, 1.0)],
#[(37, 2, 1.0), (38, 2, -1.0)],
#[(39, 2, 1.0), (40, 2, -1.0)], siehe oben verknuepfung lasteinleitung
[(41, 2, 1.0), (42, 2, -1.0)],
[(39, 0, 1.0)],
[(40, 0, 1.0)],
[(37, 2, 1.0), (41, 2, -1.0)],
[(2, 1, 1.0), (4, 1, -1.0)]
]
cp.cnstr_rhs[0] = dx
cp.u_0[2] = 0.00005
cp.u_0[5] = 0.00005
cp.u_0[20] = 0.00005
cp.u_0[23] = 0.00005
cp.u_0[35] = 0.0003
cp.u_0[8] = 0.00025
cp.u_0[11] = 0.00025
cp.u_0[14] = 0.00025
cp.u_0[17] = 0.00025
cp.u_0[32] = 0.00017
cp.u_0[38] = 0.00017
cp.u_0[41] = 0.00016334
cp.u_0[44] = 0.00016334
cp.u_0[47] = 0.00028335
cp.u_0[50] = 0.00028335
cp.u_0[53] = 0.00016334
cp.u_0[56] = 0.00016334
cp.u_0[119] = 0.00028335
cp.u_0[122] = 0.00028335
cp.u_0[113] = 0.00016334
cp.u_0[116] = 0.00016334
cp.u_0[125] = 0.00016334
cp.u_0[128] = 0.00016334
print 'n_dofs', cp.n_dofs
print 'n_c', cp.n_c
print 'n_g', cp.n_g
print 'necessary constraints', cp.n_dofs - cp.n_c - cp.n_g * cp.n_d - cp.n_l * 2
print 'cnstr', len(cp.cnstr_lhs)
return cp
def rhombus_3x3_crane(n_steps = 10, dx = 0.7):
"""
This example shows a 3x2 rhombus creasepattern.
"""
cpr = YoshimuraCreasePattern(n_steps = n_steps,
L_x = 3,
L_y = 3,
n_x = 3,
n_y = 6,
MAX_ITER = 5000)
cp = Lifting(n_steps = n_steps, MAX_ITER = 500)
caf = CnstrTargetFace(F = [r_, s_, 4 * 0.4 * t_ * r_ * (1 - r_ / 3) + 0.15])
n_arr = np.hstack([cpr.N_h[:, :].flatten(),
#cpr.N_v[:, :].flatten(),
cpr.N_i[:, :].flatten()
])
cp.init_tf_lst = [(caf, n_arr)]
cp.cp_geo(cpr)
grab_nodes = [[0.5, 0.333, 0], #31
[0.5, 0.667, 0],
[0.5, 1.333, 0],
[0.5, 1.667, 0],
[0.5, 2.333, 0], #35
[0.5, 2.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[1.5, 1.333, 0],
[1.5, 1.667, 0],
[1.5, 2.333, 0],
[1.5, 2.667, 0],
[2.5, 0.333, 0],
[2.5, 0.667, 0],
[2.5, 1.333, 0], #45
[2.5, 1.667, 0],
[2.5, 2.333, 0],
[2.5, 2.667, 0]]#48
crane_nodes = [[1.5, 0.5, 1.0], #49
[0.5, 0.5, 1],
[2.5, 0.5, 1],
[0.5, 0.333, 1.0],
[0.5, 0.667, 1.0],
[2.5, 0.333, 1.0],
[2.5, 0.667, 1.0], #55
[1.5, 0.333, 1.0],
[1.5, 0.667, 1.0],
[1.5, 1.5, 1.0],
[0.5, 1.5, 1],
[2.5, 1.5, 1], #60
[0.5, 1.333, 1.0],
[0.5, 1.667, 1.0],
[2.5, 1.333, 1.0],
[2.5, 1.667, 1.0],
[1.5, 1.333, 1.0], #65
[1.5, 1.667, 1.0],
[1.5, 2.5, 1.0],
[0.5, 2.5, 1],
[2.5, 2.5, 1],
[0.5, 2.333, 1.0], #70
[0.5, 2.667, 1.0],
[2.5, 2.333, 1.0],
[2.5, 2.667, 1.0],
[1.5, 2.333, 1.0],
[1.5, 2.667, 1.0], #75
]
cp.N = np.vstack([cp.N, grab_nodes])
cp.N = np.vstack([cp.N, crane_nodes])
crane_cl = [#crane 1
[49, 50], #72
[49, 51],
[50, 52],
[50, 53],
[51, 54],
[51, 55],
[49, 56],
[49, 57],
[52, 31],
[53, 32],
[54, 43],
[55, 44],
[56, 37],
[57, 38],
#crane 2
[58, 59],
[58, 60],
[59, 61],
[59, 62],
[60, 63],
[60, 64],
[58, 65],
[58, 66],
[61, 33],
[62, 34],
[63, 45],
[64, 46],
[65, 39],
[66, 40],
#crane 3
[67, 68],
[67, 69],
[68, 70],
[68, 71],
[69, 72],
[69, 73],
[67, 74],
[67, 75],
[70, 35],
[71, 36],
[72, 47],
[73, 48],
[74, 41],
[75, 42],
]
cp.L = np.vstack([cp.L, crane_cl])
cp.GP = [[31, 0],
[32, 21],
[33, 1],
[34, 22],
[35, 2],
[36, 23],
[37, 3],
[38, 24],
[39, 4],
[40, 25],
[41, 5],
[42, 26],
[43, 6],
[44, 27],
[45, 7],
[46, 28],
[47, 8],
[48, 29]
]
cnstr_lhs_3 = [[(49, 2, 1.0)],
[(49, 0, 1.0)],
[(49, 1, 1.0), (67, 1, 1.0)],
[(49, 2, 1.0), (58, 2, -1.0)],
[(49, 2, 1.0), (67, 2, -1.0)],
[(49, 2, 1.0), (56, 2, -1.0)],
[(49, 2, 1.0), (57, 2, -1.0)],
[(49, 0, 1.0), (56, 0, -1.0)],
[(49, 0, 1.0), (57, 0, -1.0)],
[(50, 2, 1.0), (52, 2, -1.0)],
[(50, 2, 1.0), (53, 2, -1.0)],
[(50, 0, 1.0), (52, 0, -1.0)],
[(50, 0, 1.0), (53, 0, -1.0)],
[(51, 2, 1.0), (54, 2, -1.0)],
[(51, 2, 1.0), (55, 2, -1.0)],
[(51, 0, 1.0), (54, 0, -1.0)],
[(51, 0, 1.0), (55, 0, -1.0)],
[(50, 2, 1.0)],
[(51, 2, 1.0)],
[(50, 1, 1.0), (49, 1, -1.0)],
[(51, 1, 1.0), (49, 1, -1.0)],
[(58, 0, 1.0)],
[(58, 2, 1.0), (65, 2, -1.0)],
[(58, 2, 1.0), (66, 2, -1.0)],
[(58, 0, 1.0), (65, 0, -1.0)],
[(58, 0, 1.0), (66, 0, -1.0)],
[(59, 2, 1.0), (61, 2, -1.0)],
[(59, 2, 1.0), (62, 2, -1.0)],
[(59, 0, 1.0), (61, 0, -1.0)],
[(59, 0, 1.0), (62, 0, -1.0)],
[(60, 2, 1.0), (63, 2, -1.0)],
[(60, 2, 1.0), (64, 2, -1.0)],
[(60, 0, 1.0), (63, 0, -1.0)],
[(60, 0, 1.0), (64, 0, -1.0)],
[(59, 2, 1.0)],
[(60, 2, 1.0)],
[(59, 1, 1.0)],
[(60, 1, 1.0)],
[(58, 1, 1.0)],
[(67, 0, 1.0)],
[(67, 2, 1.0), (74, 2, -1.0)],
[(67, 2, 1.0), (75, 2, -1.0)],
[(67, 0, 1.0), (74, 0, -1.0)],
[(67, 0, 1.0), (75, 0, -1.0)],
[(68, 2, 1.0), (70, 2, -1.0)],
[(68, 2, 1.0), (71, 2, -1.0)],
[(68, 0, 1.0), (70, 0, -1.0)],
[(68, 0, 1.0), (71, 0, -1.0)],
[(69, 2, 1.0), (72, 2, -1.0)],
[(69, 2, 1.0), (73, 2, -1.0)],
[(69, 0, 1.0), (72, 0, -1.0)],
[(69, 0, 1.0), (73, 0, -1.0)],
[(68, 2, 1.0)],
[(69, 2, 1.0)],
[(67, 1, 1.0), (27, 1, -1.0)],
[(68, 1, 1.0), (67, 1, -1.0)],
[(69, 1, 1.0), (67, 1, -1.0)],
#[(35, 1, 1.0), (12, 1, -1.0)],
#[(46, 1, 1.0), (13, 1, -1.0)],
#[(35, 1, 1.0), (46, 1, 1.0)],
#[(36, 1, 1.0), (47, 1, 1.0)],
[(25, 0, 1.0)],
[(17, 1, 1.0)],
#[(10, 1, 1.0)],
#[(37, 2, 1.0), (48, 2, -1.0)],
#[(26, 1, 1.0), (30, 1, -1.0)],
#[(0, 1, 1.0), (3, 1, -1.0)],
#[(37, 2, 1.0), (38, 2, -1.0)],
#[(29, 1, 1.0), (33, 1, -1.0)],
#[(31, 1, 1.0), (37, 1, -1.0)],
#[(7, 2, 1.0), (11, 2, -1.0)],
#[(22, 0, 1.0), (24, 0, -1.0)],
#[(38, 0, 1.0), (49, 0, -1.0)],
#[(48, 2, 1.0), (49, 2, -1.0)],
#[(3, 2, 1.0), (6, 2, -1.0)],
#[(24, 1, 1.0), (28, 1, -1.0)],
#[(27, 1, 1.0), (31, 1, -1.0)],
[(4, 2, 1.0), (8, 2, -1.0)],
#[(3, 1, 1.0), (6, 1, -1.0)],
#[(5, 2, 1.0), (8, 2, -1.0)],
#[(30, 0, 1.0), (31, 0, -1.0)]
#[(30, 0, 1.0), (31, 0, -1.0)],
#[(31, 0, 1.0), (32, 0, -1.0)]
# [(12, 2, 1.0)],
# [(13, 0, 1.0)],
# [(14, 2, 1.0)],
# [(15, 2, 1.0)]
]
cp.cnstr_lhs = cnstr_lhs_3
cp.cnstr_rhs[0] = dx
print 'n_dofs', cp.n_dofs
print 'n_c', cp.n_c
print 'n_g', cp.n_g
print 'necessary constraints', cp.n_dofs - cp.n_c - cp.n_g * 3 - cp.n_l * 2
print 'cnstr', len(cp.cnstr_lhs)
return cp
def rhombus_3x1_crane(n_steps = 10, dx = 1.0):
'''
This is a first modell, which should lift the creasepattern.
It shows a configuration of constrains in which the crane will lift the pattern
in the expectet form. NOTE: There is no influence of gravity.
'''
cp = Lifting(n_steps = n_steps, MAX_ITER = 500)
cp.N = [[0, 0, 0], #0
[0, 1, 0],
[1, 0, 0],
[1, 1, 0],
[2, 0, 0],
[2, 1, 0], #5
[3, 0, 0],
[3, 1, 0],
[0, 0.5, 0],
[3, 0.5, 0],
[0.5, 0.5, 0], #10
[1.5, 0.5, 0],
[2.5, 0.5, 0],
[0.5, 0.333, 0], #13
[0.5, 0.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[2.5, 0.333, 0],
[2.5, 0.667, 0],
[1.5, 0.5, 1.0],
[0, 0.5, 1], #20
[3, 0.5, 1],
[0, 0.333, 1.0],
[0, 0.667, 1.0],
[3, 0.333, 1.0],
[3, 0.667, 1.0],
[1.5, 0.333, 1.0],
[1.5, 0.667, 1.0]
]
cp.L = [[0, 2], #0
[0, 8],
[0, 10],
[1, 3],
[1, 8],
[1, 10],
[2, 4],
[2, 10],
[2, 11],
[3, 5],
[3, 10], #10
[3, 11],
[4, 6],
[4, 11],
[4, 12],
[5, 7],
[5, 11],
[5, 12],
[6, 9],
[6, 12],
[7, 9], #20
[7, 12],
[8, 10],
[9, 12],
[10, 11],
[11, 12],
[19, 20], #26
[19, 21],
[20, 22],
[20, 23],
[19, 26],
[19, 27],
[21, 24],
[21, 25],
[13, 22],
[14, 23],
[15, 26],
[16, 27],
[17, 24],
[18, 25],
# [20, 8],
# [9, 21]
]
cp.F = [[0, 2, 10],
[2, 4, 11],
[4, 6, 12],
[2, 11, 10],
[4, 11, 12],
[0, 8, 10],
[6, 9, 12],
[1, 3, 10],
[3, 5, 11],
[5, 7, 12],
[3, 10, 11],
[5, 11, 12],
[1, 8, 10],
[7, 9, 12]
]
cp.GP = [[13, 0],
[14, 7],
[15, 1],
[16, 8],
[17, 2],
[18, 9]
]
cp.cnstr_lhs = [[(19, 2, 1.0)],
[(19, 1, 1.0)],
[(19, 0, 1.0)],
[(20, 1, 1.0)],
[(20, 2, 1.0)],
[(21, 1, 1.0)],
[(21, 2, 1.0)],
[(20, 0, 1.0), (22, 0, -1.0)],
[(20, 0, 1.0), (23, 0, -1.0)],
[(20, 2, 1.0), (22, 2, -1.0)],
[(20, 2, 1.0), (23, 2, -1.0)],
[(19, 0, 1.0), (26, 0, -1.0)],
[(19, 0, 1.0), (27, 0, -1.0)],
[(19, 2, 1.0), (26, 2, -1.0)],
[(19, 2, 1.0), (27, 2, -1.0)],
[(21, 0, 1.0), (24, 0, -1.0)],
[(21, 0, 1.0), (25, 0, -1.0)],
[(21, 2, 1.0), (24, 2, -1.0)],
[(21, 2, 1.0), (25, 2, -1.0)],
[(14, 1, 1.0), (16, 1, -1.0)],
#[(8, 2, 1.0)],
[(11, 1, 1.0)],
#[(9, 2, 1.0)],
[(11, 0, 1.0)],
[(13, 0, 1.0), (14, 0, -1.0)],
[(16, 1, 1.0), (18, 1, -1.0)],
[(2, 2, 1.0), (4, 2, -1.0)],
#[(13, 2, 1.0), (17, 2, -1.0)],
[(13, 1, 1.0), (15, 1, -1.0)]
]
cp.cnstr_rhs[0] = dx
cp.u_0[2] = 0.00005
cp.u_0[5] = 0.00005
cp.u_0[20] = 0.00005
cp.u_0[23] = 0.00005
cp.u_0[35] = 0.0003
cp.u_0[8] = 0.00025
cp.u_0[11] = 0.00025
cp.u_0[14] = 0.00025
cp.u_0[17] = 0.00025
cp.u_0[32] = 0.00017
cp.u_0[38] = 0.00017
cp.u_0[41] = 0.00016334
cp.u_0[44] = 0.00016334
cp.u_0[47] = 0.00028335
cp.u_0[50] = 0.00028335
cp.u_0[53] = 0.00016334
cp.u_0[56] = 0.00016334
cp.u_0[59] = 0.00025
cp.u_0[66] = 0.0001
cp.u_0[68] = 0.00016334
cp.u_0[69] = -0.0001
cp.u_0[71] = 0.00016334
cp.u_0[72] = 0.0001
cp.u_0[74] = 0.00016334
cp.u_0[75] = 0.0001
cp.u_0[77] = 0.00016334
cp.u_0[78] = -0.0001
cp.u_0[80] = 0.00016334
cp.u_0[81] = -0.0001
cp.u_0[83] = 0.00016334
# cp.u_0[86] = 0.00025
# cp.u_0[89] = 0.00025
print 'n_dofs', cp.n_dofs
print 'n_c', cp.n_c
print 'n_g', cp.n_g
print 'necessary constraints', cp.n_dofs - cp.n_c - cp.n_g * cp.n_d - cp.n_l * 2
print 'cnstr', len(cp.cnstr_lhs)
return cp
def rhombus_3x2_crane(n_steps = 10, dx = 0.7):
"""
This example shows a 3x2 rhombus creasepattern.
"""
cpr = YoshimuraCreasePattern(n_steps = n_steps,
L_x = 3,
L_y = 2,
n_x = 3,
n_y = 4,
MAX_ITER = 5000)
cp = Lifting(n_steps = n_steps, MAX_ITER = 500)
caf = CnstrTargetFace(F = [r_, s_, 4 * 0.4 * t_ * r_ * (1 - r_ / 3) + 0.15])
n_arr = np.hstack([cpr.N_h[:, :].flatten(),
#cpr.N_v[:, :].flatten(),
cpr.N_i[:, :].flatten()
])
cp.init_tf_lst = [(caf, n_arr)]
cp.cp_geo(cpr)
grab_nodes = [[0.5, 0.333, 0],
[0.5, 0.667, 0],
[0.5, 1.333, 0],
[0.5, 1.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[1.5, 1.333, 0],
[1.5, 1.667, 0],
[2.5, 0.333, 0],
[2.5, 0.667, 0],
[2.5, 1.333, 0],
[2.5, 1.667, 0]]#33
crane_nodes = [[1.5, 0.5, 1.0], #34
[0.5, 0.5, 1],
[2.5, 0.5, 1],
[0.5, 0.333, 1.0],
[0.5, 0.667, 1.0], #38
[2.5, 0.333, 1.0],
[2.5, 0.667, 1.0],
[1.5, 0.333, 1.0],
[1.5, 0.667, 1.0],
[1.5, 1.5, 1.0], #43
[0.5, 1.5, 1],
[2.5, 1.5, 1],
[0.5, 1.333, 1.0], #46
[0.5, 1.667, 1.0],
[2.5, 1.333, 1.0],
[2.5, 1.667, 1.0],
[1.5, 1.333, 1.0],
[1.5, 1.667, 1.0], #51
]
cp.N = np.vstack([cp.N, grab_nodes])
cp.N = np.vstack([cp.N, crane_nodes])
crane_cl = [#crane 1
[34, 35], #49
[34, 36],
[35, 37],
[35, 38],
[36, 39],
[36, 40],
[34, 41], #55
[34, 42],
[37, 22],
[38, 23], #60
[39, 30],
[40, 31],
[41, 26],
[42, 27],
#crane 2
[43, 44], #65
[43, 45],
[44, 46],
[44, 47],
[45, 48],
[45, 49],
[43, 50],
[43, 51],
[46, 24],
[47, 25],
[48, 32],
[49, 33],
[50, 28],
[51, 29],
]
cp.L = np.vstack([cp.L, crane_cl])
cp.GP = [[22, 0],
[23, 14],
[26, 2],
[27, 16],
[30, 4],
[31, 18],
[24, 1],
[25, 15],
[28, 3],
[29, 17],
[32, 5],
[33, 19]
]
# cp.line_pts = [[37, 49],
# [38, 50],
# [48, 63],
# [49, 64]
# ]
#
cnstr_lhs_2 = [[(34, 2, 1.0)],
[(34, 0, 1.0)],
# [(34, 1, 1.0)],
[(34, 2, 1.0), (41, 2, -1.0)],
[(34, 2, 1.0), (42, 2, -1.0)],
[(34, 2, 1.0), (43, 2, -1.0)],
[(34, 0, 1.0), (41, 0, -1.0)],
[(34, 0, 1.0), (42, 0, -1.0)],
[(35, 2, 1.0), (37, 2, -1.0)],
[(35, 2, 1.0), (38, 2, -1.0)],
[(35, 0, 1.0), (37, 0, -1.0)],
[(35, 0, 1.0), (38, 0, -1.0)],
[(36, 2, 1.0), (39, 2, -1.0)],
[(36, 2, 1.0), (40, 2, -1.0)],
[(36, 0, 1.0), (39, 0, -1.0)],
[(36, 0, 1.0), (40, 0, -1.0)],
[(35, 2, 1.0)],
[(36, 2, 1.0)],
[(36, 1, 1.0), (34, 1, -1.0)],
[(35, 1, 1.0), (34, 1, -1.0)],
[(43, 0, 1.0)],
# [(43, 1, 1.0)],
[(43, 2, 1.0), (50, 2, -1.0)],
[(43, 2, 1.0), (51, 2, -1.0)],
[(43, 0, 1.0), (50, 0, -1.0)],
[(43, 0, 1.0), (51, 0, -1.0)],
[(44, 2, 1.0), (46, 2, -1.0)],
[(44, 2, 1.0), (47, 2, -1.0)],
[(44, 0, 1.0), (46, 0, -1.0)],
[(44, 0, 1.0), (47, 0, -1.0)],
[(45, 2, 1.0), (48, 2, -1.0)],
[(45, 2, 1.0), (49, 2, -1.0)],
[(45, 0, 1.0), (48, 0, -1.0)],
[(45, 0, 1.0), (49, 0, -1.0)],
[(44, 2, 1.0)],
[(45, 2, 1.0)],
[(44, 1, 1.0), (43, 1, -1.0)],
[(45, 1, 1.0), (43, 1, -1.0)],
[(4, 0, 1.0)],
[(1, 1, 1.0)],
[(22, 1, 1.0), (26, 1, -1.0)],
[(3, 2, 1.0), (6, 2, -1.0)],
[(22, 0, 1.0), (23, 0, -1.0)],
[(34, 1, 1.0), (18, 1, -1.0)],
[(34, 1, 1.0), (43, 1, 1.0)]
]
cnstr_lhs_1 = [[(34, 2, 1.0)],
[(34, 0, 1.0)],
[(34, 1, 1.0)],
[(34, 2, 1.0), (41, 2, -1.0)],
[(34, 2, 1.0), (42, 2, -1.0)],
[(34, 2, 1.0), (43, 2, -1.0)],
[(34, 0, 1.0), (41, 0, -1.0)],
[(34, 0, 1.0), (42, 0, -1.0)],
[(35, 2, 1.0), (37, 2, -1.0)],
[(35, 2, 1.0), (38, 2, -1.0)],
[(35, 0, 1.0), (37, 0, -1.0)],
[(35, 0, 1.0), (38, 0, -1.0)],
[(36, 2, 1.0), (39, 2, -1.0)],
[(36, 2, 1.0), (40, 2, -1.0)],
[(36, 0, 1.0), (39, 0, -1.0)],
[(36, 0, 1.0), (40, 0, -1.0)],
[(35, 2, 1.0)],
[(36, 2, 1.0)],
[(36, 1, 1.0)],
[(35, 1, 1.0)],
[(43, 0, 1.0)],
[(43, 1, 1.0), (45, 1, -1.0)],
[(43, 2, 1.0), (50, 2, -1.0)],
[(43, 2, 1.0), (51, 2, -1.0)],
[(43, 0, 1.0), (50, 0, -1.0)],
[(43, 0, 1.0), (51, 0, -1.0)],
[(44, 2, 1.0), (46, 2, -1.0)],
[(44, 2, 1.0), (47, 2, -1.0)],
[(44, 0, 1.0), (46, 0, -1.0)],
[(44, 0, 1.0), (47, 0, -1.0)],
[(45, 2, 1.0), (48, 2, -1.0)],
[(45, 2, 1.0), (49, 2, -1.0)],
[(45, 0, 1.0), (48, 0, -1.0)],
[(45, 0, 1.0), (49, 0, -1.0)],
[(44, 2, 1.0)],
[(45, 2, 1.0)],
[(44, 1, 1.0), (43, 1, -1.0)],
[(43, 1, 1.0), (19, 1, -1.0)],
#[(35, 1, 1.0), (12, 1, -1.0)],
#[(46, 1, 1.0), (13, 1, -1.0)],
#[(35, 1, 1.0), (46, 1, 1.0)],
#[(36, 1, 1.0), (47, 1, 1.0)],
[(4, 0, 1.0)],
[(1, 1, 1.0), (10, 1, -1.0)],
#[(10, 1, 1.0)],
#[(37, 2, 1.0), (48, 2, -1.0)],
#[(26, 1, 1.0), (30, 1, -1.0)],
#[(0, 1, 1.0), (3, 1, -1.0)],
#[(37, 2, 1.0), (38, 2, -1.0)],
#[(29, 1, 1.0), (33, 1, -1.0)],
[(22, 1, 1.0), (26, 1, -1.0)],
#[(22, 0, 1.0), (24, 0, -1.0)],
#[(38, 0, 1.0), (49, 0, -1.0)],
#[(48, 2, 1.0), (49, 2, -1.0)],
#[(3, 2, 1.0), (6, 2, -1.0)],
#[(24, 1, 1.0), (28, 1, -1.0)],
#[(27, 1, 1.0), (31, 1, -1.0)],
[(3, 2, 1.0), (6, 2, -1.0)],
#[(3, 1, 1.0), (6, 1, -1.0)],
#[(5, 2, 1.0), (8, 2, -1.0)],
#[(30, 0, 1.0), (31, 0, -1.0)]
#[(30, 0, 1.0), (31, 0, -1.0)],
[(22, 0, 1.0), (23, 0, -1.0)]
# [(12, 2, 1.0)],
# [(13, 0, 1.0)],
# [(14, 2, 1.0)],
# [(15, 2, 1.0)]
]
cnstr_lhs_3 = [[(34, 2, 1.0)],
[(34, 0, 1.0)],
[(34, 1, 1.0), (43, 1, 1.0)],
[(34, 2, 1.0), (41, 2, -1.0)],
[(34, 2, 1.0), (42, 2, -1.0)],
#[(34, 2, 1.0), (43, 2, -1.0)],
[(34, 0, 1.0), (41, 0, -1.0)],
[(34, 0, 1.0), (42, 0, -1.0)],
[(35, 2, 1.0), (37, 2, -1.0)],
[(35, 2, 1.0), (38, 2, -1.0)],
[(35, 0, 1.0), (37, 0, -1.0)],
[(35, 0, 1.0), (38, 0, -1.0)],
[(36, 2, 1.0), (39, 2, -1.0)],
[(36, 2, 1.0), (40, 2, -1.0)],
[(36, 0, 1.0), (39, 0, -1.0)],
[(36, 0, 1.0), (40, 0, -1.0)],
[(35, 2, 1.0)],
[(36, 2, 1.0)],
[(36, 1, 1.0), (34, 1, -1.0)],
[(35, 1, 1.0), (34, 1, -1.0)],
[(43, 0, 1.0)],
[(43, 1, 1.0), (45, 1, -1.0)],
[(43, 2, 1.0), (50, 2, -1.0)],
[(43, 2, 1.0), (51, 2, -1.0)],
[(43, 0, 1.0), (50, 0, -1.0)],
[(43, 0, 1.0), (51, 0, -1.0)],
[(44, 2, 1.0), (46, 2, -1.0)],
[(44, 2, 1.0), (47, 2, -1.0)],
[(44, 0, 1.0), (46, 0, -1.0)],
[(44, 0, 1.0), (47, 0, -1.0)],
[(45, 2, 1.0), (48, 2, -1.0)],
[(45, 2, 1.0), (49, 2, -1.0)],
[(45, 0, 1.0), (48, 0, -1.0)],
[(45, 0, 1.0), (49, 0, -1.0)],
[(44, 2, 1.0)],
[(45, 2, 1.0)],
[(44, 1, 1.0), (43, 1, -1.0)],
[(43, 1, 1.0), (19, 1, -1.0)],
#[(35, 1, 1.0), (12, 1, -1.0)],
#[(46, 1, 1.0), (13, 1, -1.0)],
#[(35, 1, 1.0), (46, 1, 1.0)],
#[(36, 1, 1.0), (47, 1, 1.0)],
[(4, 0, 1.0)],
[(1, 1, 1.0)],
#[(10, 1, 1.0)],
#[(37, 2, 1.0), (48, 2, -1.0)],
#[(26, 1, 1.0), (30, 1, -1.0)],
#[(0, 1, 1.0), (3, 1, -1.0)],
#[(37, 2, 1.0), (38, 2, -1.0)],
#[(29, 1, 1.0), (33, 1, -1.0)],
[(22, 1, 1.0), (26, 1, -1.0)],
[(22, 0, 1.0), (23, 0, -1.0)],
#[(38, 0, 1.0), (49, 0, -1.0)],
#[(48, 2, 1.0), (49, 2, -1.0)],
#[(3, 2, 1.0), (6, 2, -1.0)],
#[(24, 1, 1.0), (28, 1, -1.0)],
#[(27, 1, 1.0), (31, 1, -1.0)],
[(3, 2, 1.0), (6, 2, -1.0)],
#[(3, 1, 1.0), (6, 1, -1.0)],
#[(5, 2, 1.0), (8, 2, -1.0)],
#[(30, 0, 1.0), (31, 0, -1.0)]
#[(30, 0, 1.0), (31, 0, -1.0)],
[(22, 0, 1.0), (23, 0, -1.0)]
# [(12, 2, 1.0)],
# [(13, 0, 1.0)],
# [(14, 2, 1.0)],
# [(15, 2, 1.0)]
]
cp.cnstr_lhs = cnstr_lhs_2
cp.cnstr_rhs[0] = dx
print 'n_dofs', cp.n_dofs
print 'n_c', cp.n_c
print 'n_g', cp.n_g
print 'necessary constraints', cp.n_dofs - cp.n_c - cp.n_g * 3 - cp.n_l * 2
print 'cnstr', len(cp.cnstr_lhs)
return cp
def rhombus_3x1_crane_sticks(n_steps=10, dx=1.0):
cp = Lifting(n_steps=n_steps, MAX_ITER=500)
cp.N = [[0, 0, 0], #0
[0, 1, 0],
[1, 0, 0],
[1, 1, 0],
[2, 0, 0],
[2, 1, 0], #5
[3, 0, 0],
[3, 1, 0],
[0, 0.5, 0],
[3, 0.5, 0],
[0.5, 0.5, 0], #10
[1.5, 0.5, 0],
[2.5, 0.5, 0],
[0.5, 0.333, 0], #13
[0.5, 0.667, 0],
[1.5, 0.333, 0],
[1.5, 0.667, 0],
[2.5, 0.333, 0],
[2.5, 0.666, 0],
[1.5, 0.5, 1.0],
[0, 0.5, 1],
[3, 0.5, 1],
[0.5, 0.5, 1.0],
[2.5, 0.5, 1.0],
[0.5, 0.333, 1.0],
[0.5, 0.667, 1.0],
[2.5, 0.333, 1.0],
[2.5, 0.667, 1.0],
[1.5, 0.333, 1.0],
[1.5, 0.667, 1.0]
]
cp.L = [[0, 2], #0
[0, 8],
[0, 10],
[1, 3],
[1, 8],
[1, 10],
[2, 4],
[2, 10],
[2, 11],
[3, 5],
[3, 10], #10
[3, 11],
[4, 6],
[4, 11],
[4, 12],
[5, 7],
[5, 11],
[5, 12],
[6, 9],
[6, 12],
[7, 9], #20
[7, 12],
[8, 10],
[9, 12],
[10, 11],
[11, 12],
[19, 20], #26
[19, 21],
[22, 24],
[22, 25],
[19, 28],
[19, 29],
[23, 26],
[23, 27],
[13, 24],
[14, 25],
[15, 28],
[16, 29],
[17, 26],
[18, 27],
[20, 8],
[9, 21]
]
cp.F = [[0, 2, 10],
[2, 4, 11],
[4, 6, 12],
[2, 11, 10],
[4, 11, 12],
[0, 8, 10],
[6, 9, 12],
[1, 3, 10],
[3, 5, 11],
[5, 7, 12],
[3, 10, 11],
[5, 11, 12],
[1, 8, 10],
[7, 9, 12]
]
cp.LP = [[22, 26],
[23, 27]]
cp.GP = [[13, 0],
[14, 7],
[15, 1],
[16, 8],
[17, 2],
[18, 9]
]
cp.cnstr_lhs = [[(19, 2, 1.0)],
[(19, 1, 1.0)],
[(19, 0, 1.0)],
[(20, 1, 1.0)],
[(20, 2, 1.0)],
[(21, 1, 1.0)],
[(21, 2, 1.0)],
[(22, 0, 1.0), (24, 0, -1.0)],
[(22, 0, 1.0), (25, 0, -1.0)],
[(22, 2, 1.0), (24, 2, -1.0)],
[(22, 2, 1.0), (25, 2, -1.0)],
[(19, 0, 1.0), (28, 0, -1.0)],
[(19, 0, 1.0), (29, 0, -1.0)],
[(19, 2, 1.0), (28, 2, -1.0)],
[(19, 2, 1.0), (29, 2, -1.0)],
[(23, 0, 1.0), (26, 0, -1.0)],
[(23, 0, 1.0), (27, 0, -1.0)],
[(23, 2, 1.0), (26, 2, -1.0)],
[(23, 2, 1.0), (27, 2, -1.0)],
[(14, 1, 1.0), (16, 1, -1.0)],
#[(8, 2, 1.0)],
[(11, 1, 1.0)],
#[(9, 2, 1.0)],
[(11, 0, 1.0)],
[(13, 0, 1.0), (14, 0, -1.0)],
[(16, 1, 1.0), (18, 1, -1.0)],
[(2, 2, 1.0), (4, 2, -1.0)],
#[(13, 2, 1.0), (17, 2, -1.0)],
[(13, 1, 1.0), (15, 1, -1.0)]
]
cp.cnstr_rhs[0] = dx
cp.u_0[2] = 0.00005
cp.u_0[5] = 0.00005
cp.u_0[20] = 0.00005
cp.u_0[23] = 0.00005
cp.u_0[35] = 0.0003
cp.u_0[8] = 0.00025
cp.u_0[11] = 0.00025
cp.u_0[14] = 0.00025
cp.u_0[17] = 0.00025
cp.u_0[32] = 0.00017
cp.u_0[38] = 0.00017
cp.u_0[41] = 0.00016334
cp.u_0[44] = 0.00016334
cp.u_0[47] = 0.00028335
cp.u_0[50] = 0.00028335
cp.u_0[53] = 0.00016334
cp.u_0[56] = 0.00016334
cp.u_0[59] = 0.00025
cp.u_0[66] = 0.0001
cp.u_0[68] = 0.00016334
cp.u_0[69] = -0.0001
cp.u_0[71] = 0.00016334
cp.u_0[72] = 0.0001
cp.u_0[74] = 0.00016334
cp.u_0[75] = 0.0001
cp.u_0[77] = 0.00016334
cp.u_0[78] = -0.0001
cp.u_0[80] = 0.00016334
cp.u_0[81] = -0.0001
cp.u_0[83] = 0.00016334
cp.u_0[86] = 0.00025
cp.u_0[89] = 0.00025
print 'n_dofs', cp.n_dofs
print 'n_c', cp.n_c
print 'n_g', cp.n_g
print 'necessary constraints', cp.n_dofs - cp.n_c - cp.n_g * cp.n_d - cp.n_l * 2
print 'cnstr', len(cp.cnstr_lhs)
return cp