# IMPULSIVELY LOADED CLAMPED BEAM
#
# References
# 1. T. Belytschko, J. Lin and C. S. Tsay, "Explicit Algorithms
# for the Nonlinear Dynamics of Shells", Computational Methods
# in Applied Mechanics Engineering, 42, pp. 225-251, 1984
#
# 2. H. A. Balmer and E. A. Witmer, "Theoretical-Experimental
# Correlation of Large Dynamic and Permanent Deformation of
# Impulsively Loaded Simple Structures", Air Force Flight
# Dynamics Laboratory, Report FDP-TDR-64-108, Wright-
# Patterson AFB, Ohio, July, 1964
#
# Problem description
# An aluminum beam which is clamped at both ends is loaded
# impulsively over its central poortion.
#
# Model description
# Due to the symmetry of the geometry and loading, only a
# quarter of the beam is modeled. 10 shell elements are used.
# The end nodes are fully constrained apart from the nodes
# at the symmetry lines. Shell_BT_4 elements with 5 integration
# points through the thickness are used.
#
# Engineering data
# Length L = 10 in
# Width b = 1.2 in
# Thickness t = 0.125 in
# Youngs modulus E = 10.4E6 psi
# Density rho = 2.61E-4 lb-sec2/in4
# Poissons ratio nu = 0.3
# Yield stress sigma = 41400 psi
# Plastic modulus Ep = 10.4E3 psi
# Isotropic hardening beta = 1
# Initial velocity Vo = -5200 in/sec
#
# Reference results
# The experimental results have been given by Balmer and Witmer
# Dyna and Impact gives the folliowing displacement values
# Note: The Dyna values are estimated from a graph.
#
# Time Dyna Impact
# 0.1 -0.5 -0.50
# 0.2 -0.62 -0.64
# 0.3 -0.69 -0.70
# 0.4 -0.78 -0.79
# 0.5 -0.79 -0.82
# 0.6 -0.80 -0.83
# 0.7 -0.80 -0.83
# 0.8 -0.79 -0.82
# 0.9 -0.77 -0.81
nodes
1 x = 0.0 y = 0.0 z = 0.0 constraint = sym
2 x = 0.5 y = 0.0 z = 0.0 constraint = vel_sym_x
3 x = 1.0 y = 0.0 z = 0.0 constraint = vel_sym_x
4 x = 1.5 y = 0.0 z = 0.0 constraint = sym_x
5 x = 2.0 y = 0.0 z = 0.0 constraint = sym_x
6 x = 2.5 y = 0.0 z = 0.0 constraint = sym_x
7 x = 3.0 y = 0.0 z = 0.0 constraint = sym_x
8 x = 3.5 y = 0.0 z = 0.0 constraint = sym_x
9 x = 4.0 y = 0.0 z = 0.0 constraint = sym_x
10 x = 4.5 y = 0.0 z = 0.0 constraint = sym_x
11 x = 5.0 y = 0.0 z = 0.0 constraint = clamp
12 x = 0.0 y = 0.6 z = 0.0 constraint = vel_sym_y
13 x = 0.5 y = 0.6 z = 0.0 constraint = push
14 x = 1.0 y = 0.6 z = 0.0 constraint = push
15 x = 1.5 y = 0.6 z = 0.0
16 x = 2.0 y = 0.6 z = 0.0
17 x = 2.5 y = 0.6 z = 0.0
18 x = 3.0 y = 0.6 z = 0.0
19 x = 3.5 y = 0.6 z = 0.0
20 x = 4.0 y = 0.6 z = 0.0
21 x = 4.5 y = 0.6 z = 0.0
22 x = 5.0 y = 0.6 z = 0.0 constraint = clamp
elements of type shell_bt_4
1 nodes = [1,2,13,12] material = mat1 t = 0.125
2 nodes = [2,3,14,13] material = mat1 t = 0.125
3 nodes = [3,4,15,14] material = mat1 t = 0.125
4 nodes = [4,5,16,15] material = mat1 t = 0.125
5 nodes = [5,6,17,16] material = mat1 t = 0.125
6 nodes = [6,7,18,17] material = mat1 t = 0.125
7 nodes = [7,8,19,18] material = mat1 t = 0.125
8 nodes = [8,9,20,19] material = mat1 t = 0.125
9 nodes = [9,10,21,20] material = mat1 t = 0.125
10 nodes = [10,11,22,21] material = mat1 t = 0.125
constraints of type boundary_condition
sym_x ay = 0 vy = 0 arx = 0 vrx = 0 arz = 0 vrz = 0
vel_sym_y ax = 0 vx = 0 ary = 0 vry = 0 arz = 0 vrz = 0 az = [0,0,0.000000001,off,1,off] vz = [0,-5200,0.000000001,off,1,off]
sym ax = 0 vx = 0 ay = 0 vy = 0 arx = 0 vrx = 0 ary = 0 vry = 0 arz = 0 vrz = 0 az = [0,0,0.0000000001,off,1,off] vz = [0,-5200,0.000000001,off,1,off]
clamp ax = 0 vx = 0 ay = 0 vy = 0 az = 0 vz = 0 arx = 0 vrx = 0 ary = 0 vry = 0 arz = 0 vrz = 0
vel_sym_x ay = 0 vy = 0 arx = 0 vrx = 0 az = [0,0,0.0000001,off,1,off] vz = [0,-5200,0.000000001,off,1,off] arz = 0 vrz = 0
push az = [0,0,0.000000001,off,1,off] vz = [0,-5200,0.000000001,off,1,off]
materials of type elastoplastic
mat1 E = 10400000 rho = 0.000261 nu = 0.3 yield_stress = 41400 Ep = 10400
trackers of type nodedisplacement
1 node = [1] direction = z filename = Ver_05.trk target = [0.00060,0.000001,-0.8316,0.0001]
controls
run from 0 to 0.001
print every 0.0001 step
print tracker every 0.00001 step