# Impulsively loaded cantilever beam using Belytschko-Tsai shell elements
#
# References: 1. MSC/DYNA verification manual
# 2. 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
# 3. S. Timoshenko and J.N. Goodier, "Theory of Elasticity", 2nd ed.,
# McGraw-Hill, New York, 1951.
# 4. D. Shantaram, D.R.J. Owen and O.C. Zienkiewicz, "Dynamic
# Transient Behaviour of Two- and Three- Dimensional Structures
# Incliding Plasticity, Large Deformation Effects and Fluid
# Interaction, "Earthquake Engineering and Structural Dynamics,
# Vol. 4, pp. 561-578, 1976
#
# Problem Description
#
# An elastic cantilever beam is held fixed in one end and loaded by a uniform end
# along the length. The load is applied from the start and held constant over time.
#
# The analytical result for the deflection of the beam end and frequency is given
# by reference 3.
# deflection_in_z = (Pressure * width * Length^4 / (4 * E * I))
# frequency = (1.875^2)*sqrt(E*I/(rho*A))/Length^2
#
# Maximum deflection Period
# Analytical 0.025 in 0.005719
# LS-Dyna 0.02518 in 0.005752
# Impact 0.02556 in 0.0058
#
# Engineering data
#
# Length L = 10 in
# Width b = 1 in
# Thickness t = 1 in
# Young modulus E = 12000 psi
# Density rho = 0.1024E-5 lb-sec^2/in^4
# Poissons ratio nu = 0.2
nodes
1 x = 0 y = 0 z = 0 constraint = fixed
2 x = 2 y = 0 z = 0 load = pressure
3 x = 4 y = 0 z = 0 load = pressure
4 x = 6 y = 0 z = 0 load = pressure
5 x = 8 y = 0 z = 0 load = pressure
6 x = 10 y = 0 z = 0 load = halfpressure
7 x = 0 y = 1 z = 0 constraint = fixed
8 x = 2 y = 1 z = 0 load = pressure
9 x = 4 y = 1 z = 0 load = pressure
10 x = 6 y = 1 z = 0 load = pressure
11 x = 8 y = 1 z = 0 load = pressure
12 x = 10 y = 1 z = 0 load = halfpressure
elements of type SHELL_BT_4
1 nodes = [1,2,8,7] t = 1 material = mat_1 nip = 5 contact = off
2 nodes = [2,3,9,8] t = 1 material = mat_1 nip = 5 contact = off
3 nodes = [3,4,10,9] t = 1 material = mat_1 nip = 5 contact = off
4 nodes = [4,5,11,10] t = 1 material = mat_1 nip = 5 contact = off
5 nodes = [5,6,12,11] t = 1 material = mat_1 nip = 5 contact = off
materials of type elastic
mat_1 E = 12000 nu = 0.2 rho = 0.000001024
constraints of type boundary_condition
fixed vx = 0 vy = 0 vz = 0 vrx = 0 vry = 0 vrz = 0 ax = 0 ay = 0 az = 0 arx = 0 ary = 0 arz = 0
loads
pressure fz = -0.01
halfpressure fz = -0.005
trackers of type nodedisplacement
1 node = [6] direction = z filename = Ver_02.trk target = [0.0058,0.00001,0.0,0.0001]
controls
run from 0 to 0.01
print every 0.001 step
print tracker every 0.0001 step