# 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