# Wave propagation in a bar # # References # 1. Concepts and Applications of Finite Element Analysis # Robert D. Cook et al. Third Edition, ISBN 0-471-84788-7 # # Problem Description # An undamped uniform steel bar is loaded in the tip with a load # that is held constant from the start. # The bar is initially at rest and is modelled by 40 rod elements # of equal length. The bar is only allowed to move in one direction # making this a one dimensional problem. # # The stress / time history of element 20 midpoint is read with a # tracker. # # # Engineering Data # # Rod Length: L = 20.0 in # Cross sectional area: A = 1.0 in2 => D = 1.128 in # Young's modulus: E = 30 (E6) psi # Poissons Ratio: nu = 0.3 # Mass density: rho = 7.4E-4 lb-sec2/in4 # # Load: P0 = 100 lb applied at t=0 and constant # # Results # For exact results, see the book references. # The following description is taken from a graph in the book. # # In words, the stresses in rod 20 should remain = 0 until time # 5.0E-5 sec when a pressure of 100 psi (-100) should occur as an average level. # # This level remains until reflection of wave occurs at 1.5E-4 sec and # the pressure increases to 200 psi (-200). # # The tracker reflects this in Impact as a load (lb) in the rod. # With an area of 1 in2, this corresponds to -100 / -200 lb respectively. # nodes 1 x = 0.0 y = 0 z = 0 constraint = line load = hit 2 x = 0.5 y = 0 z = 0 constraint = line 3 x = 1.0 y = 0 z = 0 constraint = line 4 x = 1.5 y = 0 z = 0 constraint = line 5 x = 2.0 y = 0 z = 0 constraint = line 6 x = 2.5 y = 0 z = 0 constraint = line 7 x = 3.0 y = 0 z = 0 constraint = line 8 x = 3.5 y = 0 z = 0 constraint = line 9 x = 4.0 y = 0 z = 0 constraint = line 10 x = 4.5 y = 0 z = 0 constraint = line 11 x = 5.0 y = 0 z = 0 constraint = line 12 x = 5.5 y = 0 z = 0 constraint = line 13 x = 6.0 y = 0 z = 0 constraint = line 14 x = 6.5 y = 0 z = 0 constraint = line 15 x = 7.0 y = 0 z = 0 constraint = line 16 x = 7.5 y = 0 z = 0 constraint = line 17 x = 8.0 y = 0 z = 0 constraint = line 18 x = 8.5 y = 0 z = 0 constraint = line 19 x = 9.0 y = 0 z = 0 constraint = line 20 x = 9.5 y = 0 z = 0 constraint = line 21 x = 10.0 y = 0 z = 0 constraint = line 22 x = 10.5 y = 0 z = 0 constraint = line 23 x = 11.0 y = 0 z = 0 constraint = line 24 x = 11.5 y = 0 z = 0 constraint = line 25 x = 12.0 y = 0 z = 0 constraint = line 26 x = 12.5 y = 0 z = 0 constraint = line 27 x = 13.0 y = 0 z = 0 constraint = line 28 x = 13.5 y = 0 z = 0 constraint = line 29 x = 14.0 y = 0 z = 0 constraint = line 30 x = 14.5 y = 0 z = 0 constraint = line 31 x = 15.0 y = 0 z = 0 constraint = line 32 x = 15.5 y = 0 z = 0 constraint = line 33 x = 16.0 y = 0 z = 0 constraint = line 34 x = 16.5 y = 0 z = 0 constraint = line 35 x = 17.0 y = 0 z = 0 constraint = line 36 x = 17.5 y = 0 z = 0 constraint = line 37 x = 18.0 y = 0 z = 0 constraint = line 38 x = 18.5 y = 0 z = 0 constraint = line 39 x = 19.0 y = 0 z = 0 constraint = line 40 x = 19.5 y = 0 z = 0 constraint = line 41 x = 20.0 y = 0 z = 0 constraint = fixed elements of type rod_2 1 nodes = [1,2] D = 1.128 material = mat_1 2 nodes = [2,3] D = 1.128 material = mat_1 3 nodes = [3,4] D = 1.128 material = mat_1 4 nodes = [4,5] D = 1.128 material = mat_1 5 nodes = [5,6] D = 1.128 material = mat_1 6 nodes = [6,7] D = 1.128 material = mat_1 7 nodes = [7,8] D = 1.128 material = mat_1 8 nodes = [8,9] D = 1.128 material = mat_1 9 nodes = [9,10] D = 1.128 material = mat_1 10 nodes = [10,11] D = 1.128 material = mat_1 11 nodes = [11,12] D = 1.128 material = mat_1 12 nodes = [12,13] D = 1.128 material = mat_1 13 nodes = [13,14] D = 1.128 material = mat_1 14 nodes = [14,15] D = 1.128 material = mat_1 15 nodes = [15,16] D = 1.128 material = mat_1 16 nodes = [16,17] D = 1.128 material = mat_1 17 nodes = [17,18] D = 1.128 material = mat_1 18 nodes = [18,19] D = 1.128 material = mat_1 19 nodes = [19,20] D = 1.128 material = mat_1 20 nodes = [20,21] D = 1.128 material = mat_1 21 nodes = [21,22] D = 1.128 material = mat_1 22 nodes = [22,23] D = 1.128 material = mat_1 23 nodes = [23,24] D = 1.128 material = mat_1 24 nodes = [24,25] D = 1.128 material = mat_1 25 nodes = [25,26] D = 1.128 material = mat_1 26 nodes = [26,27] D = 1.128 material = mat_1 27 nodes = [27,28] D = 1.128 material = mat_1 28 nodes = [28,29] D = 1.128 material = mat_1 29 nodes = [29,30] D = 1.128 material = mat_1 30 nodes = [30,31] D = 1.128 material = mat_1 31 nodes = [31,32] D = 1.128 material = mat_1 32 nodes = [32,33] D = 1.128 material = mat_1 33 nodes = [33,34] D = 1.128 material = mat_1 34 nodes = [34,35] D = 1.128 material = mat_1 35 nodes = [35,36] D = 1.128 material = mat_1 36 nodes = [36,37] D = 1.128 material = mat_1 37 nodes = [37,38] D = 1.128 material = mat_1 38 nodes = [38,39] D = 1.128 material = mat_1 39 nodes = [39,40] D = 1.128 material = mat_1 40 nodes = [40,41] D = 1.128 material = mat_1 materials of type elastic mat_1 E = 30E6 nu = 0.3 rho = 7.4E-4 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 line vy = 0 vz = 0 ay = 0 az = 0 trackers of type rodforce 1 element = [20] filename = Ver_13.trk loads hit fx = 100 controls run from 0 to 0.2E-3 step 0.2E-6 print every 1.0E-6 step print tracker every 1.0e-6 step