ProjectFigure 1 Shear Strain vs. Distance from Center along OA for Aluminum Plate;Figure 2 Radial Strain vs. Distance from Center along the OB for Aluminum Plate;Figure 3 Convergence study of bias valueFigure 4 Model mesh of the linear axisymmetric model with quadratic elementsFigure 5 Failure moment prediction using finite element modelsM. Vable Notes for finite element method: Project1ProjectDesign of mechanically fasteneted joints in composite plates.tNutWasherCompositeplateF1F2F2F1PzTTdRrdM. Vable Notes for finite element method: Project2δ4”5”x4”5”xθyzM. Vable Notes for finite element method: Project31200 elements3360 elements5280 elements (equivalent: 10560 elements)M. Vable Notes for finite element method: Project4Figure 1 Shear Strain vs. Distance from Center along OA for Aluminum Plate; Figure 2 Radial Strain vs. Distance from Center along the OB for Aluminum Plate;Distance from the CenterShear Strain0.00 0.40 0.80 1.20 1.60 2.00-0.0025-0.0020-0.0015-0.0010-0.00050.00000.0005Mesh 1Mesh 2Mesh 3Edge of WasherBOADistance from the CenterRadial Strain0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00-0.0010.0000.0010.0020.0030.0040.0050.006Mesh 1Mesh 2Mesh 3ABOEdge of WasherM. Vable Notes for finite element method: Project5Table 1: CPU time summaryMesh CPU time Normalized to Mesh 1Mesh 1 175 s 1.00Mesh 2 882 s 5.04Mesh 3 1256 s 7.18Center Rotation (rad)Applied Moment (in-lb)0.000 0.010 0.020 0.030 0.040 0.050 0.0600.0050.00100.00150.00200.00Bonded WasherNo WasherExperimental ResultsM. Vable Notes for finite element method: Project6Table 2: CPU time of number of element in the plate thickness test models.Number of element in the plate thickness model.CPU time.seconds.Normalize to the 4 elements in the plate thickness model.4 elements 20.84 1 unit.6 elements 30.94 1.49 units.8 elements 42.50 2.04 units.2DISPLACEMENT MAGNIFICATION FACTOR = 1.42 ORIGINAL MESH DISPLACED MESH2 Deformed meshUndeformed mesh Interfaced washerr=0 r=0.5 r=4.0 r=5.0 Center Washer edge partial constrained Fully constrained0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045051015202530Center deflection (in.)Pullout load (lb.)0.5 1 1.5 2 2.5 3 3.5 4−0.00500.0050.010.0150.020.0250.030.0350.040.045Distance from the center along the radial direction (in.)Deflection in z direction (in.) (a) Pull out load vs. center deflection (b) Deflection along the radial direction 2 el. in the plate thickness model 4 el. in the plate thickness model6 el. in the plate thickness model8 el. in the plate thickness model Analytical solution +---+---+ .................o---o---oM. Vable Notes for finite element method: Project7Figure 3 Convergence study of bias valueFigure 4 Model mesh of the linear axisymmetric model with quadratic elements 20 30 40 50 60 7016001650170017501800185019001950Number of divisions in the radial direcion Pullout load (lb.)bias=0.88bias=0.90bias=0.92bias=0.94bias=0.96 r=0 r= 0.5 r=1.25 r=4.0BondedWasher20 radial Bias = 1.00 Bias = 1.00 Nodes in the 8-node quadratic elementdivisions10 radial divisions(a) Model 1r=0 r= 0.5 r=1.25 r=4.0BondedWasher20 radial 10 radial divisionsBias = 0.96 Bias = 1.00divisions(b) Model 2M. Vable Notes for finite element method: Project8Table 3: CPU time of quadratic element models.Model CPU timeNumber of nodes in the modelModel 1 5.95 sec. 215Model 2 6.20 sec. 215linear element model 12.20 sec. 3050 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04051015202530Center deflection (in.)Pullout load (lb.)0.5 1 1.5 2 2.5 3 3.5 400.0050.010.0150.020.0250.030.0350.04Distance from the center along the radial direction (in.)Deflection in z direction (in.) (a) Pull out load vs. center deflection (b) Deflection along the radial directionAnalytical solution +---+---+ Model 1 o---o---o Model 2M. Vable Notes for finite element method: Project9Figure 5 Failure moment prediction using finite element modelsTable 4: Failure moment predictionFailure criteriaFailure moment prediction (in-lbs)Three-dimensional modelTwo-dimensional modelExperimental resultBonded washer No-washer3D von Mises 269.1 261.2 352.4245502D von Misesand Tsai-Hill265.6 261.2 352.4Tsai-Wu 233.6 232.0 282.00 50 100 150 200 250 300 350 400 45000.10.20.30.40.50.60.70.80.91Applied moment (in−lbs)Failure index---- 2D bonded washer model........ 2D no-washer model + + Experimental result (o average) 3D model0 50 100 150 200 250 300 350 400 45000.10.20.30.40.50.60.70.80.91Applied moment (in−lbs)Failure index0 50 100 150 200 250 300 350 400 45000.10.20.30.40.50.60.70.80.91Applied moment (in−lbs)Failure index(a) Failure indices for the three-dimensional (b) Failure indices for the Tsai-Hill and(c) Failure indices for the Tsai-Wu criterionFailure FailureFailure plane stress (2D) von Mises criteria (3D) von Mises