1 MME3360b Assignment 0310% of final mark Due date:March 19, 2012 Five problems each worth 20% of assignment mark

2 Node 1Node 2Node 3Node 4 x Horizontal lines denote 1D springs Nodes 1 and 4 are fixed Nodes 2 and 3 can move only in x direction All nodes have mass 1kg Spring stiffness k1 = k2 = k3 = k4 = 1000N/mm Make your own 1kg mass and build an assembly; confirm results with SolidWorks Simulation Save model as problem 01.SLDASM k1k2k3 k4 PROBLEM 1 For the assembly of 1D springs shown below determine eigenvalues, eigenvectors, natural frequencies and vibration periods for all mode present in the model. Use direct stiffness method.

3 PROBLEM 1 Paper part Solution with Direct Stiffness Method: Calculate f 1 and corresponding d 2 /d 3 Calculate f 2 and corresponding d 2 /d 3 Screen shots of results showing probed displacements d 2 and d 3 for frequencies f 1 and f 2 This will be a confirmation of hand calculations Electronic part Assembly problem 01.SLDASM complete with frequency study ready to run. Make sure you have included all parts.

4 PROBLEM 2 Download 2DOF torsion.sldasm from course web site and save as problem02.sldpasm. Treat the system as 2DOF torsional vibration system by applying proper restraints. Find natural frequencies and modes of vibration. Assume that the two large cylinders do not contribute to torsional stiffness. Confirm results with SW solution as in problem 1. Find all input data from the SW assembly. Fixed restraint DOFtorsional.sldasm

5 PROBLEM 2 Paper part Solution with Direct Stiffness Method: Calculate f 1 and corresponding φ 2 /φ 3 Calculate f 2 and corresponding φ 2 /φ 3 Electronic part Assembly problem 02.SLDPRT complete with frequency study ready to run. Screen shots of results showing probed displacements φ 2 and φ 3 for frequencies f 1 and f 2 Probe here

6 Mass moment of inertia of a cylinder about its axis Torsional stiffness PROBLEM 2 Shear modulus Polar moment of inertia of a circular cross section

7 PROBLEM 3 Fixed restraint 1000N load normal to end face I BEAM.SLDPRT- chapter 12

8 PROBLEM 3 Complete the following studies in SW Simulation Study 01 – original configuration Find FOS yield Study 02 – original configuration Find FOS buckling Based on the results of Study 01 and Study 02 propose a field repair to make sure that FOS buckling > FOS yield Create the field repair in a new configuration and run two more studies: Study 03 – field repair configuration Find FOS yield Study 04 – field repair configuration Find FOS buckling Save it as problem03.SLDPRT

9 PROBLEM 3 Paper part Summary of all results, explanation of field repair design. Electronic part Part problem03.SLDPRT with two configurations and four studies ready to run. Include von MIses stress plots, FOS plots and deformed buckling shape plots (not displacements plots) where applicable..

10 PROBLEM 4 EAISI 1020 Spring stiffness k = N/m Beam cross section (both beams) 50mm x 20mm Paper part Using direct stiffness method calculate nodal displacements and reactions. Construct graph showing transverse displacements of element 1 in the coordinate system shown above Screen print of SW displacement results. Electronic part: Make your own SW model to confirm result, make comparison for node 2 only. For SW model use Save model “ready to run” as problem04.SLDASM F= 1000N 600mm 200mm y x k Element 1 Element 2

11 PROBLEM 5 y 12 Fixed support Hinge support Moment 50Nm EABS Geometry link02.sldprt (chapter 15) – delete split line from SW model Paper part Using direct stiffness method to calculate nodal displacements and reactions. Find transverse displacement along the element length (see the next slide). SW plot of DY displacements Electronic part: Confirm result with equivalent SW model (make make a plot of DY displacements). Save model “ready to run” as problem05.SLDPRT

12 The relation between nodal forces and nodal displacements: x = Shape function is defined on nodal displacements so once we know nodal displacements we can calculate displacement anywhere along the element PROBLEM 5

13 Summary of deliverables You will have created the following models: Problem 1problem 01.SLDASM Problem 2:problem 02.SLDPRT Problem 3:problem 03.SLDPRT Problem 4:problem 04.SLDASM Problem 5:problem 05.SLDPRT All problems have paper parts. Remember to include all part files necessary for assemblies. Upload everything to the assignment drop-off box.