ansys mechanical

MMAE 545 Advanced CAD/CAE

Midterm Exam

Due Saturday, April 8, 2023 at 11:59 pm (CST)

Note: Instructions for submission are on the final page. This take-home portion accounts

for 50 of 100 possible points for the midterm exam.

Problem 1 (20 Points)

Consider the plate below. It has a uniform thickness, 𝑇, in the Z-direction (out-of-the page). The

magnitude of the total force, 𝐹, applied on the right side in the X-direction is: 𝐹 = 𝑃 × (𝑊2 × 𝑇).

The bar has three holes, each with a diameter, 𝑑. It has two semicircular grooves, each with a

radius, 𝑟1. Assume the bar has a modulus of elasticity, 𝐸 = 97 𝐺𝑃𝐴, the density is 𝜌 =

8490 𝑘𝑔/𝑚3And Poisson’s ratio is 𝜈 = 0.31. Model the bar in the way you believe is the most

efficient in ANSYS/Workbench while still producing accurate results for stresses and deflections.

Applied boundary conditions must conform to the situation shown in the sketch. The uniform

pressure may be applied as a force in Workbench, as long as it is done in a way that accurately

represents a uniformly distributed load. The static analysis must be sufficiently constrained so that

“weak springs” are not needed in ANSYS/Workbench to obtain a solution. Note that the bar is

constrained from moving in the X-direction all along the left end. All students are assigned specific

dimensions, as shown on the following page. The sketch is not to scale. The bar may be assumed

to behave linearly.

In your final report, show details of your modeling, including B.C’s, Loading, and results;

a) Based on an adequately meshed model, determine the force level, 𝐹, which results in a

maximum von Mises stress in the bar that equals 95 𝑀𝑃𝑎. Report this force magnitude,

𝐹, in units of 𝑁.

b) For the force level from part (a), determine the maximum X-direction deflection at the

right end. Report this value in units of mm.

Problem 1 dimensions are shown below. All dimensions are in millimeters. For all students, the

thickness, T, is 6 𝑚𝑚. Note that 𝑊2 = 𝑊1 − 2𝑟2.

Student W1 r2 W2 d W3 L1 L2 L3 L4 r1 L5

Abdeljaber 70 10 50 8 13 53 34 45 26 6 96

Adams 80 12 56 8 14 60 36 45 30 6 101

Alvarez-Avila 90 14 62 9 16 68 41 50 34 6 112

Ashong-Katai 100 8 84 13 21 75 47 70 36 9 139

Balladares 95 14 67 10 17 71 44 55 35 7 122

Browley 85 12 61 9 15 64 39 55 32 6 111

Calo 75 10 55 8 14 56 34 45 28 6 97

Cunningham 105 10 85 13 21 79 49 70 40 9 141

Dashtgerd 115 12 91 14 23 86 54 75 43 10 155

Dorula 120 14 92 14 23 90 56 75 45 10 159

Fredricks 110 15 80 12 20 83 51 65 41 8 142

Gaff 125 14 97 15 24 94 59 80 47 11 168

Gurijala 110 9 92 12 20 79 45 65 39 9 135

Ha 130 10 110 17 28 98 61 90 49 12 179

Hidalgo 70 12 46 7 12 53 33 45 27 5 91

Iranzo Juan 80 9 62 9 16 60 36 55 30 6 105

Khan (Ammar) 90 11 68 10 17 68 41 50 35 7 113

Khan (Zaid) 100 15 70 11 18 75 48 55 38 8 128

Khraisat 115 12 91 14 21 68 41 65 28 6 125

Klemp 120 14 92 14 17 75 47 70 40 6 129

Lapanderie 110 15 80 12 15 71 44 70 43 6 119

Larkin 125 14 97 15 14 64 39 60 45 9 106

Mateu Monterde 110 9 92 12 21 56 34 75 41 7 100

Mir 130 10 110 17 23 79 49 60 47 6 123

Mszal 70 12 46 7 12 86 54 85 39 6 155

Osayande 80 12 56 8 14 60 36 45 30 6 101

Palmatier 85 12 61 9 15 64 39 55 32 6 111

Patel (Darpankumar) 115 12 91 14 23 86 54 75 43 10 155

Patel (Sahil) 70 10 50 8 13 53 34 45 26 6 96

Patel (Sarthak) 110 15 80 12 20 83 51 65 41 8 142

Podraza 125 14 97 15 24 94 59 80 47 11 168

Prava 130 10 110 17 28 98 61 90 49 12 179

Rugeles 70 10 50 8 13 53 34 45 26 6 96

Rukujzo 80 12 56 8 14 60 36 45 30 6 101

Sampath Ramadurai 90 14 62 9 16 68 41 50 34 6 112

Shah 100 8 84 13 21 75 47 70 36 9 139

Shivnay 95 14 67 10 17 71 44 55 35 7 122

Siddaramu 85 12 61 9 15 64 39 55 32 6 111

Song 75 10 55 8 14 56 34 45 28 6 97

Soni 105 10 85 13 21 79 49 70 40 9 141

Sran 115 12 91 14 23 86 54 75 43 10 155

Syed 120 14 92 14 23 90 56 75 45 10 159

Tralsawala 110 15 80 12 20 83 51 65 41 8 142

Xu 125 14 97 15 24 94 59 80 47 11 168

Zhang 110 9 92 12 20 79 45 65 39 9 135

Problem 2 (30 Points)

Model a hollow cylinder with open ends to determine deflections and stresses based on the

assumption that it is spinning about a stationary axis of rotation, where the axis of rotation passes

through the cylinder’s geometrical center. Assume the cylinder is made of the default structural

steel in ANSYS/Workbench. Model this situation in two ways, as described in parts (a) and (b)

below. Include both models in the same ANSYS/Workbench archived project file. Each student is

assigned to specific dimensions and an angular velocity, ω, as indicated in the table on the

following page. The cylinder behaves linearly.

a) Create a 3D solid body model in ANSYS/Workbench. There are multiple ways this could

be modeled with a 3D solid body model. However, in this problem, model 1/8 of the

structure. Your model will include half the total length, taking advantage of the symmetry

about a plane perpendicular to the axis of rotation, cutting through the cylinder midway

between the ends of the cylinder—also, model only a 90° sector of the cross-section. Apply

appropriate symmetry boundary conditions. Based on an adequate mesh model, determine

the radial direction normal stress, 𝜎𝑟, the tangential direction normal stress (hoop stress),

𝜎𝑡, and the longitudinal (axial) direction normal stress, 𝜎𝑙, in units of psi, at six locations,

as indicated in Tables 1 − 3. Also, determine the radial direction displacement, 𝑢𝑟, at these

same six locations, as indicated in the tables.

b) Create a 2D axisymmetric model. Model only half the length, correctly applying boundary

conditions that take advantage of the symmetry about a plane perpendicular to the axis of

rotation cutting through the cylinder midway between the ends of the cylinder. Based on

an adequately meshed model, determine the radial direction normal stress,𝜎𝑟, the tangential

direction normal stress, 𝜎𝑡, and the longitudinal direction normal stress, 𝜎𝑙, in units of psi,

at six locations, as indicated in Tables 4 − 6 that follow. Also, determine the radial

direction displacement, 𝑢𝑟, at these same six locations, as indicated in the tables. In this

2D axisymmetric case, when you apply the rotational velocity in Mechanical, in the

“Details of Rotational Velocity”, you can set “Define By” to “Components”, and specify

the only nonzero component to be the component about the direction that defines your axis

of symmetry, which must be the Y-axis in ANSYS for a 2D axisymmetric analysis.

Student di

(in)

do

(in)

L

(in)

ω

(RPM)

Abdeljaber 36 50 40 1000

Adams 38 48 42 950

Alvarez-Avila 40 50 44 900

Ashong-Katai 38 49 46 850

Balladares 36 50 48 875

Browley 34 48 50 925

Calo 32 46 52 975

Cunningham 30 42 54 1025

Dashtgerd 28 44 56 1050

Dorula 30 44 48 1075

Fredricks 32 48 50 1100

Gaff 34 48 44 1150

Gurijala 36 48 42 1125

Ha 38 48 40 700

Hidalgo 40 50 48 725

Iranzo Juan 42 54 36 750

Khan (Ammar) 40 56 34 775

Khan (Zaid) 38 54 32 800

Khraisat 32 50 46 1050

Klemp 34 48 48 1025

Lapanderie 36 50 50 600

Larkin 38 49 52 625

Mateu Monterde 40 50 54 650

Mir 42 48 56 675

Mszal 40 46 48 700

Osayande 38 48 42 950

Palmatier 34 48 50 925

Patel (Darpankumar) 28 44 56 1050

Patel (Sahil) 36 50 40 1000

Patel (Sarthak) 32 48 50 1100

Podraza 34 48 44 1150

Prava 38 48 40 700

Rugeles 36 50 40 1000

Rukujzo 38 48 42 950

Sampath Ramadurai 40 50 44 900

Shah 38 49 46 850

Shivnay 36 50 48 875

Siddaramu 34 48 50 925

Song 32 46 52 975

Soni 30 42 54 1025

Sran 28 44 56 1050

Syed 30 44 48 1075

Tralsawala 32 48 50 1100

Xu 34 48 44 1150

Zhang 36 48 42 1125

Table 1: Problem 2, Part (a)- 3D Solid Body Results Set 1- Radial Location: Inner diameter

(at the inner wall).

Axial Location 𝜎𝑟 (psi) 𝜎𝑡 (psi) 𝜎𝑙 (psi) 𝑢𝑟 (in)

Either end

Midway along

axis, a distance

L/2 from each

end.

Table 2: Problem 2, Part (a)- 3D Solid Body Results Set 2- Midway through the wall

thickness.

Axial Location 𝜎𝑡 (psi) 𝜎𝑟 (psi) 𝜎𝑙 (psi) 𝑢𝑟 (in)

Either end

Midway along

axis, a distance

L/2 from each

end.

Table 3: Problem 2, Part (a)- 3D Solid Body Results Set 3- Radial location: Outer diameter

(at the outer wall)

Axial Location 𝜎𝑟 (psi) 𝜎𝑡 (psi) 𝜎𝑙 (psi) 𝑢𝑟 (in)

Either end

Midway along

axis, a distance

L/2 from each

end.

Table 4: Problem 2, Part (b)- 2D Axisymmetry Results Set 1- Radial location: Inner

diameter (at the inner wall)

Axial Location 𝜎𝑟 (psi) 𝜎𝑡 (psi) 𝜎𝑙 (psi) 𝑢𝑟 (in)

Either end

Midway along

axis, a distance

L/2 from each

end.

Table 5: Problem 2, Part (b)- 2D Axisymmetry Results Set 2- Radial location: Midway

through the wall thickness.

Axial Location 𝜎𝑟 (psi) 𝜎𝑡 (psi) 𝜎𝑙 (psi) 𝑢𝑟 (in)

Either end

Midway along

axis, a distance

L/2 from each

end.

Table 6: Problem 2, Part (b)- 2D Axisymmetry Results Set 3- Outer diameter (at the outer

wall)

Axial Location 𝜎𝑟 (psi) 𝜎𝑡 (psi) 𝜎𝑙 (psi) 𝑢𝑟 (in)

Either end

Midway along

axis, a distance

L/2 from each

end.

For this take-home portion of the Mideterm Exam, upload three files to Blackboard,

described below.

1. A word document named XXXXexam1.docs, or a PDF fine named

XXXXexam1.pdf (where “XXXX” is the first four letters of your last name, which

contains:

a) Details of your modeling (B.C’s and loading)

b) Results

 The force from Problem 1, Part (a)

 The deflection from Problem 1, part (b)

 Completed Table 1-6 for Problem 2.

2. An ANSYS/Workbench archived file named XXXexam1p1.wbpz which contains

your final archived project file, including final solution results, from Problem 1.

3. An ANSYS/Workbench archived file name XXXXexam1p2.wbpz which contains

your final archived project file, including final solution results, from Problem 2.

This file will contain both the 3D solid body analysis and the 2D axisymmetric

analysis as separate Analyses Systems in the main Workbench “Project

Schematic”.