CAD Project 05 Report Final

PROJECT 05

FINITE ELEMENT ANALYSIS

WITH SOLIDWORKS

UB

SIDHANT SHARMA

#36819679

MAE -577

11/3/2010

2

Contents

1 Introduction…………………………………..………………3

2 Problem statement…………………..……….….........…....…3

3 Result…………………………….….……….……..………..6

3.1 2-D Truss...………………..………….………………………….…..6

3.2 Beams………………………………………………………….……14

3.2.1 Simply supported beam…………………………...………….…..……14

3.2.2 Cantilever beam………………………………………………..………19

3.3 C-link analysis……………...………………...............................….23

3.3.1 Standard mesh…………………………………..………………..……23

3.3.2 Curvature based mesh…………………………..……………..………28

3.3.3 Rounded inside edges………………………….……………..…….….34

3.3.4 Design change consideration………………...……………..……….…44

4 Discussion………………………………….....….……..….50

5 Conclusion…………………………….…...…………..…..51

6 References………………………………...……...….…….52

3

1 Introduction

This project is intended towards learning the use of Solidworks 2010 for carrying out finite

element analysis of structures and mechanical devices such as a truss or a cantilever beam. The

CAE package is very handy for doing such a type of finite element study as it is fairly easy to

define the various conditions or the constraints under which the device is being subjected to, and

it gives sufficiently accurate results required for the further analysis of the system.

The problems considered in this project such as the 2-D truss or the loaded beam problem can be

solved analytically using the basic equilibrium equations of force and moment, and the results

can be visually analyzed using the powerful MATLAB tool. The solutions obtained in

Solidworks are compared to the solutions in MATLAB with the help of various plots to explore

the accuracy of the CAE package.

FEA is being tremendously used in the industry today for design and analysis purposes.

SolidWorks provides the ability to carry out this technique in a very user friendly manner, it is

fast and the design changes can be explored by making changes in the CAD models and design

constraints. This ability of Solidworks has been depicted in this project by considering a detailed

study of a C-bracket.

In this project, we have not only learnt the basics of implementing FEA in this software through

lessons provided in the book “Introduction to Finite Element Analysis using SolidWorks

Simulation 2010” but also used explored the capability of the package for analysis using

different mesh types, mesh sizes, and observing their corresponding effects on computational

time and convergence towards the analytical solution.

2 Problem statement

We are required to study and complete the lessons 4, 7, 11 provided in the book “Introduction to

Finite Element Analysis using SolidWorks Simulation 2010”. The results obtained are to be

compared with analytical solutions plotted in MATLAB in order to explore the accuracy of the

solutions in Solidworks.

The first part of the problem deals with the analysis of a 2-D Truss element (lesson 4). This

problem has to be solved analytically using the direct stiffness method of truss elements in 2-D

space by formulating the stiffness matrix. The truss structure consists of two elements and three

joints. The two base joints are fixed and only allow rotation as a degree of freedom. The middle

joint allows rotation as well as translation and it is subjected to a force of 50 lb in the horizontal

direction as shown in Figure 1. The material is steel rod of diameter 0.25 inches.

4

Figure 1 Truss element configuration with loading

We are required to solve this problem to compute the stress in the elements and the displacement

of the middle joint. These results are to be plotted in MATLAB.

Similarly, the same problem has to be solved in Solidworks using the steps provided in Chapter 4

and thus generate the stress, displacements plots for comparison.

The second part of the problem is to solve simple beam problems analytically using the force-

moment equilibrium equations. The shear force and bending moment equations are to be

formulated and the plots are to be shown using MATLAB. The loaded beams are shown below;

Figure 2 (a) which shows a supported beam and Figure 2 (b) which shows a cantilever beam. The

material for the beams is alloy steel.

By following the steps given in Chapter 7, the same problems have to be modeled, and FEA

analysis to be carried out in SolidWorks. Finally, the solutions have to be compared with the

MATLAB plots.

5

(a) (b) Figure 2 (a) supported beam problem; and (b) cantilever beam problem

The third part of the problem deals with the Von Mises stress analysis of a C-link shown in

Figure 3. The FEA has to be carried out using standard mesh sizes of 0.15 inch, 0. 10 inch, 0.10

inch with selective refinement and automatic transition. Plots of Von Mises stress, maximum

Von Mises stress and computational time v/s mesh size are to be generated in MATLAB.

Figure 3 c-link dimensions and loading (all dimensions in inches)

6

Then the effectiveness of a curvature based mesh is to be explored. The number of elements in a

circle (parameter) is to be varied from 4 to 36 in steps of 8. We have to record the number of

elements and the solving time in each case and plot the same graphs as in first case for

comparison. Based on this, we have to decide if a curvature based mesh is necessary in this

problem.

We have to model the C-link with inner edges rounded to a certain radius and carry out the

convergence analysis as in the first case with a standard mesh. Based on this analysis, we have to

decide how this added feature affects the solution, and whether using a curvature based mesh

instead, would improve the solution. Is this feature necessary to include in the FEM analysis?

A design change has to be suggested for the same C-link to reduce the maximum stress. The

design has to be modeled and the convergence analysis has to be carried out for the same in order

to show its performance.

Another requirement is to read and discuss the following topics

- SolidWorks Simulation Help;

- Meshing Advice in SolidWorks Simulation.

3 Result

The lessons 4, 7 and 11 given in the book were completed using the step by step instructions

provided. Once the parts have been modeled, the next step is to add the Solidworks Simulation

option from Tools menu and Add Ins option. Then we start a new static study. We begin by

defining the material type, the no. of joints, degree of freedom of these joints, the forces on the

elements as per the problem. The 2-D truss and beam problems are also solved analytically in

MATLAB using valid equations. Results from both the softwares are presented in the following

sections.

3.1 2-D Truss

The 2-D truss problem is solved using the direct stiffness method in MATLAB. The global

system of equations is given by Eq. (A) where {F} is the nodal force vector, {X} is the global

displacement vector and [K] is the global stiffness matrix

{F} = [K] {X} --- Equation (A)

The transformation from global to local co-ordinates can be achieved by the Eq. (B) where Ɵ is

the angle of truss element.

7

Eq. (A) can be expanded in the form given by Eq. (C)

A – cross sectional area of element = 0.049 sq. inches

E – Youngs modulus of elasticity = 30 x psi

L – length of element

u – global displacement at node

f – global force at node

c – cos(Ɵ)

s – sin(Ɵ)

Ɵ– angle of element

Formulation of global stiffness matrix for the two elements:

Element 1:

Ɵ = (6/8) = 36.87 degree

L =

Therefore, EA/L = 147262 lb/in

--- Equation (B)

--- Equation (C)

[K] = --- Equation (D)

8

Substituting these values in Eq. (D) , the global stiffness for element 1 is obtained as below

(from MATLAB):

[K1] =

[94248 70686 -94248 -70686

70686 53014 -70686 -53014

-94248 -70686 94248 70686

-70686 -53014 70686 53014]

Element 2:

Ɵ = (6/4) = -56.31 degree

L =

Therefore, EA/L = 147262 lb/in

Substituting these values in Eq. (D) , the global stiffness for element 2 is obtained as below

[K2] =

[ 62836 -94253 -62836 94253

-94253 1.4138e+005 94253 -1.4138e+005

-62836 94253 62836 -94253

94253 -1.4138e+005 -94253 1.4138e+005]

The combined global stiffness matrix can be obtained by writing the following matrices:

[K11] =

[ 94248 70686 -94248 -70686 0 0

70686 53014 -70686 -53014 0 0

-94248 -70686 94248 70686 0 0

-70686 -53014 70686 53014 0 0

0 0 0 0 0 0

0 0 0 0 0 0]

9

[K22] =

[0 0 0 0 0 0

0 0 0 0 0 0

0 0 62836 -94253 -62836 94253

0 0 -94253 1.4138e+005 94253 -1.4138e+005

0 0 -62836 94253 62836 -94253

0 0 94253 -1.4138e+005 -94253 1.4138e+005]

Therefore the combined global stiffness matrix [K] can be formulated as shown:

[K] = [K11] + [K22]

= [ 94248 70686 -94248 -70686 0 0

70686 53014 -70686 -53014 0 0

-94248 -70686 1.5708e+005 -23568 -62836 94253

-70686 -53014 -23568 1.9439e+005 94253 -1.4138e+005

0 0 -62836 94253 62836 -94253

0 0 94253 -1.4138e+005 -94253 1.4138e+005]

10

Figure 4 Truss structure plotted in MATLAB

Figure 4 shows a MATLAB plot of the truss structure. There are three joints or nodes shown by

red dots and the two truss elements are shown by blue lines.

Figure 5 magnified displacement of node 2 under load

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Figure 5 shows the plot for displacement of joint 2 under the effect of a load of 50 lb. The

displacement has been magnified by a factor of as it is very small in magnitude. The X and

Y displacements of node 2 can be observed closely in Figure 6.

Figure 6 zoomed displacement of node 2

Comparison of results and discussion:

Figure 7 shows the X-displacement plot for the truss obtained from Solidworks. It can be

observed that node 2 is displaced by 3.193 x inches towards the right as compared to the

analytical value of 3.24 x obtained from MATLAB which can be seen in Figure 6.

Figure 8 shows the Y-displacement plot for the truss obtained from Solidworks. It can be

observed that node 2 is displaced by 3.871 x inches towards the right as compared to the

analytical value of 3.93 x obtained from MATLAB which can be seen in Figure 6. The

error computation will be discussed later.

12

Figure 7 X-displacement plot from Solidworks

Figure 8 Y-displacement plot from Solidworks

13

The MATLAB results for the stresses (in psi) in the two elements are given below:

stress_elem1 =

850.34

stress_elem2 =

-613.19

>>

Figure 9 shows the axial stress plot for the truss obtained from Solidworks. It can be observed

that stress developed in element 1 is 848.8 psi and that in element 2 is -612.1 psi as compared to

the analytical values of 850.34 psi and -613.19 psi obtained from MATLAB.

Figure 9 axial stress plot from Solidworks

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3.2 Beams

Two beam problems have been solved both in MATLAB and Solidworks and the results have

been compared in this section.

3.2.1 Simply supported beam

The first beam problem is solved in the following manner. The force and moment equations are

given by Eq. (1) and Eq. (2). The points A, B, C, D refer to the points on the beam which are

shown in Figure 2(a)

Calculation of reaction forces:

∑ - Equation (1)

∑ - Equation (2)

From Eq. (2),

= 850 lb

Therefore from Eq. (1),

= 550 lb

Formulation of shear force (V) and bending moment (M) equations:

Between A and C:

is the distance from point A to point C,

V = = 550lb - Equation (3)

M = = 550 - Equation (4)

15

Between A and D:

is the distance from point A to point D,

V = 50lb - Equation (5)

M = = 50 - Equation (6)

Between A and B:

is the distance from point A to point B,

V =

- Equation (7)

M =

= - Equation (8)

16


Figure 10 shows the shear force and bending moment diagrams for the beam problem plotted in

MATLAB. Shear force changes from 550 lbf to 50 lbf at x = 24 inches, and then reduces to -850

lbf at the extreme right end. It becomes zero at x=50 inches. The highest bending moment is

14450 lbf-in at x = 50 inches. Bending moment is zero at the two ends.

Figure 10 shear force and bending moment diagrams for beam from MATLAB

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The same problem is solved in Solidworks using the steps given in Chapter 7.

Figure 11 shows the highest axial and bending stress plot for the beam. The maximum stress of

21674.1 psi is observed in the middle portion shown in red, and the least stress of 455.2 psi is

observed in the end portions of the beam which is shown in blue.

Figure 11 highest axial and bending stress plot from Solidworks

Figure 12 shows the shear force diagram for the beam. The maximum shear force is 550

lb uptill x= 24 inches, then it reduces to 50 lb uptill x = 48 inches, after that it linearly

decreases to a minimum is -850 lb at the right end. The solution is the same as obtained

from MATLAB as seen in Figure 10.

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Figure 12 shear force plot from Solidworks

Figure 13 shows the bending moment diagram for the beam. The diagram is similar in

trend to the one obtained using MATLAB as seen in Figure 10. The maximum bending

moment is 14450 lbf-in near x= 50 inches, which is the same as the one obtained from

MATLAB solution. Also the bending moment is zero at the two ends.

Therefore the solution using Solidworks is very close to the analytical solution and the

values for both the shear force and the bending moment are very agreeable.

19


3.2.2 Cantilever beam

The cantilever beam problem is solved in the following manner. The points A, B, C, D refer to

the points on the beam which are shown in Figure 2(b)

Calculation of reaction forces:

∑ - Equation (9)

∑ - Equation (10)

Formulation of shear force (V) and bending moment (M) equations:

Between A and C:

is the distance from point A to point C,

V = = 170lb - Equation (11)

20

M = = 170 - 910 - Equation (12)

Between A and D:

is the distance from point A to point D,

V = 80lb - Equation (13)

M = = 80 - Equation (14)

Between A and B:

is the distance from point A to point B,

V =

- Equation (15)

M =

= - Equation (16)


Figure 14 shows the shear force and bending moment diagrams for the beam problem plotted in

MATLAB. Shear force changes from 170 lbf to 80 lbf at x= 36 inches and then linearly reduces

to 0 at the extreme right end which is the free end of the cantilever beam. Figure 14 also shows

the bending moment diagram. The BM is -10920 at the leftmost end and increase to zero at the

right most end. Two linear sections are followed by a quadratic section in the graph.

21

Figure 14 shear force and bending moment diagrams for cantilever beam from MATLAB

The same problem is solved in Solidworks using the steps given in Chapter 7.

Figure 15 shows the shear force diagram for the beam. The maximum shear force is 170 lb upto

x= 36 inches and it becomes constant 80lb from x= 36 to 72 inches, after that reduces linearly to

0 lb, which is the same trend as obtained from the MATLAB solution seen in Figure 14.

Figure 16 shows the bending moment diagram for the beam. The bending moment is -10920 lbf-

in at the leftmost end which is the same as the one obtained from MATLAB solution as seen in

Figure 14. It is zero at the right end. The graph is very agreeable to the one in Figure 14 from the

MATLAB solution.

Therefore the solution using Solidworks is very close to the analytical solution and the

values for both the shear force and the bending moment are accurate.

22


Figure 16 bending moment plot from Solidworks

23

3.3 C-link analysis

This section deals with results of stress analysis of an AL6061 c-link. Different mesh sizes and

mesh types are used for the FEA and their corresponding effects on the solution are observed.

3.3.1 Standard mesh

Four cases are considered for this type of mesh. The convergence analysis can be studied using

the Von Mises stress plots. Computation time of each mesh is noted for further analysis.

(a) (b)

Figure 17 (a) standard mesh with global element size 0.15 inch ; (b) Von Mises stress plot from Solidworks

Figure 17 (a) shows the generated standard mesh using global element size of 0.15 inch. The

maximum Von Mises stress can be observed at the inner radius as 20858.3 psi from Figure 17

(b).

24

Figure 18 (a) shows the generated standard mesh using global element size of 0.10 inch. It has

more elements as compared to 0.15 inch mesh. The maximum Von Mises stress can be observed

at the inner radius as 21155.6 psi from Figure 18 (b). The stress is converging towards the

analytical solution with a finer mesh.

(a) (b)


Figure 19 (a) shows the generated standard mesh using global element size of 0.10 inch and

selective refinement along the lower inner surface where the mesh is finer than the rest of the

surfaces. It has more elements as compared to previous mesh without selective refinement.

The maximum Von Mises stress can be observed at the inner radius as 21125 psi from Figure 19

(b). The stress has become lesser than the previous mesh without selective refinement and

therefore the convergence is being observed towards the analytical solution of 20946 psi.

25

(a) (b)

Figure 19 (a) standard mesh of 0.10 inch with selective refinement ; (b) Von Mises stress plot from Solidworks

Figure 20 (a) shows the generated standard mesh using global element size of 0.10 inch with

selective refinement and automatic transition. Finer mesh can be observed at the lower inner

surface and on the adjoining side surface. It has more elements as compared to previous mesh.

The maximum Von Mises stress can be observed at the inner radius as 21152.4 psi from Figure

20 (b). The stress is more than previous mesh, therefore which implies that the mesh seen in

figure 19 (a) is sufficient for our problem.

26

(a) (b)

Figure 20 (a) standard mesh of 0.10 inch with selective refinement and auto transition ; (b) Von Mises stress plot

The computational times and Max Von-Mises stress are noted for each of the above four meshes

considered. This is shown in Table 1.

mesh element size (inches)

tolerance (inches)

computation time (sec)

max von mises stress(psi)

0.15 0.015 1.00 20858.30

0.10 0.015 4.00 21155.60

0.10 + selective refinement

0.005 5.00 21125.00

0.10 + selective refinement +

automatic transition

0.005 11.00 21152.40

Table 1: computational time and max stress record

It can be observed from Figure 21, max Von Mises stress v/s mesh size plot, how the solutions

for different meshes converge towards the analytical solution of 20946 psi. The analytical value

of the max. Von-Mises stress is shown by the thick red line on the top plot. The thin blue line

shows the convergence characteristics as the mesh size is changed and finer meshes are

27

considered. The convergence is very good and the variation above and below the analytical value

is very small as can be observed in the graph. The value is less for 0.15 inch mesh and then it

becomes almost a straight line for the other three meshes.

From Figure 21, computational time v/s mesh size bar chart, it can be observed that as the mesh

becomes finer, the time of computation increases from 1 second in case of 0.15 inch mesh to 11

seconds for a 0.10 inch mesh with selective refinement and automatic transition.

Figure 21 max von-Mises stress and computational time v/s mesh size (standard mesh type) in MATLAB

28

3.3.2 Curvature based mesh

Here, a curvature based mesh has been explored for the stress analysis of the c-link. The global

element size has been fixed as 0.10 inches and the parameter that is varied is the minimum no. of

elements in a circle (N). It is varied from 4 to 36 in steps of 8. As this parameter is increased, it

also increases the total no of elements in the mesh.

(a) (b)

Figure 22 (a) curvature based mesh with N=4 ; (b) Von Mises stress plot from Solidworks

Figure 22 (a) shows the generated curvature mesh using N=4. The maximum Von Mises stress

can be observed at the inner radius as 21107.4 psi from Figure 22 (b).

Figure 23 (a) shows the generated standard mesh using N=12. It has more elements as compared

to the mesh with N=4. The maximum Von Mises stress can be observed at the inner radius as

21080.2 psi from Figure 23 (b). The stress is converging towards the analytical solution with a

finer mesh and has decreased in value than in the first case.

29

(a) (b)



to the previous mesh, and the regions with curvature like the hole surface and radial profiles have

relatively finer meshes compared to the rest of the surfaces on the c-link. This property is

observed as the value of N increases.


(b). The stress has become lesser than the previous mesh with N=12. The solution has become

closer to the analytical value of 20946 psi. Therefore convergence is being observed with

increasing value of N.

30

(a) (b)


Figure 25 (a) shows the generated standard mesh using N=28. The mesh has become very fine in

the hole region and the radial edges of the c-link. It has more elements as compared to the

previous meshes.


25 (b). The value has increased slightly from the previous mesh with N=20 but it is still in very

close range to the analytical solution. Thus the convergence towards the analytical solution using

a curvature based mesh is good. It also follows from this that the value of N=20 is sufficient for

our purpose as it gives the closest solution.

31

(a) (b)

Figure 25 (a) curvature based mesh with N=28; (b) Von Mises stress plot from Solidworks

Figure 26 (a) shows the generated standard mesh using N=36. The mesh has become more fine

in the hole region and the radial edges of the c-link. It has more elements as compared to the

previous meshes.


26 (b). The value decreases from the previous mesh with N=20 and it is still in very close range

to the analytical solution. Thus the convergence towards the analytical solution using a curvature

based mesh is good. Thus using N=36 gives the solution closest to the analytical solution. The

difference between the max stress value for N=20 and N=36 is almost zero depicting good

convergence characteristics.

32

(a) (b)

Figure 26 (a) curvature based mesh with N=36; (b) Von Mises stress plot from Solidworks

It has been observed before that as the no. of elements in a circle increases from N= 4 to 36, the

total elements making up the mesh on the c-link surface also increases. Table 2 below shows the

total no. of elements for each value of N.

curvature mesh (no of elements in

circle ‘N’) no of elements


max von mises stress(psi)

4 13711 4 21107.40

12 14707 4 21080.20

20 16795 5 21073.00

28 20550 6 21090.40

36 25720 9 21072.4

Table 2: no of elements (N), time and max stress record

The computational times and Max Von-Mises stress are noted for each of the above mesh sizes

considered. It can be observed from Figure 27, max Von Mises stress v/s mesh size plot, how the

solutions for different meshes converge towards the analytical solution of 20946 psi. The

analytical value of the max. Von-Mises stress is shown by the thick red line on the top plot.

The thin blue line shows the convergence characteristics as the mesh size is changed and finer

meshes are considered.


becomes finer, the time of computation increases.

33

Figure 27 max von-Mises stress and computational time v/s mesh size (curvature mesh type) in MATLAB


time comparison max stress comparison diff between max and min

value

std mesh computation

time (sec)

curvature mesh computation

time (sec)

std mesh max von

mises stress(psi)

curvature mesh max von

mises stress(psi)

std mesh stress(psi)

curvature mesh stress(psi)

1.00 4.00 20858.30 21107.40

297.30 35.00

4.00 4.00 21155.60 21080.20

5.00 5.00 21125.00 21073.00

11.00 6.00 21152.40 21090.40

9.00 21072.4 Table 3 : comparison of standard and curvature mesh results

34

Table 3 shows the comparison of results of standard and curvature based mesh. The

computational time for the finest mesh (0.10 + refinement + auto transition) is higher for

standard mesh than a curvature mesh (N=36) being 11 sec. and 9 sec. respectively. Observing the

max stress comparison, we see that the variation in stress is higher for a standard mesh being 298

psi, and it is very low for curvature mesh being only 35 psi.

Thus we can conclude that the curvature based mesh gives faster and more accurate results than

a standard mesh and has better convergence properties towards the analytical solution which is

20946 psi. Therefore in this specific example it is more advantageous to use a curvature base

mesh.

3.3.3 Rounded inside edges

The inside edges of the c-link are rounded to a radius of 0.05 inches. The model with the rounded

edges is shown below in Figure 28. The analysis is done using a standard mesh with the same

four cases (mesh sizes) that were considered in Section 3.3.1.

Figure 28 c-link model with rounded inner edges


maximum Von Mises stress can be observed at the inner radius as 21254.3 psi from Figure 29

(b). The effect on solution is that the stress value has increased as compared to the stress

value without rounded edges (reduced area) as observed in Figure 17 (b) which is 20858.3 psi.



at the inner radius as 21459.7 psi from Figure 30 (b).

35

(a) (b)


(a) (b)


36


selective refinement along the lower inner surface where the mesh is finer than the rest of the

surfaces. It has more elements as compared to previous mesh without selective refinement.


31 (b). The max Von-Mises stress has become greater than the previous mesh without selective

refinement.

(a) (b)



selective refinement and automatic transition. Finer mesh can be observed at the lower inner

surface and on the adjoining side surface. It has more elements as compared to previous mesh.

37


32 (b). The max. stress here is greater than all the four cases

(a) (b)



considered as shown in Table 4.


tolerance (inches)


max von mises

stress(psi)

0.15 0.015 1.00 21254.30

0.10 0.015 4.00 21459.70


0.005 5.00 21467.70



0.005 7.00 21518.60


38

It can be observed from Figure 33, max Von Mises stress v/s mesh size plot, how the solution is

affected by the rounding feature. The analytical value of the max. Von-Mises stress is shown by

the thick red line on the top plot. The thin blue line shows the max stress variation as the mesh

size changes. It can be seen that the max stress becomes higher as the mesh size becomes finer

and deviates from the analytical solution. From Figure 27, computational time v/s mesh size bar

chart, it can be observed that as the mesh becomes finer, the time of computation increases.


39

Comparison and discussion of results: The comparison between the solutions is shown in figure

34. It can be observed that the max Von-Mises stress is greater for a c-link with rounded inner

edges (thick blue line) than with sharp edges (thin red line). The black line shows the analytical

solution. It can be seen that the red line converges towards the solution, while the blue line

deviates away from the analytical value. Thus using rounded inner edges in the analysis does not

show good convergence as compared to the c-link without rounded edges.

Also the time of computation is the same for the first three cases; however for the automatic

transition case, the time of computation is lower for a c-link with rounded inner edges.

Figure 34 comparison of plots for max von-Mises stress and computational time v/s mesh size in MATLAB for c-link with sharp and rounded inner edges.

The max. stress is increased only by about 2% when the rounded feature is added to the c-link

design, while the time of computation is also not very different from first case. Therefore the

analysis gives sufficiently accurate results without the rounded inner edges and the

convergence characteristics are better. Therefore including the rounded feature in the analysis

is not necessary in our case.

40

Using a curvature based mesh for the c-link with rounded inside edges gives the results that are

described below. The cases considered are with N=4, 12, 36. The convergence characteristics

can be observed from the following plots.

(a) (b)


Figure 35 (a) shows the generated curvature mesh using N=4. The maximum Von Mises stress

can be observed at the inner radius as 21483.9 psi from Figure 35 (b).


to the mesh with N=4. The maximum Von Mises stress can be observed at the inner radius as

21450.7 psi from Figure 36 (b). The max stress is lesser than in the previous case.

41

(a) (b)




relatively finer meshes compared to the rest of the surfaces on the c-link. This property is

observed as the value of N increases.


37 (b). The stress has become lesser than the previous mesh with N=12.



relatively finer meshes compared to the rest of the surfaces on the c-link.


(b). The stress has become more than the previous mesh with N=20.

42

(a) (b)


(a) (b)


43


considered. It can be observed from Figure 39, max Von Mises stress v/s mesh size plot. The

analytical value of the max. Von-Mises stress is shown by the thick red line on the top plot. The

thin blue line shows the convergence characteristics as the mesh size is changed and finer

meshes are considered. The convergence is not very good with a curvature based mesh.


becomes finer, the time of computation increases. The times are much higher than the

computational times from standard meshes.

Figure 39 max von-Mises stress and computational time v/s mesh size (curvature based mesh type) in MATLAB

44

3.3.4 Design change consideration

The c-link used for the stress analysis previously has an analytical maximum Von-Mises stress

value of 20946 psi. In this section, our aim is to modify the design of the c-link in order to reduce

the max Von-Mises stress the c-link is being subjected to under the loading of 200 lbs. The stress

depends on the cross sectional area and the distance from the center of curvature to the neutral

axis. By changing any of these parameters, we can change the max. Von-Mises stress produced

in the link. The new design of the c-link is shown in Figure 40 (a) and 40 (b)

It can be observed in figure 40 (b) that the cross sectional area is not uniform throughout the c-

link. The c-link is now thicker in the areas where maximum stress was being observed from the

results of the previous analysis, that is along the bends of the inner surface. Increasing the cross

section in those areas will reduce the max. Von-Mises stress. The results of the stress analysis of

the redesigned c-link have been presented in the following sections.

(a) (b)

Figure 40 (a) CAD model of redesigned c-link (fillet radius of 0.05 inches); (b) 2-D view (all dimensions in inches)

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maximum Von Mises stress can be observed at the inner middle section as 13425.3 psi from

Figure 41 (b). Therefore the stress value has decreased as compared to the stress value in the

older design which was in the range of 20,000 – 22000 psi

(a) (b)




at the inner mid portion as 13420 psi from Figure 42 (b) which is lower than the previous mesh.


selective refinement along the middle inner radial section where the mesh is finer than the rest of

the surfaces. It has more elements as compared to previous mesh without selective refinement.


43 (b). The max Von-Mises stress has become lesser than the previous mesh without selective

refinement. Thus convergence is being observed as the mesh is becoming finer.

46

(a) (b)


(a) (b)


47


selective refinement and automatic transition. Finer mesh can be observed at the inner mid

surface and in some spots on the adjoining surfaces. It has more elements as compared to the

previous mesh. The maximum Von Mises stress can be observed at the inner middle section as

13307.1 psi from Figure 44 (b) which is lowest in all the four cases. Therefore the convergence

is very good.

(a) (b)



considered as shown in Table 5.


tolerance (inches)


max von mises

stress(psi)

0.15 0.015 2.00 13425.3

0.10 0.015 3.00 13420.4


0.005 4.00 13308.5



0.005 6.00 13307.5


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It can be observed from Figure 45, max Von Mises stress v/s mesh size plot, how the solution

converges. The thin blue line shows the max Von-Mises stress variation as the mesh size

changes. It can be seen that the max stress becomes lesser as the mesh size becomes finer. From

Figure 45, computational time v/s mesh size bar chart, it can be observed that as the mesh

becomes finer, the time of computation increases.


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Comparison and discussion of results: The comparison between the solutions is shown in figure

46. It can be observed that the max Von-Mises stress is lesser for the new design of a c-link lying

in the range of 13300 -13500 psi(thick blue line) than the old design where it lies in the range of

20800 - 21200 psi (thin red line). Thus there is a high reduction the value of maximum stress.

Also the time of computation is almost same for the first three cases; however for the automatic

transition case, the time of computation is lower for the redesigned c-link as seen in the bar chart

in Figure 46, the difference being 5 seconds.

Figure 46 comparison of plots for max von-Mises stress and computational time v/s mesh size in MATLAB for old and redesigned c-link

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4 Discussion

As a part of this project, we have also read through the Solidworks Simulation documentation for

a better understanding of the system, and acquired some information on meshing. A brief

discussion about them follows.

Solidworks Simulation Help: Solidworks simulation help is a feature available that is very

useful for learning and getting familiar with the techniques used for implementing simulation.

The web-based help provides options for topic search, navigation, and upto date documentation.

It has user friendly conventions, bold indicates user interface items, and italic green is for

jumping to specific topics. The analysis background section gives explanation and steps to

perform each type of analysis for example static, dynamic, thermal, frequency, fatigue, etc.

Solidworks simulation is the system which we have used in this project; it has fast solvers and

one screen resolution for results. The documentation provides help with steps, meshing, material

and specifying conditions for analysis.

The Solidworks simulation system has an interactive simulation tree and a good graphical

interface. The simulation studies section provides detailed information about the studies possible,

mesh types, types of solvers, steps to create and run studies along with exporting data.

Solidworks simulation has the property of working with composite materials which are used in

many real-life applications. Different types of loading according to the problem can be specified;

also movement and boundary constraint help is available to fully define a problem. To carry out

FEA, a mesh has to be generated. Two types of meshes, standard and curvature based mesh are

available. Help provides documentation related to changing mesh parameters, analyzing changes,

control and mesh plot probing. Through the help option, we can learn about applying materials,

creating libraries, specifying properties, etc. Optimizations in design can be carried out using

Design Study option using parameters. It is possible to create analysis libraries for frequently

used analysis features. There is a lot of help available for plotting graphs and report making in

order to support analysis. Checking stress results is possible; factor of safety definitions help

realize failure criteria.

Meshing advice in Solidworks Simulation: Reading through this article by Brian Zias from

Alignex, we not only realize the importance of meshing in an FEA analysis software but also the

problems related to it. Meshing heavily depends on the amount of RAM and the processor

speed. A slow processor leads to high solution times and a less amount of RAM leads to crashes

as it does have the capacity for large no. of elements in the mesh. Therefore with these

restrictions, we must strive to optimize the meshing.

One of the important techniques is the mixed mesh creation. Mixed-mesh refers to the

simultaneous use of solid, shell, and beam elements in the same study. Thus it helps in reducing

the no. of elements in the mesh.

In Solidworks 2008, we had to specify a „mixed mesh' in the study. Once the study was created,

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every component was solid type by default unless specified. The great thing about Solidworks

2009 is that there is no longer an option to create a „mixed mesh' study. All studies are enabled to

be mixed mesh always. Also, there are some default options embedded for example any surface

bodies will be treated as shell elements, any structural members (weldment parts) will be treated

as beam elements, and everything else will be treated as solid elements.

For carrying out assembly analyses, one of the important considerations is the contact sets or

connectors. The three important types of contacts are bonded, free and no penetration. For large

models, it is best to start with everything bonded and then start adding other interactions in a step

by step manner.

Mesh size and no. of nodes are restricted by the amount of RAM. In order to maximize the

available RAM we can try fresh reboots, simplify meshes and resolve issues, use mixed mesh or

curvature based meshes, improvement in modeling, or upgrading as the last option.

5 Conclusion

This project has made us aware of the capabilities of Solidworks in carrying out finite element

analysis of devices such as beams, trusses and c-links. The lessons provided in the book are very

helpful in understanding the method of carrying out such analyses as it provides step by step

instructions. The solutions obtained through these simulations may not always be accurate and

therefore a thorough understanding of the equations behind them are to be studied carefully to

understand these inaccuracies. We have explored different mesh types, sizes, loading and

constraints in this project, and have developed a good understanding of the importance and

problems related to meshing and loading in FEA simulations.

We have also learnt how to use MATLAB for solving trusses by the direct stiffness method and

formulation of shear force and bending moment equations in beam problems. These are very

easy to formulate and give accurate results.

Thus the project has given us an insight into carrying out FEA through the use of packages such

as MATLAB and Solidworks.

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6 References

BOOKS

[1] Introduction to Finite Element Analysis using SolidWorks Simulation 2010–by RH Shih

WEBSITES

[1] www.wikipedia.com

[2] www.youtube.com

[3] http://help.solidworks.com

[4] http://blog.alignex.com/mechanical-technical-blog

Documents

CAD Project 05 Report Final