ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
Objectives
Part 1: Finite Element Analysis
1) Use basic (2D) finite element analysis to evaluate truss designs.
2) Become familiar with different truss designs.
3) Evaluate the strengths and weaknesses of different truss designs.
4) Determine the load/deflection characteristics of truss structures.
5) Quantify the efficiency (stiffness/weight) of different structures.
6) Determine the sensitivity of your analysis to changes in material properties and yield characteristics.
7) Compare hand calculated and finite element predicted outcomes.
Part 2: Solder Station Training
8) Learn solder techniques for brass.
9) Develop a Standard Operating Procedure (SOP) for soldering of brass.
Equipment
1) Brass pieces.
2) Solder Stations.
3) Computer with Matlab and FE code.
Deliverables
1) Lab Report - Finite element analysis of truss design (maximum of 2 written pages, plots and tables of data can
be additional)
a. Introduction
b. Methods (brief)
c. Results
d. Discussion
e. Conclusions
2) Protocol for brass soldering (1 page)
a. Write a “Standard Operating Procedure” (SOP) that all group members can follow when soldering
brass pieces.
b. Organize in a point form or stepwise manner.
c. Provide diagrams (additional pages allowed) if necessary.
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
Part 1 - Introduction:
Finite Element Analysis
Finite element analysis provides a quick and efficient means to predict the mechanical behaviour of complex structures
when it is difficult (or impossible) to determine an analytical solution. However, care must be taken when implementing
finite element methods as there are a number of limitations of this analysis technique and outcomes are significantly
affected by model design and input parameters.
This lab will use custom finite element code written by Dr. Gary Wang and his research group to calculate the stresses,
deflections and forces in the members of two dimensional truss structures. Several sample truss designs will be
provided, and your groups will be responsible for devising additional designs to analyze.
The results of the finite element analysis (2D) will be combined with engineering knowledge and analytical methods to
draw conclusions regarding the optimal truss configuration (3D) you will design and build for the robotic arm project. An
introduction to finite element theory and application will be presented in a future lecture.
Material Properties of Brass
Calculations of stresses, forces and deflections in a truss structure depend on the material properties assigned to each
members of the structure (E = Young’s Modulus). In addition, prediction of failure and calculation of a factor of safety
depend on the defined values of the yield and ultimate failure stress of the material. However, the composition of the
brass alloy, heat treatments and cold working of the rod are known to significantly affect the material properties (Table
1). To understand the sensitivity of the finite element model predictions to the assumed material properties it is
important to run repeated analyses varying the material properties across the reported range of values. This is known as
a material sensitivity analysis and is a critical component in the development of any finite element model.
Table 1: Properties of brass (30% Zn alloy) show significant variation in material properties because of the differing
effects of heat treatment, annealing and cold working.
Brass (~30%
zinc)
Density
(g/cm3)
Modulus (GPa)
Yield Stress (MPa)
Ultimate Stress (MPa)
8.49
96-110
70-550
200-620
Buckling – Longitudinal compression of thin rods
Axial compression of a thin rod may lead to the rod buckling before it experiences compressive failure. In truss
structures, long thin members experiencing compressive loads may be at risk for buckling failure long before the yield
strength of the material is exceeded. Standard finite element methods (as in the code provided, and the basic COSMOS
package provided with the SolidWorks software suite) do not account for buckling failure (complex, non-linear finite
element analysis may be used to model buckling modes but require advanced knowledge of mechanical theory and
specialized FE code that are beyond the scope of this course). To determine if a truss member has exceeded the buckling
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
limit it is possible to use the Euler buckling theory to determine the critical load (Pcr) above which buckling has occurred
in a member (Refer to Mott Chapter 6-6 for a discussion of column buckling). Compressive forces in each member,
predicted by the finite element analyses, that exceed the critical load indicate a member that will fail due to buckling.
The critical load is calculated using the Euler formula (for a round rod):
Pcr 
 2 EA
( KL / r )2
Where: E = Young’s Modulus
A = cross sectional area
L = column length
R = minimum column diameter
K = end fixity constant
End Condition
Free-Free
Pinned-Free
Pinned – Pinned
Guided – Free
Guided – Pinned
Guided – Guided
Fixed – Free
Fixed – Pinned
Fixed – Guided
Fixed – Fixed
Theoretical Fixity Constant (K)
1.0
1.0
1.0
2.0
2.0
1.0
2.0
0.707
1.0
0.5
Part 1 - Methods:
Finite element code is provided in matlab (see Appendix for code introduction). Students will need to implement the
following basic truss structures in the finite element program and analyze the stresses, forces and deflections in each
structure (Figure 1). Pay careful attention to the units of each parameter in the finite element code (units of results are
dependent upon input units), the node numbering, and connectivity of the elements.
1) Using the provided matlab code and trusses shown in Figure 1, build finite element models of each truss
structure. To begin assign a load of 1 N and use the mean value for material modulus.
2) Load the finite element model geometry file into the graphical user interface (GUI) matlab code and confirm
truss structure and boundary conditions (end fixation and loading direction) match the diagrams (Figure 1).
3) Record the magnitude and direction of forces and stresses in each member. Also record the deflection (x and y)
of the end point where the load is applied.
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
Figure 1: Two dimensional truss sections to be modeled in the matlab finite element code. Use this diagram to number
nodes and elements for each structure before coding into matlab. Nodes on the left are pinned, no x or y displacement
but rotation is permitted. Connections between members are assumed to be pin-joints, allowing only tension and
compression in each element.
4) Return to the geometry file and increase the load on the truss in increments (10 N, 20 N, 30 N, 40 N, 50 N) and
rerun the analysis. Record stresses and forces in each member and the deflection at the end point where the
load is applied.
5) Return to the geometry file and vary the material modulus across the range of values given (keep the load fixed).
Record the stresses and forces in each member and end point deflection.
6) Calculate the net stiffness of each truss structure (applied force vs deflection) and determine its overall
efficiency (stiffness/structure weight). To calculate the weight of each structure, assume brass has a density of
8.49 g/cm3.
7) Observe how the structure efficiency changes with the truss designs. What design features make the truss
structure more or less efficient?
8) Design five additional truss structures of your own with the objective to optimize the efficiency of the structure
(stiffness/weight) while maintaining a sufficient factor of safety to guard against failure (yield and/or buckling).
Use the finite element code to analyze their behaviour and compare to the five provided designs.
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
9) Calculate the critical buckling load for each member of the truss structure undergoing compressive load. Note
that the length of the member is the distance between the nearest 2 points of attachment with other members
(not only the anchor points). Calculate the factor of safety for buckling failure for each truss structure.
10) Choose 2 truss designs and calculate the forces and deflections in the members using indeterminate structure
theory (will be presented in class and tutorial Thursday May 20).
Part 1 – Discussion
1) Using your two-dimensional finite element analysis of truss structure behaviours discuss the strengths and
weakness of different truss designs and highlight design features that you think will be most effective for your
design project. (Your project truss must span 30 cm – from motor shaft to electromagnet center and carry the
electromagnet (25 g) and mass (10g) with less than 0.05 mm deflection).
2) Discuss the limitations of using a 2D analysis to predict the behaviour of a 3D structure. How will the 3D
structure behaviour differ from the 2D? What other concerns do you have for predicting the behaviour of the
truss structure? How can you analyze those forces and deflections? (remember, the truss structure will be
rotating about one end to move an object as quickly and accurately as possible from point A to point B)
3) Compare the finite element predicted outcomes with your indeterminate structure calculations and discuss the
accuracy of each method (keep in mind the assumptions that go into both methods).
4) Discuss how you will use these different analysis methods to optimize your final truss design, are there other
analysis methods or software that you will use? What are their advantages/disadvantages over the methods
used here?
5) What other factors will contribute to your truss design? Identify other resources (not calculations) that could
assist in your truss design optimization.
6) What else can you do to improve the efficiency of your truss structure?
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
Part 2 – Introduction: Brass Soldering Standard Operating Procedure
Research laboratories and businesses depend on workers being able to reliably repeat complex tasks and pass on their
knowledge to colleagues and co-workers. Procedures that are regularly repeated or developed for a specific task are
often outlined in step-wise protocols called Standard Operating Procedures (SOPs). Laboratories and workplaces compile
and regularly review these SOPs to ensure high quality work, adherence to safety standards and consistency across
employees. To ensure all group members can reliably create sufficient solder joints it is important to develop a Standard
Operating Procedure that details the step-wise methods necessary for soldering brass rod.
Proper joining of brass rods will be critical to the overall mechanical properties of the truss structures used for the
remainder of the course. While soldering is a straightforward, economical and efficient joining method, the quality of
the results and strength of the finished joint depend upon soldering technique. You will have the opportunity to try your
soldering techniques and determine a soldering protocol that will provide strong and robust joints. Pay particular
attention and document the changes in joint strength and quality based on duration of contact between the solder iron
and material (the amount of heat in the structure), the order of contact (e.g. heat material, then add solder or hold
solder to surface before applying heat), surface cleaning methods, quantity of solder, and solder iron settings.
Part 2 – Methods
1) Brainstorm with your group members other approaches that may be effective (e.g. tack soldering two pieces
together, then reinforcing the joint with additional solder on all sides).
2) Strictly adhering to all safety rules outlined in your introduction to soldering techniques (i.e. using safety glasses,
gloves, long hair tied back etc) try different joining methods to determine the most effective protocol.
3) Record all relevant parameters in a Standard Operating Procedure.
4) Have each group member repeat the recorded protocol to ensure no steps have been missed and that
consistent results are achieved.
5) Qualitatively evaluate each solder joint, describe the flexibility and fragility of the joints (e.g. do they pull apart
by hand? Do they fail after cyclic loading? How much does each member move before the joint breaks?)
Part 2 – Results/Discussion
Discuss with your group the solder techniques that provided the most reliable joints. Record a step-wise protocol that all
members of your group can abide by. Provide a list of necessary equipment and safety precautions at the beginning of
your standard operating procedure.
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
Appendix: Introduction to Truss Beam FEM (Dr. G. Wang’s FE code)
The program was written by Dr. Gary Wang, in Matlab and initially introduced to students in his ENSC 281 class at Simon
Fraser University. A user can define a structure of trusses or beams and the program can calculate all forces, moments,
and deformation at each joint (or node). Below list the steps that one need to follow to run the program.
Step 1: Prepare the geometry and Finite Element model
Use the example program “createmodel_truss.m” (other examples are given in the same directory, e.g.,
createmodel1.m, createmodel2.m, createmodel3.m, etc.). This function is to create a model file “*.mat” that will be
used for computation. The model file includes the parameters of the nodes, elements, material and the section. The
typical format of the program is listed as follows. You need to read all the comments to make sure you enter the correct
data. Note this program does not specify the unit system. You need to make sure your units are consistent in one
system (metric or imperial). After running of the program, a model file, e.g., “truss3.mat,” will be created in the same
folder. You can change the model file name in the last sentence of the “createmodel_truss.m” file.
global node;
global element;
global material;
global section;
%%node information: Node No., Degree of Freedom (DOF), X coordinate, Y %coordinate, constraint along x, constraint
along y, constraint on %rotation(1 means constrained; 0 is free), load on the node Fx, Fy, and %Moment
node=...
[ 1 2 0.0
2 3 1.0
3 3 1.0
4 3 2.0
1.0
2.0
0.0
1.0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
-1000 -1000 100
0
0
0
0
0
0];
%element information: Element No., node1, node2, Element Type(1 is Truss,2 is %Beam), Material No., Cross-Section
No.
element=...
[ 1 1 2
1 1 1
2 1 3
1 1 1
3 2 3
2 1 2
4 3 4
2 1 2
5 2 4
2 1 2];
%Material information: Material No, Modulus of elasticity
material=[ 1 2e11];
ENSC 384 Mechatronics Design II
Lab #1: May 17/20, 2010
Solder Station Training
Finite Element Analysis of Truss Design
%Cross-Section No., Cross-sectional area, Moment of Inertia, the Maximum
% distance from Neutral axis
section=...
[ 1 0.01 0.01 0.01
2 0.02 2.0e-7 0.02];
save('model1.mat','node','element','material','section');
Step 2 Run the FEA program
Find the function “truss_beam_fem_GUI.m” in the folder named “truss_beam_fem.” Type “truss_beam_fem_GUI” in
the command window. The main window of the program shows as the following.
There is a menu named File at the top of the window. The button Open can open a model file. You can then choose to
open the model generated in the first step, e.g., truss3.mat. The button named Finite element Analysis can run the FEA.
The results of the node and the element list in the text box at the bottom of the window. The slide control can show the
deflected structure of different scales.
Final remarks:
(1) The units of inputs should be consistent. For example if the inputs use (N-m-s), then the output deformation Ux and
Uy will be in meter, the force in Newton, and moment in (N.m).
(2) The DOF of the node will be calculated in the program. If you do not know the right DOF of node, you can simply
input 2 or 3.