Computational Kinematics - question
There are two moving parts (Part 2 and Part 3) connected at points O and A. Part 1 is a fixed part connected to absolute ground. Part 2 is rotating at a constant angular velocity of ω2 and Part 3 is rotating at a constant angular velocity of ω3 .
Please state what the joints are in the system.
Using your knowledge of computational kinematics determine the following:
- q - {qC}
- c(q,t) - {tc}
If you cannot do the mathematics, then please explain what you believe is the procedure to calculate each variable. Also, explain what each of the above variables means.
Kinetics
Coal cart
Determine the maximum mass m of the cylinder for which the loaded 2000-kg coal car will not overturn about the rear wheels B (think about the rotations around G). Neglect the mass of all the pulleys and the wheels. (Note that the tension in the cable at C is not 2mg).
Wheel Hub
A wheel with outer radius of 0.6m and a hub radius of 0.3m, has a mass of 30kg and a radius of gyration about the centre of 0.450m (I = mass*(rgyation)2). A cord wrapped securely around the hub is attached to the fixed support and the wheel is released from rest on the incline. The static and kinetic coefficients of friction between the wheel and the incline are 0.4 and 0.3, respectively.
Calculate the acceleration a of the centre of the wheel. First prove that the wheel slips.
Swinging Bar
The uniform slender bar AB has a mass of 0.8kg and is driven by crank 0A and constrained by link CB (of negligible mass). Crank OA has an angular acceleration 0 = 4 rad/s2 and an angular velocity ω0 = 2 rad/s when both OA and CB are perpendicular to AB.
Calculate the force in CB for this instant. (Hint: Consider Point B and use equation ∑ Mp = Ipα + r' × mαp where r' is the vector from P to mass centre G, is mass moment of inertia about an axis through P, is the acceleration of point P).
Suspension set-up
This is a multi-link suspension, it is currently missing the spring and damper.
Draw the system and explain each of the components in the suspension system, please include the spring and damper in your system. Determine the correct type of joints on the multi-link suspension system. Show your Degrees of Freedom calculations. Also please explain why we need five links, what happens if you only have four links?
Gearbox set-up
This is a planetary gear system. Automatic transmissions make use of planetary systems.
Draw this system and explain each of the main components in this system. Please explain how many gear ratios are available from the system and in which direction do they turn the output. Please also explain what type of planetary system this is.
Planetary Gear System
Given N2 = 30 teeth, N3 = 45 teeth, N4 = 25 teeth, N5 = 30 teeth, N6 = 160 teeth. Assume that the input shaft (2) is rotating at ω2 = 50, and the arm (1) is rotating at ω1 = -75.
Calculate the output rotation velocity ω6
Computational dynamics
Explain:
-Augmented Lagrangian method
-Embedding technique
-Amalgamated formulation
What are the differences? What are the benefits and negatives of each method?
Non-linear FEA Solvers
Consider the following beam loaded axially by a concentrated mass hanging on the end:
The stiffness of the Beam is given by the following equation
K = Ko(u)-0.25 N/mm
Where Ko = 1000 and w = 100kg.
Starting from displacement u =0.1 as a first guess, show a Newton Raphson method solution to this problem (i.e. find and show the final tensile displacement of the beam) use a tolerance of ±10N.
Now show the solution using the Modified Newton Scheme. Use a tolerance of ±10N or a maximum iteration of 4.
Finally use a Quasi-Newton method to find a solution, with a tolerance of ±10 N or a maximum iteration of 4.
Non-linear FEA Solvers - Implicit vs Explicit
Explain the complexity versus model size with respect to implicit and explicit systems. Explain the differences in efficiency between implicit and explicit systems as the event time becomes smaller.
If we form a metal sheet into a circular cup slowly, then which solver method would you choose? And Why?
Elements - Solid Shell
Explain what the difference is between shell elements and solid-shell elements. You may want to refer to the degrees of freedom of each.
Explain the need for reduced enhanced solid shell elements.
Hyper elastic material models
Draw a stress-strain curve of a hyper-elastic material with hysteresis. If the J value for the hyper elastic material was not equal to 1, then what do you know about the hyper-elastic material?
What model would you choose if you material experienced strains up to 700%?
Design of Experiments and FEA
Explain the full factorial method. How many samples would be created if you had 3 factors with 3 levels, and you needed 5 repetitions to gain a statistically significant average for each point on the hypercube array?
If your simulations were taking 1 week to solve, and you had 10 factors to consider, what type of design of experiment system would you choose to analyse the data?
Non-linearities
Describe the different types of non-linearities in finite element analysis and give (draw some pictures) examples.
Multi-scale material modelling
Explain when you may need to use Multi-scale modelling, with particular reference to the material behaviour.
You are going to model the atomic structure of steel to show the movements and effects of dislocations, what simulation model type would you choose? What are some of the problems of linking this simulation to your macro based simulations of steel sheet forming?
Non-linear Material Behaviour
Explain what is meant by flow stress. What is the associative flow rule and normality rule?
Contact
What basic things need to be defined to set up a simple contact kinematic system? When all else has failed, what contact method would you turn to?
Modelling Fibre-Matrix composites
Are fibre matrix composites anisotropic? Please use diagrams and examples to explain your answer.
Elements contain layers for modelling fibre-matrix composites, what information do you need to properly represent a layer?
Mass-scaling in explicit models
Δt < L√Ρ(1-2θ/2μ(1-θ))
Explain this equation and its context to mass scaling.
Explain how you can monitor whether you have added too much mass scaling.
Integration points
Explain the difference between Trapezoidal, Simpson, and Gauss rules in approximate integration.
What is the meaning of Gauss points in an element?
Viscoelastic Materials
Viscoelastic materials are those which display non-linear behaviour over time.
Explain the difference between relaxation and creep for viscoelastic materials.
What are the differences between the Maxwell Model and the Kelvin-Voight Model of viscoelastic materials?
Adaptive meshing and Mesh refinement
Mesh refinement techniques need to estimate the local error for the techniques to be able update the mesh. What are some of the common error indicators used in mesh refinement?
Explain H-enrichment mesh refinement.
Multi-physics modelling
What are the classifications of Multi-physics models? What are some of the problems you face when coupling two or more physical models
together?
Modelling the Bauschinger Effect
For a one-dimensional test (such as a tension/compression test) explain the Bauschinger effects on the stress-strain curve.
In the case of the Chaboche material model, what is meant by the term back stresses? Use diagrams where possible.
Modelling joints
Using diagrams explain the difference between spider configurations 1, 2, and 3.
Explain why using an individual rigid beam model to represent a spot weld can lead to inaccuracies.
Advanced Yield Models
The basic material model can be broken into four separate areas. What are those areas?
Briefly explain each area.
Draw a Tresca, a Von Mises, and a Hill (anisotropic) yield locii.
Damage modelling of materials
Explain the Basic Void Damage Equations, and in simple words what does the parameter D represent.
Once damage is initiated, does the effective stress increase or decrease in the element?
Modelling heat flow
What is convection? Explain the correlation between Structural and Thermal parameters. What is the problem of having sharp corners in your heat flow model?
Modelling fracture of materials
Explain the difference between ductile and brittle fracture.
What are some of the ways that a crack can be modelled? Can the crack be free to find its own path?
Topology optimisation
What are the benefits of topology optimisation?
The stiffness optimisation can be stated as
minimise f = C(x) = PTu
Subject to g = W* - Σni-1 Wixi = 0,
xi ∈ {0, 1}.
What is meant by the overall mean compliance? Why should it be minimised?
Adhesive and Cohesive Elements
What is a cohesive element? Draw a typical traction-separation response, explain what the diagram means.
What experimental tests are generally used to inform cohesive element based simulations?