The solutions here are given in General Tensors rather than Cartesian tensors. Most problems only include General tensor constructs that have Cartesian equivalents. Here are a few modifications you can make:
1. Note that you can convert superscripts to subscripts and the Cartesian tensor meaning remains intact.
2. The base tensors change from g to e. Again, downgrade the superscripts.
3. When a term has both superscripts and subscripts, let the superscripts downgraded come consistently after the subscripts at the same position.
4. The six indexed Kronecker deltas are simply products of two three indexed Levi-Civita third order alternating tensors.
To make matters simple and easy, We have restricted considerations to Cartesian coordinates here. For full general tensor results, consult the notes in SSG 805 (on this site) given to graduate students.
After creating a 3D model of your design, the next most important step is to impress constraints, loads and define the contact relationships on the model. To prepare for the finite element simulation, you will also be called upon to convert the region occupied by the material to simplified meshes of tetrahedrons or other simple geometrical entities. Fusion 360 provides the Simulation Work Space that gives you the facilities you need to do these and much more as we shall see. The attached video takes you through this process for the simple hinge we created early on after briefly introducing the governing equations the embedded Finite Element package are designed to solve.
Furthermore, you can also download the Mathematica Notebook that can provide you the governing equations in any coordinate system desired once you supply the tensor equations. Caution:
I hereby remind students in this class to desist from sending me personal mails unless it becomes absolutely necessary to do so. I want your comments in open fora to enable other students to benefit from specific Q&A from you.
By a modest adjustment to the previous post, we can use the same cylinder units to create a V8 Engine with two sides offset as a result of putting two connecting rods together on the same crank section. A special connecting rod to avoid this offset was popular in old aircraft engines. It is called “Blade and Fork: connecting rods”. We will be aiming at a parametric model of the Blade and Fork in our simulations and analyses later. Another video will be done on that. Here is the V8:
It is easy to reorient the crank and the piston sets for different orientations and cylinder offset preferences.
For your simulation, do not forget that we are going to do failure, displacement and stress analyses on several of the components you are creating in these assemblies. The use of simulating the engine is to make the force applications realistic.
Here you have the second and final installment of the slides and videos of our class last week. As usual, the slides are presented first. Some of these slides are repeated in the video for elucidation.
I need your comments to know if the video is too long and I can give you a shorter one next time. My opinion of the ones online is that they are too short. Of course, one can easily over do!
Watch out for Part Two
I am concentrating this week on Fusion 360 3-D Modeling power. I am using Hinge design as a very simple design problem that everybody can understand: Hinges are everywhere! You will be surprized to know how much of your engineering theory they carry! This week is the beginning of a strategy that I will follow till the end of the term. I think I know enough about this class and I want to maximize my time with you.
I have noticed the weaknesses. Some can be worked on in the term. Others are too fundamental and will take time. However, I want you to note a few points:
1. One of the goals of a design course is to orient your mind to THINK LIKE AN ENGINEER. When you look at an object, there are things that will be going on in your mind that an untrained eye cannot imagine. This course should move you in that direction. We will therefore, beginning from this lecture, look around campus and Omu Aran town, see all the things that, from an engineer’s perspective, can be done better. We shall, using 3-D Solid models and simulations, propose superior solutions. This will be your preparation ground to redesign Nigeria.
2. The ability to turn physical objects to 3-D solid models, if that is ALL you learn in this course, will be sufficient to give you a comfortable living. There is NO STUDENT in this class that is not capable of mastering that. Your background is sufficient to learn if you want to. If at the end, you still don’t know, blame your laziness. On my part, I will give the time and will be ready to assist you.
3. There will be some necessary theory. Here, you need to improve your background in some basic stuff like Vectors, Tensors, Differential Equations and Numerical Analysis. What you absolutely need is not beyond you. I will teach some in this course; the rest will be done in MCE534 as we do not have sufficient time here. This will be the basis of explaining what is going on in Simulations to you. An Engineer that can properly simulate linear and nonlinear elasticity, thermal and vibrational problems, etc. that can be done inside Fusion 360, will be competitive with any other engineer in the world no matter where they might have been trained. Its up to you to learn to simulate and animate.
4. As we shall combine simulation with animation, we shall be able to do digital prototyping. At that level, you will be able to get jobs anywhere in the world – which I expect you to reject because Indians, Vietnamese, Chinese, etc are coming in here to make millions and billions and there is no need for you to go and live in the margins of Western society.
This week, we will look at two different hinge designs. Our job for the week is to be able to do 3-D models of them and use that to master some aspects of modeling. I have one of my workflow timelines here: It is silent and too fast. I will try to improve on that in subsequent weeks. The slides try to explain the same things as I will go through them in class.
The same slides are here in .pdf files
Here are the things I require from you:
1. Each one should add me to his/her design group in Fusion 360. Here is how you can invite me: That will give me direct access to the projects you are working on for this course. That way, I will be able to have the basis to award your grades for each week’s work done. Note that the continuous assessment for this course carries a lot more weight than end of term exams which can only test theory. Therefore be serious now rather than later.
2. Try to complete the hinge design this week so we can go into other designs next week. I want us to have a few well done 3D models before we go into simulation and analyses.
To change the default coordinates in Fusion 360, go through these steps:
1. Click on your name near the top right corner of the Fusion 360 working screen
2. Look in the preferences where it says “Y-up”. It is number 6 under “Controlling general UI behaviour”.
This means the coordinate y is going vertically upwards.
3. Click on it, you will see that there are two options: Select “Z-up”
4. Accept the result.
5. Enjoy the bliss of 3D parametric modeling.
MCE511 Computer-Aided Engineering Design and Analysis (2 Units)
Overview of Computer-Aided Design and Analysis: History of CAD/E, characteristics of CAD/E, overview of the industrial application of CAD, CAE, and CAM, functions of CAD/CAE/CAm systems, information embedded in a CAD system, tools commonly used in CAD. Hardware and software of a CAD/E System;Computer hardware, typical CAD/CAE.CAM system configuration, concepts of graphics display, various input and output devices, data structure and database management systems, graphical coordinate systems, software function and application modules, current Geometric Transformation – 2-D and 3-D geometric transformation, projections, generation of multiple views for an engineering drawing Curve and Surface Modeling; Parametric representation, analytical and synthetic curves, Hermite cubic splines, Bezier curves, B-Spline curves, introduction of NURBS, surface patch, bilinear surface, lofted surface, bi-cubic surface, Bezier surface, B-spline surface, surface offset and blend Geometric Modeling; Comparison of wireframe, surface and solid modeling, CSG, B-rep solid modeling techniques, feature-based parametric modeling, CAD/CAM data exchange methods, IGES, STEP and PDES. Basics of Finite Element Analysis (FEA) – Concepts of elements and discretization, unit displace method, procedure of finite element analysis on computer; automatic mathematical problem formulation in computer, truss element, commonly used model and element types, limitations and common misconceptions about FEA