MEEN 3360 Engineering Design and Simulation Spring 2016 Homework #1 This homework is due Tuesday, February 2, 2016 1.0 From your book and other sources, write a paragraph explaining CFD and finite element analysis are and how they are used. 2.0 Discuss the importance of the matrix equation F=KX, and how we can solve it computationally. 3.0 On the SolidWorks site (solidworks.com), click on /Products/Simulation. Read about these tools. Give a brief description of SolidWorks Simulation Premium and SolidWorks Flow Simulation. 4.0 Go to the ANSYS web site http://www.ansys.com and read about ANSYS Mechanical and ANSYS Workbench. Briefly describe what they do, and how we could use them in this course. We have an ANSYS academic package, as described in http://www.ansys.com/products/academic/academic- Product-Portfolio available on campus. 5.0 I strongly recommend that you download and install the free ANSYS Student, from here: http://www.ansys.com/products/academic/ansys-student 6.0 Search on the web, on asme.net, in the library, and elsewhere for the names and descriptions of various finite element and CFD analysis packages. Examples are MSC-NASTRAN, ADINA, FLUENT. Find 4 each of general purpose, dynamic analysis, and fluid (CFD) analysis packages (besides the ones mentioned above). Give the names of each, a web address, and a short description word description. Type these up and send to me in an email. 7.0 Not including the packages in 4.0, find 6 shareware or demonstration Structural Finite Element Analysis (FEA) packages, list their web addresses and stipulations for use. Note that 3-D graphics, computational fluid dynamics (CFD), meshing, and solid modeling software are different than finite element analysis (FEA) packages, and do not count. Please type the answer or results of each item above, using a word processor, with your name and email address at the top, hand it in, and also send it in an email to Larry.Peel@tamuk.edu. I will compile all of the web addresses and send a more complete list back to you.
Review Problems: 7.0 For the following figure: a) find the maximum normal force, N x, max shear force in the y- z plane, and the maximum moment as a vector quantity at the fixed end of the pipe, b) Using the above numbers, determine σ x max τ xy max at the positive y side of the pipe. Assume that the external diameter is 40 mm, and pipe thickness is 4 mm.
8.0 The following represents a semi end-dump trailer. It is 40 ft long, is raised to an angle of 45 degrees, has a distributed load of 100 lbs/in that represents its load and weight, and has a pressure of 0.1 psi acting in the +y direction, on the side of the trailer. a) find the maximum normal force, N z, max shear force in the x-y plane, and the maximum vector moment at the fixed end (A) of the hydraulic cylinder, b) Using the above numbers, determine σ z max τ xy max on the cylinder. Assume that the external diameter is 8 in, and pipe thickness is 0.5 in.
9.0 For the following chart, with f(x) given and a line at y=14, determine how you could numerically or computationally find the coordinates of their intersection (x,y). Show me your logic, and sketch how you would converge on a result. f(x) 40 35 30 25 20 15 10 5 0-5 -10 f(x)=x 2-2x-8 0 1 2 3 4 X values
What is Finite Element Analysis (FEA)? A computerized or automated method for predicting how a component will react to external forces, moments, heat, vibration, and so on. The first part of this course will concentrate on structural FEA
For Structural FEA the basic equation is F= force vector K = stiffness matrix X = displacement vector F=KX, What would K be for a cantilever beam with a force on the end? (δ = PL 3 / 3EI)
Basic FEA Theory (4.1) Where {F} is a vector representing forces acting on the nodes in a structure, {U} is the displacement vector for each degree of freedom of the nodes (translation and rotation). The matrix [K] is known as the stiffness matrix and is dependent upon the physical characteristics of the elements including shape, size, and the Young s Modulus of the material the element is to represent. Figure 4.2 shows how a simple beam can be represented as a spring with stiffness [K] from which the displacement {U} can be solved when {F} is applied to the end. = Figure 4.1 Simple fixed beam analyzed as a simple spring with stiffness K. The analytical solution for the displacement U from solid mechanics is
Where A is the cross-section area of the beam and E is its Young s Modulus. In order to utilize Hooks Law, when Equation 4.2 is solved for F in terms of U, the following result is obtained, (4.2) (4.3) resulting in (4.3b) Equations 4.2 through 4.3a 4.3b describe a simple situation for which a set of scalar equations are suitable to solve for the displacement of the single node in the system. When more complicated systems are analyzed, the one in Figure 4.3 can be formed with multiple nodes and forces. Then Equations 4.1-4.3 must be written in matrix notation. Figure 4.2 A Slightly more complex element that contains two nodes with still only 1 DOF for which matrix notation must be used.
Hook s Law is used to solve F 1 at node 1 and is defined as follows: Assuming equilibrium, F 2 can be solved: (4.4) (4.4b) Now that F 1 and F 2 have been defined, Equation 4.1 can be expressed in matrix form. Equation 4.5 accurately describes the relationship between {F},[K], and {U} for a single element, but FEA involves working with a network of elements with varying {F} and [K] values that share common nodes. Figure 4.4 shows a multi-spring structure that illustrates this concept. (4.5) Figure 4.3 System of elements with different K values that share node 2. Here two elements with different K values share node 2. To solve this problem the same approach used to obtain Equations 4.4a and 4.4b is used. By applying Hooks Law to all three nodes the following relationships are obtained.
(4.6a) (4.6b) (4.6c) Rewriting in matrix form yields: (4.7) The [K] matrix in Equation 4.7 is referred to as the Global Stiffness Matrix (GSM) and in this case {U} can easily be solved, given that the values for {F} and [K} are known. This is done by inverting [K] and performing a matrix multiplication operation with {F}. Such a procedure is an option for solving for the unknown displacement {U} when the GSM is relatively small but it is important to understand that the size of this matrix increases dramatically as the system becomes more complex. The size of the GSM is equal to the number of nodes times the number of degrees of freedom. In the example shown in Figure 4.4, there were 3 nodes with only a translational displacement in one direction will yield a 3 X 3 GSM. This can easily be solved by hand, but for a system with 1,000 nodes that allows for translation and rotation in X,Y and Z directions, will produce a 6,000 x 6,000 GSM. A matrix of this size cannot be solved by hand.
How FEA works: A component is created in a CAD package (2-d or 3-d) The geometry may be modified or simplified from what the original drawing shows The component is then meshed or broken into small or finite chunks or elements. Loads and constraints are applied.
An analysis is run, and force/stress/deflection results are displayed graphically or numerically.
Other Examples of Finite Element Meshes and Results Curved Mesh Mesh-less FEA Adaptive Meshing (http://www.designnews.com/author.asp?section_id=1386&dfplayout=blog&dfplayout=blog&dfppparams=ind_183%2caid_278873&dfppparam s=ind_183%2caid_278873&doc_id=278873&image_number=1)
Cool Stuff This is a meshing and FEA problem involving twisted fibers/wires that I am working on.