Processes
What do we need to learn more about before we start prototyping?
Behavior of the design
What is a structure divided into in FEA?
Elements
What is K?
Potassium
Stiffness matrix (F=Kd) or (M=Ktheta)
What is the node numbering convention for CST's?
Node numbers must follow a CCW path around the element for area to be positive
What is the rule of thumb for how elastic modulus values are related?
E_metals > E_metals >> E_polymers
Sketch the design process without FEA
Briefly describe nodes and how they correspond to elements?
Nodes are shared and wed to connect elements.
What is the generalized stiffeness matrix? What does each term represent?
k=int(B^T * E * B * dV)
B = strain displacmeent matrix
E = material property matrix
What is the element stiffness matrix for a CST triangle
k = B^T E B t A
What are common range for yield strengths?
Metals (10 to 1750 MPa)
Polymers (10 to 60 MPa)
Ceramic (??)
What are the 3 key components of the FEA Process?
1. Pre-Processor
2. Solver
3. Post-processor
In general, increasing the number of elements does what to accuracy? How can we visualize.
More elements = more accuracy
What are the two limitations of 1D elements?
constant state of strain between nodes
Distributed axial loads, causes approximate solution
Two types of deformation?
Elastic and Plastic
What are yield strength rules of thumb?
Yield_ceramic > Yield_metals >> Yield_polymers
Physical Problem ==> Mathematical Problem (model) ==> FE soln for model ==> intrepret results ==> either refine analysis and improve model or improve the design and change the physical problem
What are the four common element types (1D/2D), how many DOF does each one have? What type of loading is present
Bar, truss, beam, frame, 2,4,4,6
Axial, Axial, Shear and bending, all 3
What is the simplest 2D element? What is the approximation that is made in its use?
Constant Strain Triangle (CST), assumption of small to no strains
What are the common states of stress?
Simple tension, compression, torsion, bi-axial tension, hydrostatic compression
Draw and Label the stress strain curve?
You know
What are the 8 common steps to FEA?
1. Evaluate the problem and make assumptions
2. Describe the finite elements behaviro.
3. build the module 4. form element eqn's
5. Assemble into global eqn. 6. Specify Loads & BC's
7. Solve the global problem. 8. Evaluate Results
What are the two explanations for the term "finite element"
(a) elements are finite; infinitesimal element used with governing eqn.
(b) DOF are finite; infinite # of DOF for a continous system
How do strains change within the element of a CST?
Strains are constant within the element.
What are common elastic modulus ranges for 4 main material types?
Metals - (45 to 400 GPa)
Ceramics - (30 to 1200 GPa)
Polymers (0.01 to 4 GPa)
Bone (-14 GPa)
What does the B matrix represent?
Matrix that yields curvature d2v/dx2 of the beam element from product Bd?