MET 415 Lecture Notes

Text: Building Better Products with FEA,
by V. Adams & A. Askenazi, (Read Chapter 3)

Capabilities and Limitations of FEA

FEA goes beyond classical formulae (e.g., Poisson effects), but always remember, FEA is an approximation.

Actual Performance vs. FEA: Assumption = Possible source of error

Stiffness:  effected by actual E, cold working, porosity, processing

Geometric:  tolerance vs. nominal, curvature is approximated, ignoring small features (holes, fillets, chamfers, etc.)

How FEA Calculates Data (pp. 94-95)

Simple Two Spring Model (1D)

F = K*x means

Applied Force = Internal Force in the Spring

leads to a [K] matrix with both spring constants:

DEFINITIONS (page 96)

Degrees of Freedom (DOF):  motions that are possible at a node.

In 3D, maximum = 6   (3 translations + 3 rotations)

Also, shows ability to transmit loads.

In 3D, maximum = 6   (3 forces + 3 moments)

Boundary Conditions:  constraints and loads on a model

Nodes:  points in space, corners, ends, or mid-edge points of elements

Elements:  stiffness relationship between nodes

Shape functions:  represent assumed shape (i.e., behavior) of elems.

• Higher-order elements: > 1^st order shape functions
• Lower-order elements: linear (1^st order) shape functions

Smaller element size makes the shape functions a better approx.

Convergence: reducing local error in a model, by either:

1. refining the mesh
2. using higher-order shape functions

(Either method will improve the solution’s accuracy)

H-elements vs. P-elements (pp. 97-98)

• H-elements: accuracy depends on element size (H = elem "height")
• P-elements: accuracy depends on the order of the element shape functions (P = polynomial order)
• Some programs have both types of elements (i.e., ANSYS)
• Some programs have only one type of element (i.e., MECHANICA)

ACCURACY (page 99) comes from:

1. refining the mesh
2. fine tuning the B.C.’s
3. correcting assumptions

KEY ASSUMPTIONS IN FEA (p. 100-102)

FOUR PRIMARY ASSUMPTIONS:

1. Geometry: "the mesh represents the geometry adequately"
2. Properties: "all parts produced have the same properties"
3. Mesh: "Accuracy depends on the mesh quality"
       "A good-looking mesh has well-shaped elements"
4. Boundary Conditions: "do the B.C.’s really represent the parts and effects which are not explicitly modeled ?"

DISAGREE:  The analyst's job is to make a proper mesh that will be accurate and represent the geometry adequately.  How do YOU do this ?

LINEAR STATIC (pp. 103-6): Is it linear ? Is it static ?

• LINEAR material: Obeys Hooke’s Law ( s = E e )
• LINEAR geometry: no stress stiffening and small deflections
      (Small angles approx. cos q = 1, sin q = q )
• LINEAR B.C.’s: loads don’t change from application to final deformed shape
• Static loading: Not varying with time. No impact, no vibration

OTHER COMMONLY USED ASSUMPTIONS (p. 108-112)

• No stress stiffening, small deflections, ignore cosmetic features,
• 2D cases, reflective symmetry
• 3D shells and beams (we will do later): thickness, intersections
• Linear material, nominal properties, independent of load rate,
• isotropic, homogeneous, no voids/imperfections,
• ignore material changes in weld heat zone
• ignore stress in a part due to fabrication
• Static, no friction, rigid supports, uniformly distributed pressure
• Treatment of fasteners between parts of an assembly (approximate them: seldom do we model each rivet or bolt/nut)
• Ignore environmental factors: temperature, humidity, moisture, corrosion/oxidation, etc.

Think about:

Christopher Wright P.E. (XANSYS, 10/26/06):
"You can also find yourself in a position where 80% of an answer in time to make changes is worth a great deal more than 100% of an answer furnished after the point where the design can't be modified".

Einstein quote: "simplify as much as possible - but not more!"

Hamming's Motto: "the purpose of computing is insight, not numbers."

CONCLUSION:

Behind every decision you make are assumptions that may effect the accuracy and correctness of the model.