MET 415 Lecture Notes

Text: Building Better Products with FEA,
by V. Adams & A. Askenazi, (Read pp. 259-302)

Boundary Conditions: the loads and constraints that represent the effect of the surrounding environment on the model.  (Everything else, that you have not modeled).

Example 1: Motorcycle wheel (p.259-260)

"How did you obtain the load ? Did you consider the tire/wheel interface ? Does the tire provide a constraint on the rim or a force/moment ? Is the hub fully constrained ? How to treat the bearings ? How about braking loads ? How about the driving load from the sprocket ?"

Example 2: Chair (p.261-262)

"Model the chair legs or not ? Do the legs slide on the floor or "attach rigid" ? Do the legs bend or not ? Is the load on the seat centered ? Is it evenly distributed ?"

(p. 263) "... the choice of where to stop modeling is related to the goals of the analysis and your ability to the define boundary conditions that accurately represent the world beyond the stopping point"

Types of Boundary Conditions: constraints and loads

Loads: forces, moments, pressures, temperatures, accelerations

Constraints: Resist the deformations induced by the loads

Spatial DOF’s: in 3D: three translations and three rotations are possible.  If one is left unconstrained, the FEA solution will fail.   What happens in our 2D models (only UX & UY DOF’s) ?

Element DOF’s: each element may or may not have all six possible DOF’s

UNWANTED EFFECTS (p. 264-270)

Overconstrained, redundant supports, excessive constraint

• tend to add stiffness to the model (stiffer than the real system)
• Also, prohibits Poisson contraction (making excessive stress)
• example of excessive constraint in thermal expansion

Underconstrained, understiffened, insufficient stiffness

• if rigid-body motion can occur, cracks, un-"glued" parts
• (p. 270) "Ask yourself if the parts that were not modeled could really allow the deformation that you are seeing." (Proj 1)

(p. 271) If you notice high stress near the boundary conditions, are they fictitious or real ?

SINGULARITIES (p.271-274)

Point load: local stress is infinite, but is meaningless (Fig. 8.6, p.272)

If you are concerned with locations "far" removed from locations which have singularity, then you can use the point loads.

Singular conditions (with high local, meaningless stress) may obscure or confuse the interpretation of important results

Singularities can occur at a point constraint, usually not accomplishing what you intended (Proj 1)

In a nonlinear analysis, singularities produce local yielding which may not be desired, and causes longer solution runs.

BRACKETING (p.274-5)

When you are unsure, try for best case/worst case models. Then, if you are rushed, use the highest stress (conservative)

Apply B.C.’s to Geometry (p. 276) = Use solid model loads

Using Load and Constraint Sets (p. 277) = Using Load Steps (in ANSYS)

Coordinate Systems (p. 278-80) = Local Coordinate Systems, Rotated Nodal Directions (in ANSYS)

CONSTRAINTS (p. 280-87)

• Constraints remove spatial DOF’s from the model.
• Appropriate constraints depend on the element types you are using.
• Symmetry: Smaller models, more accurate, less confusion
• i.e., consider Fig. 8.11 (p. 283) with "stability" springs
• Enforced Displacement (non-zero imposed displacement) forces the nodes to move to a new location, i.e., their final position

LOADS (p. 288-295)

• Applying loads consists of: magnitude, direction, distribution, time dependence
• "... be diligent with the units you use."
• Load Distribution: uniform, interpolated, or described by a function
• (p. 290) BRIDGING: redistribution of load after the part deforms
• In a linear analysis, you put in the final distribution of loads.
• Nonlinear Forces: large deflection analyses, including follower forces
• (In ANSYS, pressure loads follow the element face)
• Acceleration Loads (p. 294) "You may usually ignore gravity or any other type of acceleration if the resulting inertia loads are small compared to the applied loads."

COMPARISON OF BOUNDARY CONDITION SCHEMES (p. 295-300)

Considers various approaches for modeling a pin-in-a-hole loading

SUMMARY (p.300-302)

"... boundary conditions are arguably the toughest aspect of FEA"