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Finite Element Method
Finite Element Method Assessment
Quiz 1
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Q.1
In FEM, which option is a negative aspect of the mixed formulation?
a) Presence of zeros on matrix diagonals corresponding to pressure variable
b) Involves a natural and direct formulation
c) It is a velocity-pressure formulation
d) It is similar to the Lagrange multiplier method
Q.2
Which option is correct regarding constraints in the viscous flow problems governed by the continuity and momentum equation?
a) Constrains are readily available
b) Constraints are created by the elimination of pressure
c) Constraints are created by the elimination of velocity
d) No constraints are dealt with in penalty formulation
Q.3
In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?
a) Velocity-pressure formulation
b) Penalty formulation
c) Mixed formulation
d) Lagrange multiplier formulation
Q.4
In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of an unconstrained function, whereas in the penalty method, a problem with differential constraints is reformulated to one without constraints.
a) True
b) False
Q.5
For the functional IL(v,λ)≡Iv(v)+∫ΩcλG(v)dxdy, what is the necessary condition for IL to have a stationary value?
a) δvxIL+δvyIL+δλIL=0
b) δvxIL-δvyIL-δλIL=0
c) δvxIL-δvyIL+δλIL=0
d) δvxIL+δvyIL-δλIL=0
Q.6
In the computation of mixed formulation in FEM, which option is correct for the nodal DOF of the following element?
a) o nodes with u,v and P
b) * nodes with u,v and P
c) o nodes with P only
d) *nodes with u and v
Q.7
For the following slider bearing, the upper pad is inclined to the base pad. Which option is correct for a load applied normal to the base pad?
a) A pressure gradient develops in the lubricant, and the bearing can support some transverse load
b) The pressure remains uniform in the lubricant, and the bearing can support some transverse load
c) A pressure gradient develops in the lubricant, and the bearing cannot support any transverse load
d) The pressure remains uniform in the lubricant, and the bearing cannot support any transverse load
Q.8
For the following slider bearing, the upper pad is parallel to the base pad. Which option is correct for a load applied normal to the base pad?
a) The pressure in the lubricant is atmospheric, and the bearing cannot support any load
b) The pressure in the lubricant is greater than atmospheric, and the bearing can support any load
c) The pressure in the lubricant is less than atmospheric, and the bearing cannot support any load
d) The pressure in the lubricant is atmospheric, and the bearing can support some load
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