FEA STUDY SET EXAM QUESTIONS And CORRECT Answers

FEA STUDY SET EXAM QUESTIONS And
CORRECT Answers
B) Temperature can vary in the y-direction but not in x and z directions.



In the coordinate system we have selected, temperature varies only in the x direction i.e. T=T(x)
- CORRECT ANSWERS Big Ideas in Finite-Element Analysis (FEA): Introduction



Which of the following assumptions is NOT made in our simple heat conduction example?



A) Temperature at any point does not vary with time

B) Temperature can vary in the y-direction but not in x and z directions.

C) Temperature is constant on any cross-section



B) False



To calculate the net flow out, one needs to calculate:

Heat flowing out - Heat flowing in:

(qy+dqydyΔy−qy)

And qy=−kdTdyΔxΔz

Then, the net heat flow out would be −kd2Tdy2ΔxΔyΔz - CORRECT ANSWERS Governing
Equation Derivation



Consider extending the above derivation to account for heat conduction in the y direction also.
The net heat flow out through the faces due to heat conduction in the y direction would be
equal to −kdTdyΔxΔz

,A) True

B) False



A) True



This is the definition of a boundary value problem. - CORRECT ANSWERS Mathematical
Model Summary



A boundary value problem consists of differential equation(s) defined within a domain and
boundary conditions defined at the edges of the domain.



A) True

B) False



6



With 5 elements, we have a total of 6 nodes. We need to obtain the temperature at each of
these 6 nodes.

Increasing the number of elements is referred to as mesh refinement. - CORRECT
ANSWERS Discretization



In the above example, we divided the domain into 3 elements. By doing so, we reduce the
problem to determining a finite number of temperature values. Later, we will see how to obtain
these values from governing equations and/or boundary conditions. For now, answer the
following question based on the concepts covered in the above video.



Let's consider the case when we increase the number of elements to 5. How many temperature
values will we need to obtain to determine the variation of temperature along the line?

, A) FALSE: Each algebraic equation will relate the temperature at a node to the temperature at
NEIGHBORING nodes only.

B)TRUE: The assumed polynomial variation within each element is the basis for deriving the
algebraic equations.

C)TRUE: This can be done through interpolation of nodal temperature values in the post-
processing step. The assumed polynomial variation within each element that is used for deriving
the algebraic equations is also used for post-processing. - CORRECT ANSWERS How to
Find Nodal Temperatures



Select the false statement.



A) In the finite-element method, we go from differential equations to a set of algebraic
equations. Each algebraic equation will relate a nodal temperature to all other nodal
temperatures.

B) To derive the algebraic equations, we need to assume a polynomial variation for the
temperature within each element. In our example, this polynomial is linear.

C) Once the nodal temperatures are determined by solving the system of algebraic equations,
one can find the temperature at any point in the domain.



B) False



This temperature distribution T(x) will satisfy the weighted integral form only when the variation
of w(x) is also given by a piecewise linear variation. It can NOT satisfy the weighted integral form
for any ARBITRARY variation of w(x). This means our finite-element solution for T(x) is
approximate!

In contrast, the exact solution will satisfy the weighted integral form for any arbitrary function
w(x). - CORRECT ANSWERS How to Derive Algebraic Equations