Module 1 Finite Element Analysis (FEA) – Exam with Questions and Answers –
100% Solved
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.
EXPLANATION
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. - ✔✔✔-One of the following
statements is false. 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. 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.
Answer: 6
, Module 1 Finite Element Analysis (FEA) – Exam with Questions and Answers –
100% Solved
EXPLANATION:
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. - ✔✔✔-Let's consider the
case when we increase the number of elements to 5. 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.
How many temperature values will we need to obtain to determine the variation of
temperature along the line?
A.) 2
B.) 3
C.) 4
D.) 5
E.) 6
B.) Temperature can vary in the y-direction but not in x and z directions. - correct
EXPLANATION:
In the coordinate system we have selected, temperature varies only in the x direction i.e. T =
T(x) - ✔✔✔-Which of the following assumptions is NOT made in our simple heat conduction
example?
100% Solved
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.
EXPLANATION
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. - ✔✔✔-One of the following
statements is false. 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. 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.
Answer: 6
, Module 1 Finite Element Analysis (FEA) – Exam with Questions and Answers –
100% Solved
EXPLANATION:
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. - ✔✔✔-Let's consider the
case when we increase the number of elements to 5. 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.
How many temperature values will we need to obtain to determine the variation of
temperature along the line?
A.) 2
B.) 3
C.) 4
D.) 5
E.) 6
B.) Temperature can vary in the y-direction but not in x and z directions. - correct
EXPLANATION:
In the coordinate system we have selected, temperature varies only in the x direction i.e. T =
T(x) - ✔✔✔-Which of the following assumptions is NOT made in our simple heat conduction
example?
