Finite Element Method Questions and Answers – One Dimensional Problems – Assembly of the Global Stiffness Matrix and Load Vector

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This set of Finite Element Method Interview Questions and Answers focuses on “One Dimensional Problems – Assembly of the Global Stiffness Matrix and Load Vector”.

1. How is Assembly of stiffness matrix symbolically denoted?
a) K={k}e
b) K←∑eKe
c) K←∑Ke
d) Undefined
View Answer

Answer: b
Explanation: The stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to differential equation.
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2. What is the Strain energy equation?
a) Ue=\(\frac{1}{2}\)qTkeq
b) Ue=\(\frac{1}{2}\)qekeq
c) Ue=\(\frac{1}{2}\)qke
d) Ue=\(\frac{1}{2}\)qTke
View Answer

Answer: a
Explanation: Strain energy is defined as the energy stored in the body due to deformation. The strain energy per unit volume is known as strain energy density and the area under stress-strain curve towards the point of deformation. When the applied force is released, the system returns to its original shape.

3. What is the actual equation of stiffness matrix?
a) K=\(\begin{bmatrix}1 & -1 \\ -1 & 1 \end{bmatrix}\)
b) K=\(\frac{AE}{l}\begin{bmatrix}1 \\ -1 \end{bmatrix}\)
c) K=\(\frac{AE}{l}\)
d) K=\(\frac{AE}{l}\begin{bmatrix}1 & -1 \\ -1 & 1 \end{bmatrix}\)
View Answer

Answer: d
Explanation: Stiffness matrix represents the system of linear equations that must be solved in order to ascertain an approximate solution to the differential equation. The stiffness matrix is an inherent property of the structure. A stiffness matrix is a positive definite.
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4. From where does the global load vector F is assembled?
a) Element force vectors only
b) Point loads only
c) Both element force vectors and point loads
d) Undefined
View Answer

Answer: c
Explanation: Global load vector is assembling of all local load variables. This global load vector is get from assembling of both element force vectors and point loads.

5. For an element as given below, what will be the 1ST element stiffness matrix?
Find the 1st element stiffness matrix for the given element
a) \(\frac{EA_1}{l_1}\begin{bmatrix}1 & -1 & 0 & 0 & 0 \\ -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}\)
b) \(\frac{EA_1}{l_1}\begin{bmatrix}0 & 0 & 0 & 0 & 0 \\ 0 & 1 & -1 & 0 & 0 \\ 0 & -1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}\)
c) \(\frac{EA_1}{l_1}\begin{bmatrix}0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 0 \\ 0 & 0 & -1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}\)
d) \(\frac{EA_1}{l_1}\begin{bmatrix}0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1\\ 0 & 0 & 0 & -1 & 1 \end{bmatrix}\)
View Answer

Answer: a
Explanation: For the given object we firstly write an element connectivity table and then we check that where the load is acting on that object and next we write the element stiffness matrix of each element. For this object first element stiffness matrix is as given.
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6. Principal of minimum potential energy follows directly from the principal of ________
a) Elastic energy
b) Virtual work energy
c) Kinetic energy
d) Potential energy
View Answer

Answer: b
Explanation: The total potential energy of an elastic body is defined as sum of total strain energy and the work potential energy. Therefore the principal of minimum potential energy follows directly the principal of virtual work energy.

7. The points at where kinetic energy increases dramatically then those points are called _______
a) Stable equilibrium points
b) Unstable equilibrium points
c) Equilibrium points
d) Unique points
View Answer

Answer: b
Explanation: If an external force acts to give the particles of the system some small initial velocity and kinetic energy will developed in that body then the point where kinetic energy decreased that point is Stable equilibrium point and the point where the kinetic energy dramatically increased then the point is called Unstable equilibrium points.
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8. We can obtain same assembly procedure by Stiffness matrix method and _______
a) Potential energy method
b) Rayleigh method
c) Galerkin approach
d) Vector method
View Answer

Answer: c
Explanation: Galerkin method provides powerful numerical solution to differential equations and modal analysis. Assembling procedure is same for both stiffness matrix method and galerkin approach method in Finite element modeling.

9. By element stiffness matrix we can get relation of members in an object in _____
a) Different matrices
b) One matrix
c) Identity matrix
d) Singular matrix
View Answer

Answer: b
Explanation: Element stiffness matrix method is that make use of the members of stiffness relations for computing member forces and displacement in structures. So by this element stiffness matrix method we can get relation of members in an object in one matrix.
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10. What is the Global stiffness method called?
a) Multiple matrix
b) Direct stiffness matrix
c) Unique matrix
d) Vector matrix
View Answer

Answer: b
Explanation: Global stiffness matrix method makes use of the members stiffness relations for computing member forces and displacements in structures. Hence Global stiffness matrix or Direct stiffness matrix or Element stiffness matrix can be called as one.

11. Which technique do traditional workloads use?
a) Scale out technique
b) Scale up technique
c) Building technique
d) Shrinking technique
View Answer

Answer: b
Explanation: When the workload increases on the system, the machine scales up by adding more RAM, CPU and storage spaces.

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