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Finite Element Method MCQ

1. Skyline matrix storage is in the form of ______

Banded matrix

Sparse matrix

Singular matrix

Identity matrix

Answer

Correct Answer: Sparse matrix

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2. What is a banded matrix?

Sparse matrix

Rectangular matrix

Unit matrix

Square matrix

Answer

Correct Answer: Sparse matrix

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3. The truss element is a _____ when we see it in a local coordinate system.

Three dimensional

One dimensional

Two dimensional

Thermal component

Answer

Correct Answer: One dimensional

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4. Plane truss element can be shown in _____

Local coordinate system

Global coordinate system

Local and global coordinate systems

Dimensional structure

Answer

Correct Answer: Local and global coordinate systems

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5. A truss structure consists only of ___ force members.

Only one

Two

Three

Poly

Answer

Correct Answer: Two

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6. Plane trusses are also known as _____

One–dimensional trusses

Two-dimensional trusses

Three-dimensional trusses

Poly dimensional trusses

Answer

Correct Answer: Two-dimensional trusses

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7. Nodal displacement as _____

U=Nq

N=uq

Q=Nu

Program SOLVING

Answer

Correct Answer: U=Nq

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8. By Hooke’s law, stress is ______

σ=Bq

σ=EB

B=σq

σ=EBq

Answer

Correct Answer: σ=EBq

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9. The _ and __ can vary linearly.

Force and load

Precision and accuracy

Strain and stress

Distance and displacement

Answer

Correct Answer: Strain and stress

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10. Quadratic shape functions give much more _______

Precision

Accuracy

Both Precision and accuracy

Identity

Answer

Correct Answer: Accuracy

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11. What is a shape function?

Interpolation function

Displacement function

Iterative function

Both interpolation and displacement function

Answer

Correct Answer: Both interpolation and displacement function

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12. For modelling of inclined roller or rigid connections, the method used is ___

Elimination approach

Multiple constraints

Penalty approach

Minimum potential energy theorem

Answer

Correct Answer: Multiple constraints

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13. In the penalty approach evaluate _______ at each support.

Load vector

Degrees of freedom

Force vector

Reaction force

Answer

Correct Answer: Reaction force

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14. The first step of the penalty approach is adding a number C to the diagonal elements of the stiffness matrix. Here C is a __________

Large number

Positive number

Real number

Zero

Answer

Correct Answer: Large number

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15. If Q 1 =a 1 then a 1 is _________

Displacement

Symmetric

Non symmetric

Specified displacement

Answer

Correct Answer: Specified displacement

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16. Penalty approach method is easy to implement in a ______

Stiffness matrix

Iterative equations

Computer program

Cg solving

Answer

Correct Answer: Computer program

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17. In the elimination approach method, extract the displacement vector q from the Q vector. By using ___

Potential energy

Load

Force

Element connectivity

Answer

Correct Answer: Element connectivity

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18. In elimination approach, which elements are eliminated from a matrix ____

Force

Load

Rows and columns

Undefined

Answer

Correct Answer: Rows and columns

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19. Equilibrium conditions are obtained by minimising ______

Kinetic energy

Force

Potential energy

Load

Answer

Correct Answer: Potential energy

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20. Types of Boundary conditions are ______

Potential- Energy approach

Penalty approach

Elimination approach

Both penalty approach and elimination approach

Answer

Correct Answer: Both penalty approach and elimination approach

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21. Element stiffness is obtained with respect to its ___

Degrees of freedom

Nodes

Axes

Elements

Answer

Correct Answer: Axes

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22. The size of the global stiffness matrix will be equal to the total ______ of the structure.

Nodes

Degrees of freedom

Elements

Structure

Answer

Correct Answer: Degrees of freedom

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23. In the stiffness matrix, all the _____ elements are positive.

Linear

Zigzag

Diagonal

Rectangular

Answer

Correct Answer: Diagonal

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24. Stiffness matrix is _____

Non symmetric and square

Symmetric and square

Non symmetric and rectangular

Symmetric and rectangular

Answer

Correct Answer: Symmetric and square

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25. In many one-dimensional problems, the banded matrix has only two columns. Here NBW=____

Answer

Correct Answer: 2

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26. The dimension of K banded is _____ (Here NBW is half bandwidth)

[N X NBW ]

[NBW X N]

[N X N]

[NBW X NBW]

Answer

Correct Answer: [N X NBW ]

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27. Global stiffness K is a______ matrix.

Identity matrix

Upper triangular matrix

Lower triangular matrix

Banded matrix

Answer

Correct Answer: Banded matrix

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28. Each node has only _______

Two degrees of freedom

One degree of freedom

Six degrees of freedom

Three degrees of freedom

Answer

Correct Answer: One degree of freedom

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29. Which technique do traditional workloads use?

Scale out technique

Scale up technique

Building technique

Shrinking technique

Answer

Correct Answer: Scale up technique

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30. What is the Global stiffness method called?

Multiple matrix

Direct stiffness matrix

Unique matrix

Vector matrix

Answer

Correct Answer: Direct stiffness matrix

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31. By element stiffness matrix we can get relation of members in an object in _____

Different matrices

One matrix

Identity matrix

Singular matrix

Answer

Correct Answer: One matrix

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32. We can obtain same assembly procedure by Stiffness matrix method and _______

Potential energy method

Rayleigh method

Galerkin approach

Vector method

Answer

Correct Answer: Galerkin approach

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33. The points at where kinetic energy increases dramatically then those points are called _______

Stable equilibrium points

Unstable equilibrium points

Equilibrium points

Unique points

Answer

Correct Answer: Unstable equilibrium points

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34. Principal of minimum potential energy follows directly from the principal of ________

Elastic energy

Virtual work energy

Kinetic energy

Potential energy

Answer

Correct Answer: Virtual work energy

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35. From where does the global load vector F is assembled?

Element force vectors only

Point loads only

Both element force vectors and point loads

Undefined

Answer

Correct Answer: Both element force vectors and point loads

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36. In basic equation Lu=f, L is a ____________

Matrix function

Differential operator

Degrees of freedom

No. of elements

Answer

Correct Answer: Differential operator

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37. By the Galerkin approach equation can be written as __________

{P}-{K}{Δ}=0

{K}-{P}{Δ}=0

{Δ}-{p}{K}=0

Undefined

Answer

Correct Answer: {P}-{K}{Δ}=0

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38. To solve a galerkin method of approach equation must be in ___________

Equation

Vector equation

Matrix equation

Differential equation

Answer

Correct Answer: Differential equation

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39. Element connectivities are used for _____

Traction force

Assembling

Stiffness matrix

Virtual work

Answer

Correct Answer: Assembling

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40. Galerkin technique is also called as _____________

Variational functional approach

Direct approach

Weighted residual technique

Variational technique

Answer

Correct Answer: Weighted residual technique

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41. Formula for global stiffness matrix is ____________

No. of nodes*Degrees of freedom per node

No. of nodes

Degrees of freedom per node

No. of elements

Answer

Correct Answer: No. of nodes*Degrees of freedom per node

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42. What are the basic unknowns on the stiffness matrix method?

Nodal displacements

Vector displacements

Load displacements

Stress displacements

Answer

Correct Answer: Nodal displacements

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43. Continuum is discretized into_______ elements.

Infinite

Finite

Unique

Equal

Answer

Correct Answer: Finite

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44. Stresses due to rigid body motion are _______________

Zero

Considered

Not considered

Infinite

Answer

Correct Answer: Not considered

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45. In shape functions, _________ must be continuous across the element boundary.

Derivatives

Nodes

Displacement

Shape function

Answer

Correct Answer: Displacement

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46. In shape functions, first derivatives must be _______ within an element.

Infinite

Finite

Natural

Integer

Answer

Correct Answer: Finite

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47. Shape function is just a ___________

Displacement function

Equation

Interpolation function

Matrix function

Answer

Correct Answer: Interpolation function

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48. Natural or intrinsic coordinate system is used to define ___________

Co-ordinates

Shape functions

Displacement functions

Both shape functions and coordinate functions

Answer

Correct Answer: Shape functions

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49. Local node number corresponds to ______________

Entire body

On element

On interface

On surface

Answer

Correct Answer: On element

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50. Global nodes corresponds to _______

Entire body

On surface

On interface

On element

Answer

Correct Answer: Entire body

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51. The loading on an element includes _______

Body force

Traction force

Point load

Body force, Traction force & Point load

Answer

Correct Answer: Body force, Traction force & Point load

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52. Discretization includes __________ numbering.

Element and node

Only nodal

Only elemental

Either nodal or elemental

Answer

Correct Answer: Element and node

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53. Modelling is defined as ________________

Elemental area with uniform cross section

Elemental area with non uniform cross section

Structural area with uniform cross section

Non structural area with non uniform cross section

Answer

Correct Answer: Elemental area with uniform cross section

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54. One dimensional element is the linear segments which are used to model ________

Bars and trusses

Plates and beams

Structures

Solids

Answer

Correct Answer: Bars and trusses

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55. In one dimensional problem, each node has _________ degrees of freedom.

2 degrees of freedom

3 degrees of freedom

No degrees of freedom

1 degree of freedom

Answer

Correct Answer: 1 degree of freedom

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56. In finite element modelling every element connects to _______

4 nodes

3 nodes

2 nodes

Infinite no of nodes

Answer

Correct Answer: 2 nodes

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57. In finite element modelling nodal points are connected by unique ________

Surface

Shape

Eigenvalues

Matrix

Answer

Correct Answer: Surface

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58. If the structure is divided into discrete areas or volumes then it is called an _______

Structure

Element

Matrix

Boundaries

Answer

Correct Answer: Element

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59. Frontal method involves __________

Computer programming

Manual programming

C- programming

Computing

Answer

Correct Answer: Computer programming

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60. Frontal method is implemented for ________

Hexahedral element

Polyhedral element

Octahedral element

Both Hexahedral and Polyhedral

Answer

Correct Answer: Hexahedral element

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61. Frontal method is a _______ of Gaussian elimination method that uses the structure of finite element problem.

Structure

Variation

Algorithm

Data

Answer

Correct Answer: Variation

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62. The line separating from the top zeros from the first non-zero element is called ____

Equation

Gaussian solution

Skyline solution

Both Gaussian and skyline solutions

Answer

Correct Answer: Skyline solution

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63. A banded matrix is defined as ____________

Non zero elements are contained in band

Zero elements are contained in a band

Non zero elements are contained out of a band

Both Non zero elements and Zero elements

Answer

Correct Answer: Non zero elements are contained in band

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64. Step number in Gaussian elimination is denoted as ___________

Superscript

Subscript

Unknown

Elimination

Answer

Correct Answer: Superscript

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65. Gaussian elimination is a name given to a well known method of solving simultaneous equation by successively eliminating _________

Variables

Equations

Unknown

Algorithms

Answer

Correct Answer: Unknown

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66. Det(A-λI)=0 is a ________

Characteristic equation

Matrix equation

Inversion of matrix

Cholesky’s equation

Answer

Correct Answer: Characteristic equation

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67. A positive definite symmetric matrix A can be decomposed into form A=LL T this decomposition is called ________

Cholesky

Rayleighs

Galerkins

Potential energy

Answer

Correct Answer: Cholesky

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68. A is a condition for ________

Singular matrix

Nonsingular matrix

Matrix inversion

Adjoint of matrix

Answer

Correct Answer: Matrix inversion

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69. A symmetric matrix is called ____________, if all its Eigenvalues are strictly positive i.e., greater than zero.

Negative definite

Positive definite

Co- definite

Alternative definite

Answer

Correct Answer: Positive definite

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70. What is a matrix?

Group of elements

Array of elements

Group of columns and rows

Array of numbers

Answer

Correct Answer: Array of elements

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71. Quadratic Gaussian quadrature element can be used to accurately determine the integral of a polynomial function with a degree not exceeding ______.

Answer

Correct Answer: 3

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72. Determinant of Jacobian (J) of a domain is greater than zero?

When the geometry of the element is convex.

When the geometry of the element is concave.

When geometry of the element is convex and local node numbering

Is anticlockwise.

Answer

Correct Answer: When geometry of the element is convex and local node numbering

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73. Symmetry of a finite element problem depends upon its:

Geometry.

Boundary conditions.

Material properties.

All of these.

Answer

Correct Answer: All of these.

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74. The number of columns in a connectivity matrix corresponds to _______.

Total number of nodes in the entire domain.

Minimum number of nodes in any element.

Maximum number of nodes in any element.

Number of elements

Answer

Correct Answer: Maximum number of nodes in any element.

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75. For a 3D element, the boundary integral (Qi) for a finite element equation is a ______.

Surface integral

Line integral

Volume integral

None of these

Answer

Correct Answer: Volume integral

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76. In discretization of 2D FEA problems higher order elements should be used in region of:

Lower gradient

Higher gradient.

No gradient.

None of these.

Answer

Correct Answer: No gradient.

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77. As the degree of interpolation function increases,___________________.

Convergence decreases.

Convergence increases.

Convergence is unaffected.

None of these.

Answer

Correct Answer: Convergence is unaffected.

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78. Indicate the right statement:

FEA solution under predicted displacement (u).

FEA solution under predicted energy (E).

FEA solution under predicts stiffness (k).

None of the statements are true.

Answer

Correct Answer: FEA solution under predicted energy (E).

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79. FEA solution_____ energy when compared to its exact solution.

Over predicts.

Under predicts.

Exactly predicted.

None of these.

Answer

Correct Answer: Over predicts.

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80. Which of the following options is a 3D FEA element?

Tetrahedron.

Wedge.

Hexahedron.

All of these

Answer

Correct Answer: Tetrahedron.

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81. Essential boundary conditions are conditions that _____________.

Specify primary variable

Specify secondary variables.

Specifies the value that the derivative of a primary variable on the

Boundary of the domain.

None of these.

Answer

Correct Answer: Specifies the value that the derivative of a primary variable on the

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82. The values obtained at boundaries of the structure are called as ________________.

Boundary Conditions

Boundary Values

Both a & b

None of these

Answer

Correct Answer: Both a & b

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83. Which of the following approaches is not used in FEM?

Elimination Approach

Penalty Approach

Direct Stiffness Method

None of these

Answer

Correct Answer: Direct Stiffness Method

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84. For 2 dimensional elements, the degree of freedom per node is __.

Indefinite

Answer

Correct Answer: 2

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85. Which of the following is not FEA Software?

NASTRAN

ABACUS

Solid Works

ANSYS

Answer

Correct Answer: Solid Works

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86. The force applied over the surface per unit volume is known as __________

Point Load

Body Force

Surface Traction

Tangential Force

Answer

Correct Answer: Body Force

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87. ________________________ is the frame of reference for the entire body in FEM.

Global Coordinate System

Local Coordinate System

Natural Coordinate System

General Coordinate System

Answer

Correct Answer: Global Coordinate System

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88. To solve the FEM problem, it subdivides a large problem into smaller, simple parts that are called

Static Elements

Dynamic Elements

Infinite Elements

Finite Elements

Answer

Correct Answer: Finite Elements

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89. Numerical algorithms are based on ____________

TD & FD

FEM & IFEM

FEM & FDTD

FEM & FD

Answer

Correct Answer: FEM & FDTD

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90. FEM gives an accurate representation of ____________________

Real Geometry

Complex Geometry

Real & Complex Geometry

Complete Geometry

Answer

Correct Answer: Complex Geometry

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91. The finite element method is formulation of the problem results in a system of _________________

Algebraic Equations

Logical Equations

Arithmetic Equations

Flow Equation

Answer

Correct Answer: Algebraic Equations

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92. 20 Sum of all shape functions is equal to ____

Zero

-1

Answer

Correct Answer: +1

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93. Range of Poisson’s ratio for metals is _____________ .

0.25 – 0.33

0.22 – 0.45

0.22 – 0.25

0.25 – 0.50

Answer

Correct Answer: 0.25 – 0.50

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94. The eight node quadrilateral element belongs to _________ family of elements.

Serendipity

Interdipity

Saradipity

None of These

Answer

Correct Answer: Serendipity

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95. The finite element method is mostly used for________________________

Structural Mechanics

Classical Mechanics

Engineering Mechanics

Applied Mechanics

Answer

Correct Answer: Engineering Mechanics

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96. The geometry & other parameters of an element in terms of only one spatial coordinate then the element is ___________

Two dimensional

Three dimensional

One dimensional

None.

Answer

Correct Answer: None.

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97. Three noded triangular element is called as __________________________

Linear Strain Triangular Element

Constant Strain Triangular Element

Variable Strain Triangular Element

Differential Stain Triangular Element

Answer

Correct Answer: Constant Strain Triangular Element

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98. In Finite Element Method, system of equations is given by, _____________

F=K.UN

F= UN.K

K= UN.F

K= F.UN

Answer

Correct Answer: F=K.UN

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99. The higher ordered elements are also called as ____________________

Complex Elements

Compound Elements

Linear Elements

None of these

Answer

Correct Answer: Complex Elements

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100. The displacement function for 1-D two noded linear element in terms of shape functions will be:

U =N1u1+N2u1

U =N1u2+N2u1

U =N2u1+N1u2

U =N1u1+N2u2

Answer

Correct Answer: U =N1u1+N2u2

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Finite Element Method MCQ

1. Skyline matrix storage is in the form of ______

2. What is a banded matrix?

3. The truss element is a _____ when we see it in a local coordinate system.

4. Plane truss element can be shown in _____

5. A truss structure consists only of ___ force members.

6. Plane trusses are also known as _____

7. Nodal displacement as _____

8. By Hooke’s law, stress is ______

9. The _____ and ______ can vary linearly.

10. Quadratic shape functions give much more _______

11. What is a shape function?

12. For modelling of inclined roller or rigid connections, the method used is ___

13. In the penalty approach evaluate _______ at each support.

14. The first step of the penalty approach is adding a number C to the diagonal elements of the stiffness matrix. Here C is a __________

15. If Q 1 =a 1 then a 1 is _________

16. Penalty approach method is easy to implement in a ______

17. In the elimination approach method, extract the displacement vector q from the Q vector. By using ___

18. In elimination approach, which elements are eliminated from a matrix ____

19. Equilibrium conditions are obtained by minimising ______

20. Types of Boundary conditions are ______

21. Element stiffness is obtained with respect to its ___

22. The size of the global stiffness matrix will be equal to the total ______ of the structure.

23. In the stiffness matrix, all the _____ elements are positive.

24. Stiffness matrix is _____

25. In many one-dimensional problems, the banded matrix has only two columns. Here NBW=____

26. The dimension of K banded is _____ (Here NBW is half bandwidth)

27. Global stiffness K is a______ matrix.

28. Each node has only _______

29. Which technique do traditional workloads use?

30. What is the Global stiffness method called?

31. By element stiffness matrix we can get relation of members in an object in _____

32. We can obtain same assembly procedure by Stiffness matrix method and _______

33. The points at where kinetic energy increases dramatically then those points are called _______

34. Principal of minimum potential energy follows directly from the principal of ________

35. From where does the global load vector F is assembled?

36. In basic equation Lu=f, L is a ____________

37. By the Galerkin approach equation can be written as __________

38. To solve a galerkin method of approach equation must be in ___________

39. Element connectivities are used for _____

40. Galerkin technique is also called as _____________

41. Formula for global stiffness matrix is ____________

42. What are the basic unknowns on the stiffness matrix method?

43. Continuum is discretized into_______ elements.

44. Stresses due to rigid body motion are _______________

45. In shape functions, _________ must be continuous across the element boundary.

46. In shape functions, first derivatives must be _______ within an element.

47. Shape function is just a ___________

48. Natural or intrinsic coordinate system is used to define ___________

49. Local node number corresponds to ______________

50. Global nodes corresponds to _______

51. The loading on an element includes _______

52. Discretization includes __________ numbering.

53. Modelling is defined as ________________

54. One dimensional element is the linear segments which are used to model ________

55. In one dimensional problem, each node has _________ degrees of freedom.

56. In finite element modelling every element connects to _______

57. In finite element modelling nodal points are connected by unique ________

58. If the structure is divided into discrete areas or volumes then it is called an _______

59. Frontal method involves __________

60. Frontal method is implemented for ________

61. Frontal method is a _______ of Gaussian elimination method that uses the structure of finite element problem.

62. The line separating from the top zeros from the first non-zero element is called ____

63. A banded matrix is defined as ____________

64. Step number in Gaussian elimination is denoted as ___________

65. Gaussian elimination is a name given to a well known method of solving simultaneous equation by successively eliminating _________

66. Det(A-λI)=0 is a ________

67. A positive definite symmetric matrix A can be decomposed into form A=LL T this decomposition is called ________

68. A is a condition for ________

69. A symmetric matrix is called ____________, if all its Eigenvalues are strictly positive i.e., greater than zero.

70. What is a matrix?

71. Quadratic Gaussian quadrature element can be used to accurately determine the integral of a polynomial function with a degree not exceeding ______.

72. Determinant of Jacobian (J) of a domain is greater than zero?

73. Symmetry of a finite element problem depends upon its:

74. The number of columns in a connectivity matrix corresponds to _______.

75. For a 3D element, the boundary integral (Qi) for a finite element equation is a ______.

76. In discretization of 2D FEA problems higher order elements should be used in region of:

77. As the degree of interpolation function increases,___________________.

78. Indicate the right statement:

79. FEA solution_____ energy when compared to its exact solution.

9. The _ and __ can vary linearly.