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Finite Element Methods MCQ

1. What is the reason for an element in the Serendipity family to have a smaller size of stiffness matrix compare to a similar element in the Lagrange family?

Answer

Correct Answer: Third-order Lagrange element has fifteen nodes

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2. Which nodes of the higher-order elements of the Lagrange family do not contribute to the inter-element connectivity?

Answer

Correct Answer: Interior nodes

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3. What is the number of nodes present on the boundary of the Lagrange quadratic rectangular element used in FEM?

Answer

Correct Answer: 8

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4. Which option is not correct about the Lagrange rectangular element used in FEM?

Answer

Correct Answer: Third-order Lagrange element has fifteen nodes

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5. In FEM, what are the elements in which the same shape functions describe the geometry and field displacement variables?

Answer

Correct Answer: Iso-parametric

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6. In FEM, which option is used to develop the Higher-order rectangular elements (i.e., rectangular elements with interpolation functions of higher degree) systematically?

Answer

Correct Answer: A rectangular array of binomial coefficients

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7. In FEM, what is the name of the shape function of an Euler-Bernoulli beam element?

Answer

Correct Answer: Hermite cubic interpolation function

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8. In FEM, what is the name of the element specified by a polynomial of order two or more?

Answer

Correct Answer: Higher-order element

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9. If the geometry and other parameters of an element are defined in terms of only one spatial coordinate, then the element is a one-dimensional element?

Answer

Correct Answer: True

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10. In the FEM element library, what is the correct name for a three noded triangular element?

Answer

Correct Answer: Constant strain triangular element

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11. In the FEM element library, what is the correct name for a six noded triangular element?

Answer

Correct Answer: Linear strain triangular element

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12. In the FEM element library, an eight noded quadrilateral element belongs to which family?

Answer

Correct Answer: Serendipity

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13. In the FEM element library, what is the other name of a higher-order element?

Answer

Correct Answer: Complex element

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14. Which option is not correct about the four-noded rectangular plane stress element used in FEM?

Answer

Correct Answer: Its Delaunay triangulation is unique

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15. Concerning triangular elements in FEM, which option is not correct about the mathematical formula of Pascal’s triangle?

Answer

Correct Answer: A triangular element of order 2 corresponds to the second row

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16. In FEM, What is the number of displacement polynomials necessary for finding displacements in a linear triangular element?

Answer

Correct Answer: 2

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17. In FEM, which option is used to develop the Higher-order triangular elements (i.e. triangular elements with interpolation functions of higher degree) systematically?

Answer

Correct Answer: Pascal’s triangle

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18. Which option is not correct about the three-noded triangular plane stress (linear) element used in FEM?

Answer

Correct Answer: It can be improved by the addition of internal degrees of freedom

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19. Which of the following equations give the relation between material properties like modulus of elasticity (E), modulus of rigidity (G), and Poisson’s ratio (u)?

Answer

Correct Answer: E = 2*G*(1+u)

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20. Traction is force acting on an area in any direction other than normal.

Answer

Correct Answer: True

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21. Which of the following boundary conditions cannot be directly applied on solid elements?

Answer

Correct Answer: Torque

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22. Which of the following conditions must be fulfilled to apply symmetry in a finite element model?

Answer

Correct Answer: Geometry of the model is symmetric and boundary conditions to be applied are symmetric

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23. Which of the following is the correct equation for stiffness (K) of an element given value of force (F) and displacement (Q)?

Answer

Correct Answer: KQ=F

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24. Boundary conditions are applied to simulate the physical constraints on the finite element model.

Answer

Correct Answer: True

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25. Symmetry in application of boundary conditions should be avoided in which of the following types of analysis?

Answer

Correct Answer: Modal analysis

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26. For a taper beam element two cross sections are necessary to define the geometry.

Answer

Correct Answer: True

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27. The application of force at which of the following points on a beam will nullify the effect of torsion?

Answer

Correct Answer: Shear centre

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28. Three geometrically identical beams made out of steel, aluminium, and titanium are axially loaded. Which of are the following statements correct?

Answer

Correct Answer: Stress in all three beams is the sam

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29. Which of the following is not a one dimensional element?

Answer

Correct Answer: Brick

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30. In the Galerkin method we convert a continuous operator problem into a discrete problem.

Answer

Correct Answer: True

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31. Which of the following statements is correct?

Answer

Correct Answer: Stiffness coefficient value for numerical solution is greater than the value of exact solution

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32. In beam elements the cross section of the element is assumed.

Answer

Correct Answer: True

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33. The shape functions for interpolation on beam elements are defined on the range of ________

Answer

Correct Answer: -1 to +1

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34. The displacements in beam elements are interpolated using _______

Answer

Correct Answer: Shape functions

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35. The total number of degrees of freedom in a beam with four nodes is ______

Answer

Correct Answer: Eight

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36. Beams are horizontal members used for supporting transverse loading.

Answer

Correct Answer: True

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37. During finite element formulation of beam each node has _______ degrees of freedom.

Answer

Correct Answer: Two

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38. In a nine node quadrilateral, the shape functions can be defined as _______

Answer

Correct Answer: Generic shape functions

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39. The gauss points for a triangular region differ from the _____ region.

Answer

Correct Answer: Square

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40. The nodal temperature load can be evaluated by using _____

Answer

Correct Answer: Numerical integration

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41. The mid node should not be outside of the triangular element this condition should ensures that det J does not attain a value ____

Answer

Correct Answer: Zero

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42. In six node triangular element, the gauss points of a triangular element can be defined by ____

Answer

Correct Answer: One point rule

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43. Six node triangular elements is also known as _____

Answer

Correct Answer: Quadratic triangle

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44. Eight-Node Quadrilateral. This element belongs to the ________ family of elements.

Answer

Correct Answer: Serendipity

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45. A _________ element by using a nine-node shape function.

Answer

Correct Answer: Sub parametric

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46. In the four-node quadrilateral element, the shape functions contained terms _________

Answer

Correct Answer: ξ

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47. Gauss points are also the points used for numerical evaluation of _____ Surfaces

Answer

Correct Answer: E

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48. For degenerate four noded quadrilateral element the errors are _____

Answer

Correct Answer: Higher

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49. For quadrilaterals with 2X2 integration gives _____ sets of stress values.

Answer

Correct Answer: Four

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50. The stresses are evaluated at the __________

Answer

Correct Answer: Gauss points

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51. The stresses in the quadratic element are not ______

Answer

Correct Answer: Constant

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52. Shape functions are linear functions along the _____

Answer

Correct Answer: Edges

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53. For four noded quadrilateral element, the global load vector can be determined by considering the body force term in _____

Answer

Correct Answer: Potential energy

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54. The stiffness matrix from the quadrilateral element can be derived from _____

Answer

Correct Answer: Strain energy

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55. The master element is defined in ______

Answer

Correct Answer: Natural coordinates

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56. For a four noded quadrilateral, we define shape functions on _____

Answer

Correct Answer: Master element

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57. In two dimensional isoparametric elements, we can generate element stiffness matrix by using ____

Answer

Correct Answer: Numerical integration

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58. Increasing the number of nodes in coarse mesh regions where stress variations are high, should give better results. This method is called _____

Answer

Correct Answer: Convergence

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59. Coarser meshes are recommended for _____

Answer

Correct Answer: Initial trails

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60. The _____ can be obtained even with coarser meshes by plotting and extrapolating.

Answer

Correct Answer: Maximum stresses

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61. The Constant strain triangle can give____ stresses on elements.

Answer

Correct Answer: Constant

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62. Stresses can be change widely at ____

Answer

Correct Answer: Notches and fillets

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63. In dividing the elements a good practice may be to choose corner angles in the range of ____

Answer

Correct Answer: 30-120°

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64. When dividing an area into triangles, avoid large _____

Answer

Correct Answer: Aspect ratios

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65. Boundary conditions can be easily considered by using _______

Answer

Correct Answer: Penalty approach method

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66. For a circular pipe under internal or external pressure, by symmetry all points move _____

Answer

Correct Answer: Radially

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67. In deformation of the body, the symmetry of ______ and symmetry of ____ can be used effectively.

Answer

Correct Answer: Geometry and loading

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68. Finite element method is used for computing _____ and _____

Answer

Correct Answer: Displacement and strain

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69. I the distribution of the change in temperature ΔT, the strain due to this change is ____

Answer

Correct Answer: Initial strain

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70. Principal stresses and their directions are calculated by using ____

Answer

Correct Answer: Mohr’s circle method

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71. In the equation KQ=F, K is called as ____

Answer

Correct Answer: Modified stiffness matrix

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72. For plane stress or plane strain, the element stiffness matrix can be obtained by taking _____

Answer

Correct Answer: Material property matrix, D

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73. The equation u=Nq is a _____ representation.

Answer

Correct Answer: Isoparametric

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74. The shape functions are physically represented by _____

Answer

Correct Answer: Area coordinates

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75. In two dimensional problems x-, y- coordinates are mapped onto ____

Answer

Correct Answer: ξ-η-Co-ordinates

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76. In particular, N 1+N 2 +N 3 represent a plane at a height of one at nodes ______

Answer

Correct Answer: One, two and three

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77. Linear combination of these shape functions represents a ______

Answer

Correct Answer: Plane surface

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78. For constant strain elements the shape functions are ____

Answer

Correct Answer: Linear

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79. Finite element method uses the concept of _____

Answer

Correct Answer: Shape functions

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80. The information of array of size and number of elements and nodes per element can be seen in ___

Answer

Correct Answer: Element connectivity table

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81. In two dimensional modelling each node has ____ degrees of freedom.

Answer

Correct Answer: Two

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82. The finite element method is used to solve the problem ______

Answer

Correct Answer: Approximately

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83. Each triangle formed by three nodes and three sides is called a ______

Answer

Correct Answer: Element

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84. In 2D elements. Discretization can be done. The points where triangular elements meet are called ____

Answer

Correct Answer: Nodes

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85. The details of a skyline assembly matrix are implemented in a program called ____

Answer

Correct Answer: Trussky program

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86. The second step in skyline approach is assembling the element stiffness values into _____

Answer

Correct Answer: Column vector

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87. The first step of skyline assembly matrix involves evaluation of ____

Answer

Correct Answer: Column height

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88. In Skyline matrix, the elements in a stiffness matrix can be placed in _______

Answer

Correct Answer: Vector form

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89. In a banded matrix, elements are _____ placed in the stiffness matrix.

Answer

Correct Answer: Directly

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90. Which of these was one of the methods for determining assembly of the global stiffness matrix?

Answer

Correct Answer: Skyline approach

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91. Symmetry and sparsity of the global stiffness matrix can be approached by _____ methods.

Answer

Correct Answer: Two

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