# Finite Element Analysys [FEA] MCQ with Answer - Part 1.

Q.no 1. Parent element of four nodded Isoparametric quadrilateral element in natural coordinate system is

A : Eight nodded rectangular element

B : Four nodded rectangular element

C : Nine nodded rectangular element

D : Twelve nodded rectangular element

Answer :- B

Parent element of four nodded isoparametric quadrilateral element in narural coordinate system is four nodded rectangular element.

Q.no 2. When displacement nodes are greater than geometry nodes, it is known as

A : Isoparametric

B : Subparametric

C : Superperametric

D : CST

Answer :- B

When displacement nodes are greater than geometry nodes it is known as subparametric.

Q.no 3. Isoparametric finite elements are based on the parametric definition of

A : both coordinate and displacement functions.

B : coordinates functions only

C : displacements functions only

D : boundary conditions

Answer :- A

Isoparametric finite elements are based on the parametric defination of both coordinate and displacement function.

Q.no 4. Pick the correct statement

A : Flat shell elements are created by combining plane and bending plate elements.

B : Flat shell elements are always higher order elements.

C : Flat shell elements are necessarily 3-D elements

D : Flat shell's elements can be analysed using kirchoff's plate theory

Answer :- A

Q.no 5. The following methods assumes that trial functions over entire solution

A : Finite Element Method

B : Finite Difference Method

C : Rayleigh-Ritz method

D : Central Difference method

Answer :- C

Q.no 6. No of coeficients in an displacement function are equal to

A : no. of nodes x dof per node

B : Total no of degrees of freedom x degree of the equation

C : Rigid body displacement term plus total degrees of freedom

D : Degrees of freedom per node.

Answer :- A

No of coeficients in an displacement function are equal to no of nodes x dof per node.

Q.no 7. When displacements and geometry nodes are equal, it is known as

A : Isoparametric

B : Subparametric

C : Superperametric

D : CST

Answer :- A

Q.no 8. For four nodded serendipity element which condition is true?

A : Nodes at corner only

B : Nodes on middle of the edges

C : One node must be at center

D : nodes anywhere on the element

Answer :- A

Q.no 9. Principle of the stationary value of the potential energy is also called as

A : Principle of virtual work

B : Principle of work energy

C : Principle of conservation momentum

D : Principle of minimum potential energy

Answer :- D

Q.no 10. Number of shape functions in two nodded bar element are

A : 2

B : 3

C : 4

D : 6

Answer :- A

Q.no 11. Why do we need a Jacobian matrix in the finite element method?

A : The Jacobian matrix is required to determine displacements

B : The Jacobian matrix is required to determine stresses

C : The Jacobian matrix is required to determine strains

D : The Jacobian matrix is required to map the natural coordinate system to the cartesian coordinate system.

Answer :- D

Q.no 12. Stress -strain relationship matrix of axisymmetric element consists of terms related to

A : radial distance r and angular deformation Theta

B : angular deformation theta and z coordinate

C : poisson's ratio and modulus of elasticity

D : z coordinate and radial distance

Answer :- C

Q.no 13. If a domain is discretized into N linear 1-D elements, then the number of nodes will be

A : N

B : N plus 1

C : N minus 1

D : 2N

Answer :- B

Q.no 14. Stresses normal to the plate is neglected in

A : Mindlin Theory

B : Kirchhoff Theory

C : Membrane theory

D : Bending and Membrane theory

Answer :- B

Q.no 15. The art of subdividing a structure into a convenient number of smaller components in finite element analysis is known as

A : triangulation

B : grid

C : descretization.

D : division

Answer :- C

Q.no 16. When geometry nodes are greater than displacement nodes, it is known as

A : Isoparametric

B : Subparametric

C : Superperametric

D : CST

Answer :- C

Q.no 17. The displacement function U for 1 dimensional two node linear element using standard notations in terms of shape function will be

A : u equals to N1X1 plus N2X2

B : u equals to N2X1 plus N1X2

C : u equals to N1U2 plus N2U1

D : u equals to N1U1 plus N2U2

Answer :- D

Q.no 18. Sum of the shape functions is

A : between -1 to 1

B : always 1

C : always zero

D : any number

Answer :- B

Q.no 19. In variational principles, which of the following quantities are to be used.

A : Scalar

B : Vector

C : Both Scalar and Vector

D : 0

Answer :- A

Q.no 20. Which statement is not true when related to degenerated solid element

A : Degenerated solid shell elements may be formed from regular elements by defining duplicate node numbers.

B : A degenerated element is an element whose characteristic face shape is quadrilateral, but is modeled with at least one triangular face

C : Degenerated elements are often used for modeling transition regions between fine and coarse meshes, or for modeling irregular and warped surfaces.

D : A degenerated element is an element is plane 2-D element.

Answer :- D

Q.no 21. Number of shape functions for 3D hexahedron element with nodes at corners only in natural coordinate system are

A : 2

B : 4

C : 6

D : 8

Answer :- D

Q.no 22. The degrees of freedom for regular flat shell elments are

A : three translations and two rotations

B : three translations and three rotations

C : two translation and two rotations

D : one translation normal to plane and two rotations

Answer :- A

Q.no 23. Pascals Triangle is used for writng

A : stress equation

B : displacement equation

C : stress strain equation

D : stiffness terms

Answer :- B

Q.no 24. Number of shape functions in two nodded beam element are

A : 2

B : 3

C : 4

D : 6

Answer :- C

Q.no 25. Which is not example of serendipity rectangular element?

A : 8 nodded element

B : 12 nodded element

C : 4 nodded element

D : 9 nodded element

Answer :- D

Q.no 26. What is the value of shape function at middle node of three nodded bar element in natural coordinate system

A :

B :

C :

D :

Q.no 27. How many nodes are there in a tetrahedron element?

A : 3

B : 4

C : 6

D : 8

Answer :- B

Q.no 28. As per the theory of thin plate with small deflection, the ratio of thickness to span (R) should be

A : R > (1/10)

B : R > (1/15)

C : R < (1/10)

D : R < (1/5)

Answer :- A

Q.no 29. For CST element, if N1=0.3 and N2-0.2 what is the value of N3

A : 0.6

B : 0.4

C : 0.7

D : 0.5

Answer :- D

Q.no 30. The variational principle corresponding to the weak form of elasticity is called as

A : Theorem of minimum potential energy

B : Theorem of maximum potential energy

C : Theorem of least square

D : All theorems

Answer :- A

Q.no 31. As per the theory of thin plate with small deformation, The ratio of maximum deflection to thickness (S) should be

A : S > (1/5)

B : S > (1/10)

C : S < (1/5)

D : S < (1/10)

Answer :- C

Q.no 32. Which is not the characteristic of CST element

A : The strain displacement matrix for CST element is a single term matrix

B : The variation of displacement field variable will be flat for CST element

C : The displacement function for CST is linear functio

D : The strain remains constant over the elment.

Answer :- A

Q.no 33. Choose the correct statement

A : Principle of minimum potential energy states among all the displacement equations that internal

compatibility and the boundary condition those that also satisfy the equation of equilibrium make the

potential energy a minimum is a unstable system

B : Principle of Virtual work states among all the displacement equations that internal compatibility and the boundary condition those that also satisfy the equation of equilibrium make the potential energy a minimum is a stable system

C : Principle of minimum potential energy states among all the displacement equations that internal compatibility and the boundary condition those that also satisfy the equation of equilibrium make the potential energy a maximum is a stable system

D : Principle of minimum potential energy states among all the displacement equations that internal compatibility and the boundary condition those that also satisfy the equation of equilibrium make the potential energy a minimum is a stable system.

Answer :- D

Q.no 34. The shear deformation in plate is considered using following theory

A : Bernoulli theory

B : Timoshenko Theory

C : Kirchhoff Theory

D : Mindlin Theory

Answer :- D

Q.no 35. Accuracy of solution in finite element can be increased by

A : Using higher order element

B : adopting grid refinement

C : Selection of proper displacement function

D : adopting all the three options

Answer :- D

Q.no 36. For constant strain triangle element, the shape function is

A : N1+N2+N3=1

B : N1+N2+N3=0

C : N1+N2+N3=3

D : N1+N2+N3=4

Answer :- A

Q.no 37. The following method assumes trial functions only over an element.

A : Rayleigh-Ritz method

B : Method of least square

C : Galerkin method

D : Finite Element Method.

Answer :- D

Q.no 38. The eight node quadrilateral element belongs to which family of elements?

A : Serendipity

B : Lagrange

C : Octane

D : interdipity

Answer :- A

Q.no 39. This form states the condition that must be met at every material point

A : Strong Form

B : Weak Form

C : Both Strong and Weak Form

D : Neither Strong nor Weak Form

Answer :- A

Q.no 40. This form states the condition that must be met only in an average sense.

A : Strong Form

B : Weak Form

C : Both Strong and Weak Form

D : Neither Strong nor Weak Form

Answer :- B

Q.no 41. w, qx, and qy are considered in

A : Mindlin element

B : Kirchhoff-Love element

C : ACM element

D : BFS element

Answer :- A

Q.no 42. Axis-Symmetric element is

A : 3D element only

B : 2D element only

C : 1D element only

D : Both 2D and 1D elements

Answer :- D

Q.no 43. If the plate thickness to span ratio is less than (1/10) then it is called as

A : Thin plate with small deformation

B : Thin plate with large deformation

C : Thick Plate

D : Moderately thick plate

Answer :- A

Q.no 44. How many nodes are there in a hexahedron element?

A : 3

B : 4

C : 6

D : 8

Answer :- D

Q.no 45. Shape functions for 1D Isoparametric elements are

A :

B :

C :

D :

Q.no 46. The following integral formulation is used in weighted residual method. Identify the form of integral

A : Linear form

B : Bilinear Form

C : Quadratic Form

D : Cubic Form

Answer :- A

Q.no 47. Determine the Cartesian coordinates of any point P if N1=0.05, N2=0.15, N3=0.6 and N4=0.2. Coordinates of nodes are x1=2, x2=8, x3=7, x4=3, y1=1, y2=3, y3=7, y4=5.

A : 6.1, 5.7

B : 1.6, 7.5

C : 6.7, 5.1

D : 6.6, 5.5

Answer :- A

Q.no 48. Which statement is not true when related to curved shell elements

A : It is assumed that the normal stress component in the normal direction of a lamina basis is forced to

zero

B : It is assumed that the normal strain component in the normal direction of a lamina basis is forced to

zero

C : For curved shell elemnts , it is assumed that normals remain straight, but not necessarily normal to

the reference surface

D : Transverse shear deformation is included.

Answer :- B

Q.no 49. The following element is only used in non conforming variational correctness.

A : Kirchhoff-Love element

B : BFS element

C : ACM element

D : Mindlin element

Answer :- C

Q.no 50. Classical thin plate theory is called as

A : Kirchhoff Theory

B : Mindlin Theory

C : Membrane theory

D : Bending and Membrane theory

Answer :- A

Q.no 51. Which is not the characteristic of Flat shell element?

A : The Flat shell element must plane, i.e., the coordinates of the element nodes must be in one plane.

B : Force loads F may act in any direction between perpendicular to the plane and in the plane

C : Moment loads M must act in the plane of the element.

D : They must be thick and the variation of stresses take place along the thickness of element

Answer :- D

Q.no 52. For 1-D bar elements if the structure is having 3 nodes then the stiffness matrix formed is having an order of

A : 2x2

B : 3x3

C : 4x4

D : 1x1

Answer :- B

Q.no 53. Which is not a convergenece requirement of the displacement function

A : The displacement function should consists of constant strain term

B : The displacement function should have rigid body displacement term

C : The displacement function should be geometrically invariant

D : The displacement function should be continous function

Answer :- C

Q.no 54. If natural coordinates xi=0.5, eta=0.6, the values of shape functions of four nodded Isoparametric rectangular element in natural coordinates are

A : 0.5, 0.15, 0.6, 0.2

B : 0.05, 0.5, 0.6, 0.2

C : 0.05, 0.15, 0.6, 0.2

D : 0.5, 0.5, 0.6, 0.2

Answer :- C

Q.no 55. If the length of element is 5mm , cross section area is 20 mm2 and E is 210 GPa, the axial stiffness is

A : 5x210000000/20

B : 5x20/210000000

C : 20x210000000/5

D : none of the givn options

Answer :- C

Q.no 56. Consider a bar of uniform cross section as shown in figure. The distributed force acting on the bar is varying linearly with ‘x’, thus identify the proper polynomial functions for approximation of solution.

A : u(x) = a1 x + a2 x2

B : u(x) = a1 x

C : u(x) = a1 x + a2 y + a3 x2

D : u(x) = a1 x + a2 xy + a3 x2

Answer :- A

Q.no 57. four nodded rectangular element in natural coordinate system belongs to

A : lagrangence family

B : Serendipity family

C : Both lagrangence and serendipity families

D : Neither lagrangence or serendipity families

Answer :- C

Q.no 58. The following integral formulation is used in weighted residual method. Identify the form of integral

A : Linear form

B : Bilinear Form

C : Quadratic Form

D : Cubic Form

Answer :- B

Q.no 59. For an axial bar divided into three elements, which of the following statements is not true?

A : The size of global stiffness matrix is 8X8.

B : The size of global primary variable vector is 4X1.

C : The size of global force vector is 4X1.

D : The size of local stiffness matrix will be 2X2.

Answer :- D

Q.no 60. Shape functions for two noded beam bending element

A : At node 1; x = 0 N1 = 1, N2 = 0, N3 = 0, N4 = 0 and At node 1; x = L N1 = 0, N2 = 0, N3 = 1, N4

= 0

B : At node 1; x = 0 N1 = 0, N2 = 1, N3 = 0, N4 = 0 and At node 1; x = L N1 = 0, N2 = 0, N3 =0 , N4

= 1

C : At node 1; x = 0 N1 = 1, N2 = 1, N3 = 0, N4 = 0 and At node 1; x = L N1 = 0, N2 = 1, N3 = 1, N4

= 0

D : N1+N2+N3+N4=1

Answer :- A

Q No 61 : 6. A A-1=A-1A is a condition for ........

A) Matrix inversion

B) Ad joint of matrix

C) Singular matrix

D) Nonsingular matrix

Answer: A

Explanation: If det A not equal to zero, then A has an inverse, denoted by A-1. The inverse satisfies the relation

A A-1 =A-1A= I

Q No 65 : A banded matrix is defined as ............

A) Non zero elements are contained in band

B) Non zero elements are contained out of a band

C) Zero elements are contained in a band

D) Both Non zero elements and Zero elements

Answer: A

Explanation: A band matrix is a sparse matrix whose non zero entries are confined to a diagonal band. In a banded matrix, all of the non zero elements are contained within a band; outside of the band all elements are zero.

Q No 66 : Step number in Gaussian elimination is denoted as ..............

A) Elimination

B) Subscript

C) Superscript

D) Unknown

Answer: C

Explanation: Gaussian elimination is an algorithm for solving systems of linear equations. The idea at step 1 is to use equation 1 (first row) in eliminating x1 from remaining equations. We know the step numbers as superscript set in parentheses.