Fem Objective Bits

MLR INSTITUTE OF TECHNOLOGY Dundigal, Hyderabad - 500 043 MECHANICAL ENGINEERING

UNIT-I

1. The solution by FEM is (a) always exact (b) mostly approximate 2. Primary variable in FEM structural analysis is

(c) sometimes exact

[ B ] (d) never exact [ A]

(a) displacement (b) force (c) stress (d) strain 3. The art of subdividing a structure into convenient number of smaller components is known as [ C] (a) global stiffness matrix (b) force vector (c) discretization 4. _______ is/are the phase/s of finite element method

(d) none [ D]

(a) Preprocessing (b) Solution (c) Post Processing (d) a, b & c 5.The points in the entire structure are defined using coordinates system is known as [ C] (a) local coordinates (b) natural coordinates (c) global coordinate system (d) none 6.Determinant of assembled stiffness matrix before applying boundary conditions is [ B] (a) < 0 (b) = 0 (c) > 0 (d) depends on the problem 7. All the calculations are made at limited number of points known as [A] A) Elements B) Nodes C) descritization D) mesh 8. Displacements and rotations at the end of a beam are accompanied by [C] A) Forces B) moments C) Force reactions and bending moment D) shear stress 9. The minimum number of dimensions are required to define the position of a point in space is: [C ] a) one b) two c) three d) four 10. All the calculations are made at limited number of points known as [A] A) Elements B) Nodes C) descritization D) mesh 11. Displacements and rotations at the end of a beam are accompanied by [C] A) Forces B) moments C) Force reactions and bending moment D) shear stress 12. The finite element methods can be applied in ____________areas. [D] a) Thermal b) soil and rock mechanics c) noise problems d) all 13. If the structure is more complex in order to simplify the model, we need to subdivide the structure in to sub structures. These substructures are termed as [B] a) elements b) modules c) links d ) models 14. Which of the following is not a method for calculation of stiffness matrix? [D] A) Minimum potential energy principle B) Galerkin‟s principle C) Weighted residual method D) Inverse matrix method 15.A small units having definite shape of geometry and nodes is called _Finite element. 16.Each kind of finite element has a specific structural shape and is inter- connected with the

adjacent element by Nodes 17. Ritz method or Ray-Leigh Ritz method is the variation method. 18.Aspect ratio is defined as the ratio of the largest dimension of the element to the smallest dimension. 19.Shape functions are used to express the geometry or shape of the element. 20.Units for point load are N

UNIT-II

1. The element displacement vector q represented by T

A) q = [ q1, q2]

B) q = [ q1, q2]

[ A ] T

C) q = [ q1x q2]

D) q = [ q1/q2]

2.All the calculations are made at limited number of points known as

T

[ A ]

A) Elements B) Nodes C) descritization D) mesh 3.When thin plate is subjected to loading in its own plane only, the condition is called [ A ] A) plane stress B) Plane strain C) zero stress D) zero strain 4.Which of the following is not a method for calculation of stiffness matrix? [ D ] B) Galerkin‟s  principle A) Minimum potential energy principle C) Weighted residual method D) Inverse matrix method 5.Sum of shape functions = [ A ] A) 1 B) 2 C) 3 D) 0 6.Domain is divided into some segment is called [ A ] A) Element B) node C) segment D) points 7.In one dimentional, the stress and strain relation is given by [ A ] A) σ = Ε ∈ B) σ = Ε /∈ C) σ = ∈/ Ε D) σ = Ε - ∈ 8.The art of subdividing a structure into convenient number of smaller components is known as [ C ] (a) global stiffness matrix (b) force vector (c) discretization (d) none 9. _______ is/are the phase/s of finite element method [D] (a) Preprocessing (b) Solution (c) Post Processing (d) a, b & c 10.The characteristics of the shape functions is/are [C] (a) the shape function has unit value at one nodal point and zero value at the other nodes (b) the sum of the shape function is equal to one (c) a & b (d) none 11.The points in the entire structure are defined using coordinates system is known as [C] (a) local coordinates (b) natural coordinates (c) global coordinate system (d) none 12. The finite element methods can be applied in ____________areas. [D] a) Thermal b) soil and rock mechanics c) noise problems d) all 13. If the structure is more complex in order to simplify the model, we need to subdivide the structure in to sub structures. These substructures are termed as [B] a) elements b) modules c) links d ) models 14.Band width of global stiffness matrix depends on D.O.F and system

15.In order of geometric shape function is equal to the order of displacement Shape function is called Isoperimetric 16.The unknown displacement field within an element will be interpolated by a Polynomial 17.If the band width is_Less _computational effort required is less. 18.Linear shape function values lie between _0 & _______1____

1 −1

19.Selection of approximation functions is difficult in Complex 20. The boundary condition which in terms of the field variables is known as Primary boundary condition UNIT-III

1.A plane truss element has a stiffness matrix of order

[ b]

(a) 2 x 2 (b) 4 x 4 (c) 6 x 6 (d) 1 x 1 2. The Pin  joints are used to join the truss members. 3.How many nodes in 3-D brick element [ D ] A) 3 B) 5 C) 6 D) 8 4. The minimum number of dimensions are required to define the position of a point in space is: [C ] a) one b) two c) three d) four 5. The quadratic shape function (N1) at node ‘1’ of the three nodded linear one dimensional element is [ A ] a) -1/2ξ(1- ξ) b) (1- ξ )/2 c) (1+ ξ) / 2 d) (1+ ξ)(1- ξ) Where ξ is natural coordinate 6.The Conceptualization and development of scientific and technological models need a  _____________ both by the creator and the user. [D] a) Greater degree of abstraction b) precision c) profound utility of physical tools d)greater degree of abstraction, precision and profound utility of physical and mathematical tools. 7.Geometrical coordinate systems comprise of locating points in a given space by means of numerical quantities termed as: [B] a) frames b) coordinates c) elements d) local axes 8. The coordinate system limited to the sub-domains is [C] a) local b) global c) continuum d) discrete global 9. If the natural coordinate (ξ) is 10mm, the nodal displacements q1 and q2 are 0.075 mm and - 0.125mm,respectively. Then the linear displacement field (u) is [A] a) 1.025mm b) 10.25 mm c) 2.35mm d) 23.5 mm 10.The total strain energy (U) for the general elastic body is [ B ] T d) (½) ∫v σ ε a) (½) ∫v σ ε dv b) (½) ∫v σ ε ds c) (½) ∫v σ ε dx dx 11.The force acting on the two nodded truss element making an angle ‘θ’ with horizontal plane can be calculated by using the relation (F12) is [ C ] T

a) AE/l [ C,S,C,S][u1,v1,u2,v2]

T

T

 b) AE/l [ C,S,-C,-S][u1,v1,u2,v2]

c) AE/l [ C+S-C+S][u1,v1,u2,v2] d) AE/l [ C+S-C+S][u1,v1,u2,v2] 12. The applications of Finite Element Method in two dimensional analyses are: [ C ] a) stretching of plates b) gravity of dams c) axi-symmetric shells d) all

13.Determinant of assembled stiffness matrix before applying boundary conditions is (a) < 0 (b) = 0 (c) > 0 (d) depends on the problem

[B]

14.Sum of shape functions = [A] A) 1 B) 2 C) 3 D) 0 15.Domain is divided into some segment is called [A] A) Element B) node C) segment D) points 16.The rows of pascals triangle for the generation of the ____family of the triangular elements.[A ] a) Lagrange b) Hermite c) polynomial d) cubic polynomial 17.Element stress can be calculated by using the relation σ = EBq, where „B‟ is element strain displacement matrix‟ that is equal to [1/(X2-X1)] [-1,1] 18.If the body is in a state of equilibrium then the energy is minimum, This is the statement of PRINCIPLE OF MINIMUM POTENTIAL ENERGY 19.The boundary condition which in terms of the field variables is known as PRIMARY BOUNDARY CONDITION 20.The number of independent parameters that are essential for characterizing the system are termed as DEGREES OF FREEDOM

UNIT-IV

The characteristics of the shape functions is/are [ c] (a) the shape function has unit value at one nodal point and zero value at the other nodes (b)the sum of the shape function is equal to one (c) a & b (d) none 2.Displacements and rotations at the end of a beam are accompanied by [ C ] A) Forces B) moments C) Force reactions and bending moment D) shear stress 1.

3. Each

node of a 1-D beam element has _______degrees of freedom

(a) 1 (b) 2 (c) 3 (d) 4 4.The 1-D beam element should have ______ continuity 3

(a) C

2

(b) C

1

(c) C

[ b] [ c]

0

(d) C

5.When the functions and its derivatives are interpolated, the resulting interpolation functions are known as [ D ] a) Lagrange interpolation function b) Hermite family of interpolation functions c) Hermite and Lagrange interpolation functions d) none 6.One of the following is property of the stiffness matrix (K) [ A ] a) K is banded matrix b) K is un-symmetric c)the dimension of global K is (N X N + 1) where N is number of nodes d)K is un-banded matrix

7.Beam finite elements are [ D] A)Related not directly to matrix analysis of structures B)Different from finite elements with do not respect to the order of the governing differential equations C)Used with fourth order ordinary partial differential equations D)Related directly to matrix analysis 8. The element displacement vector q represented by [A] A) q = [ q1, q2]T B) q = [ q1, q2] C) q = [ q1x q2]T D) q = [ q1/q2]T 9. The coordinate system has a unique origin and span the entire domain is [B]

a) local b) global c) continuum d) discrete global 10.Units for point load are N 11.Basic 2-D element (triangular) has 3 no. of nodes. 12.The Strain- Displacement matrix of 1-D bar element is given by [ B] = 1

[ B] =

l 

[− 1 1]

13. The Transverse displacement and rotation at each end of the beam element are treated as the unknown degrees of freedom. 14.The size of stiffness matrix for 1-D, beam element with 2-nodes and 2-DOF is 4 x 4

15. The element stiffness matrix for 1-D beam element is given by [ K ] = 6l  −12 6l  12 [ K  ] =

 EI  l

6l 

4l 

2

−6l 

2l 

2

12 −6l 

−12 −6l 

6l 

2l 

2

−6l 

4l 

2

16. The force necessary to create unit displacement. This is the property of spring termed as STIFFNESS 17. Non-dimensional coordinates such as three independent volumes in a tetrahedral domain termed as VOLUME coordinates. 18.ASPECT RATIO is defined as the ratio of the largest dimension of the element to the smallest dimension. 19. The unknown displacement field within an element will be interpolated by a POLYNOMIAL 20. In order of geometric shape function is equal to the order of displacement Shape function is called ISOPARAMETRIC

UNIT-V

1.The iso-parametric method is possible to use identical set of interpolation functions for approximating [ D ] a) geometry b) field c) geometry or field d) both the geometry and the field. 2.Triangles with straight edges for specifying quadratic fields: this is the category of [ B ] a) Iso-parametric b) sub-parametric c) super-parametric d) none 3.One of the following is not the crack deformation modes [ C ] a) Opening b) sliding c) bending d) tearing 4.Gaussian points are used for [A ] a) Numerical integration b) displacement calculation c) Stress calculation d) strain calculation 5.The process of reducing number of mid-side or internal noses before assembling element stiffness matrices is called [ D ] a) Gauss reduction b) Jacobin reduction c) Choleski reduction d) Static condensation 6.Actual thickness of plane strain element is [ A ] a) Very large b) any specified value c) assumed by software d) assumed by designer 7.In 2-D the equation of element stiffness matrix is ____________ [D ] e e e e a) k  = t A B  D b) k  = t A BDB c) k  = 2t A BDB d) k  = t A B  DB 8.The FEA of plane stress and plane strain problems is identical except _________ [B ]

a) [B] matrix b) [D] matrix c) [U] matrix d) [F] matrix 9.When there are less geometric nodes than shape function nodes then the element is called [ A ] a) sub parametric b) super parametric c ) iso parametric d) a,b,&c 10.The use of same shape functions for both Cartesian coordinate system and natural coordinate system is known as ____________ [A ] c) a&b a) Isoparametric representation b) Numerical integration d) None 11.Actual thickness of plane strain element is [ A] a) Very large b) any specified value c) assumed by software d) assumed by designer 12.The shape function for a four node element is [A ] a)

 b)

(1 −ξ )(1 −η)  N = c(1 −ξ )  N = c(1 −η)  N  = c

c) d) d) none 13.The order of B Matrix for a CST is 3x6 14.If lower order function is used to represent displacement and a higher order function is used to represent geometry it is called Super- parametric T  15. The triangular element stiffness metrics for axi-symmetric body is 2π rAe B  DB 16.Jacobian is a partial derivative of global coordinates with respect to natural coordinates. 17.Three node triangular element can be also called as Constant strain Triangle (CST) 18. A thin plate with in plane loading is example of Plane stress problem 19.“Skyline method of assembly” this is the technique for Storage the matrix with min. space 20. The shape functions of a 2 –  D element in terms of area co-ordinates is N1=A1/A, N2=A2/A,  N3=A3/A UNIT-VI

1.The triangular element stiffness metrics for axi-symmetric body is T

[A] T

a) 2 π r¯ A B¯   D B

d) 2 π r¯ A B  b) 2 π r¯ A D B c) 2 π r¯ B¯ D B 2.If r 1, r 2, r 3 are radial distance of node 1, 2, 3 respectively of the triangular element of [C] Axi-symmetric body: then the radius of centroid r¯ is: a) (r 1 + r 2) / 2

b) r 1/2

c) (r 1 + r 2 + r 3) /3

3.Refines the element size based on solution gradients is called

d) r 3 / 3

[C]

a) Mesh refinement method b) h-method c) Mesh refinement method or h- method d) r method 4.If r1, r2, r3 are radial distances of node 1, 2, 3 respectively of the triangular element of Axisymmetric body: then the radius of centroid r is: [C ] a) (r1 + r2)/2 b) (r1)/2 c) (r1 + r2 + r3)/3 d) (r3) / 3 5.What is the traction force of a 2D body? [B] a) Force per unit areab) force per unit length c) force per unit volume d) all of these 6.For an Axisymmetric triangular element what is the size of the Jacobian Matrix [B] d) 4 x 2 a) 4 x 4 b) 2 x 2 c) 2 x 4 7.Axisymmetric solids subjected to axisymmetric loading, the stress-strain relations are [A] a) σ = D ∈ b) σ = D /∈ d) σ = D - ∈ c) σ = ∈/ D 8.The stiffness matrix for a triangular element in a two dimensional problem is often derived Using   [A]

a) area coordinates  b) Surface coordinates d) mass coordinates c) volume coordinates 9.A constant term in the displacement function ensures [C] a) Constant mode b) zero stress c) rigid body mode d) zero deformation 10.Number of shape functions the quadrilateral plane stress elements are [B] a) 8 b) 4 c) 3 d) 2 11.A 3 noded simply supported beam gives __________ number of frequencies [A] a) 3 b) 7 c) 4 d) 5 12.A linear term in the displacement function ensures [D] a) rigid body mode b) zero deformation c)zero stress d) constant mode 13.If lower order function is used to represent displacement and a higher order function is used to represent geometry it is called Super- parametric 2 14.The interpolation function of displacement for 1-D beam element at node one is [(1 – ξ )  ( 2 + ξ 3 ( 2 –  3 ξ + ξ  ) / 4 )] / 4 or 15.The number of node along the side of a 2-D or 3- D element decide the Order of displacement  polynomial 16.(Max.  node number difference for any one element + 1) X number of DOF per node is _Half  band width (b) 17.The size of stress- strain matrix for axi-symmetric element is 3 x 3 18.The analysis of long cylinders such as tunnel, culvert or buried pipe is example of _ Plain strain  problem 19. In axi-symmetric problem geometry and loading is independent of Angle of rotation „θ‟ 20.Most FEM software use Displacement method Method UNIT-VII

1.The governing equation for convection process is a) q = h A Ts b) q = h A[ Th - Ts] c) q = h A Th 2.Number of DOF per node in a triangular thermal element is a) 4 b) 1 c) 3 3. The governing equation for convection process is

[D] d) q = h A [ Ts - Th ] [C ] d) 2 [D]

4. Conductance matrix is the equivalent of stiffness matrix in _____ analysis [C] a) dynamic b) fluid flow c)thermal d) static structural 5. Number of DOF per node in a triangular thermal element is _________ [C] a) 4 b) 1 c) 3 d) 2 6.Conductance matrix is the equivalent of stiffness matrix in _____ analysis [C] a) dynamic b) fluid flow c)thermal d) static structural 7.Conductance matrix is the equivalent of stiffness matrix in THERMAL analysis. 8.In a 1D steady state heat transfer problem, the shape function matrix is N= [N1,N2] 9.Thermal conductivity Kx=Ky=Kz in case of ISOTROPIC material. 10.A fin is an external surface which is added on to a surface to increase the RATE OF HEAT TRANSFER 11.Only [ D ] matrix is different in case of plane strain and plane stress. 12. Heat transfer occurs when there is a temperature difference within a body or between a body and its surrounding medium. 13.When fewer nodes are used to define the geometry than are used to define the shape function, the element is termed as Sub-parametric 2 14.Units for convection heat transfer coefficient is w/m  K

15.The consistent mass matrix size for beam element is 4x4 16.In a 1D steady state heat transfer problem, the shape function matrix is N=[ N1,N2] 17.The consistent mass matrix size for bar element is 2x2 18.Thermal conductivity K x=K y=K z in case of Isotropic material. 19.The shape functions of a 2  –   D element in terms of area co-ordinates is N1=A1/A, N2=A2/A,  N3=A3/A 20.A fin is an external surface which is added on to a surface to increase the Rate of heat transfer UNIT-VIII

1.Deformed shape in ANSYS is drawn with a) Actual nodded displacements b) Normalized nodded displacements c) Magnified nodded displacements d) Reduced nodded displacement 2. The Eigen vector is to be non- trivial, the required condition is

[C]

[ C]

a) (k − λ M )U = 0 b) (k − λ M )= 0 c) det(k − λ M )= 0 d) det(k − λ M )U = 0 3.The equation of Langrangean in dynamic analysis [ A] d) none a) L = T −π  b) L = T +π  c) L =T  /π  4. A 3 noded simply supported beam gives _______ number of frequencies [A] a) 3 b) 7 c) 4 d) 5 5.The points in the entire structure are defined using coordinates system is known as [ C] (a) local coordinates (b) natural coordinates (c) global coordinate system (d) none 6.Determinant of assembled stiffness matrix before applying boundary conditions is [ B] (a) < 0 (b) = 0 (c) > 0 (d) depends on the problem 7.In one dimentional, the stress and strain relation is given by [ A ] A) σ = Ε ∈ B) σ = Ε /∈ C) σ = ∈/ Ε D) σ = Ε - ∈ 8.The art of subdividing a structure into convenient number of smaller components is known as [ C ] (a) global stiffness matrix (b) force vector (c) discretization (d) none 9.Sum of shape functions = [A] A) 1 B) 2 C) 3 D) 0 10.Domain is divided into some segment is called [A] A) Element B) node C) segment D) points 11. Principal modes of vibration of a multi-dof system are ORTHOGONAL 12.Most FEM software use DISPLACEMENT Method 13.Natural frequencies obtained with lumped mass matrix are LOWER than those obtained with consistent mass matrix when the mode shapes are practically same. 14.The consistent mass matrix size for bar element is 2X2 15.The consistent mass matrix size for beam element is 4X4 16.Many general purpose software such as, ANSYS, NISA, NASTRAN, ASKA, etc are used to do the analysis of mechanical, civil and aircraft structures based on FEM. The data to be input to tress software generally is SAME 17.The boundary condition which in terms of the field variables is known as PRIMARY BOUNDARY CONDITION 18.The number of independent parameters that are essential for characterizing the system are termed as DEGREES OF FREEDOM 19.The units of stresses in most Fem software are given by UNITS BASED ON INPUT DATA 20.Conductance matrix is the equivalent of stiffness matrix in Thermal analysis.