Finite Element Model MCQ

Test your knowledge with important Finite Element Model MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Finite Element Model MCQs at Bissoy

• In FEM, which option is a negative aspect of the mixed formulation?
  ক

  Presence of zeros on matrix diagonals corresponding to pressure variable

  খ

  Involves a natural and direct formulation

  গ

  It is a velocity-pressure formulation

  ঘ

  It is similar to the Lagrange multiplier method
• For the functional IL(v,λ)≡Iv(v)+∫ΩcλG(v)dxdy, what is the necessary condition for IL to have a stationary value?
  ক

  δvxIL+δvyIL+δλIL=0

  খ

  δvxIL-δvyIL-δλIL=0

  গ

  δvxIL-δvyIL+δλIL=0

  ঘ

  δvxIL+δvyIL-δλIL=0
• In the Lagrange multiplier method, a constrained problem is reformulated as one of finding the stationary points of an unconstrained function, whereas in the penalty method, a problem with differential constraints is reformulated to one without constraints.
  ক

  True

  খ

  False
• In the finite element method, which option is not a natural and direct formulation of momentum and continuity equations?
  ক

  Velocity-pressure formulation

  খ

  Penalty formulation

  গ

  Mixed formulation

  ঘ

  Lagrange multiplier formulation
• Which option is correct regarding constraints in the viscous flow problems governed by the continuity and momentum equation?
  ক

  Constrains are readily available

  খ

  Constraints are created by the elimination of pressure

  গ

  Constraints are created by the elimination of velocity

  ঘ

  No constraints are dealt with in penalty formulation
• Which option is not correct concerning the bilinear term B(v,w) in the variational problem of the viscous fluid flow equation?
  ক

  It is symmetric

  খ

  It contains the viscosity matrix

  গ

  Bv(w,v)= Bv(v,w)

  ঘ

  It is bilinear in both w and v
• In the weak forms of the fluid flow model, since the weight functions are linearly dependent on each other, the sum of the three weak forms is the same as the three individual equations.
  ক

  True

  খ

  False
• In the following variational problem of finding velocity components and pressure, which bilinear form includes time-derivative terms? Bt(w,v)+Bv(w,v)-B̅p(w,P)=l(w); –Bp(w3, v)=0
  ক

  Bt(w,v)

  খ

  Bv(w,v)

  গ

  B̅p(w,P)

  ঘ

  Bp(w3,v)
• In finite element modeling, which formulation introduces constraints on variables and satisfies them in an approximate sense?
  ক

  Velocity-pressure formulation

  খ

  Penalty formulation

  গ

  Mixed formulation

  ঘ

  Lagrange multiplier formulation
• In the penalty formulation of the fluid flow model, if the velocity field (vx, vy ) satisfies the continuity equation, then the weight functions (w1, w2) also satisfy the continuity equation.
  ক

  True

  খ

  False
• In the interest of the simple formulation of viscous flows, which case does not involve time derivative terms?
  ক

  Static case

  খ

  Transient case

  গ

  Unsteady case

  ঘ

  Non-periodic
• Which type of problem can be obtained by reformulating a problem with differential constraints by using the penalty method?
  ক

  A problem with no constraints

  খ

  A problem with variable constraints

  গ

  A problem with fixed constraints

  ঘ

  A problem with structural constraints
• What is the other name of a linear triangular element for plane elasticity problems?
  ক

  Constant-strain triangle

  খ

  Linear-strain triangle

  গ

  Quadratic-strain triangle

  ঘ

  Variable-strain triangle
• What is the correct statement regarding the shape function S of a linear triangular element?
  ক

  The first derivatives of S and hence, all the strains are element-wise constant

  খ

  The first derivatives of S are linear, but the strains are element-wise constant

  গ

  The first derivatives of S and hence the strains are linear functions

  ঘ

  The first derivatives of S are element-wise constant, but the strains are linear
• What are the simplest elements that fit for the finite element model of the plane elasticity equations?
  ক

  Linear triangular and quadratic quadrilateral elements

  খ

  Quadratic triangular and linear quadrilateral elements

  গ

  Linear triangular and linear quadrilateral elements

  ঘ

  Quadratic triangular and quadratic quadrilateral elements
• Which interpolation functions must be used for the primary variables in weak forms of plane elasticity equations?
  ক

  Hermite family interpolation function

  খ

  Lagrange family interpolation function

  গ

  Hierarchical interpolation function

  ঘ

  Quadratic interpolation function
• What can one conclude about the displacement components ux and uy in the finite element model of the plane elasticity equations?
  ক

  They are primary variables and must be carried as primary nodal degrees of freedom

  খ

  They are secondary variables and must be carried as primary nodal degrees of freedom

  গ

  They are primary variables and must be carried as secondary nodal degrees of freedom

  ঘ

  They are secondary variables and must be carried as secondary nodal degrees of freedom
• In FEM, if two independent variables are components of the same vector, then they can be approximated by two different types of interpolations.
  ক

  True

  খ

  False
• If only the first derivatives of ux and uy appear in the weak forms, then their interpolation must be at least bilinear.
  ক

  True

  খ

  False