Finite Elements Methods Imp Questions – FEM Imp Questions 2020

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Finite Elements Methods (FEM) -Question Bank

Finite Elements Methods UNIT – I

  • Using a potential energy approach, describe FE formulation for plane truss Element.
  • Define the principle of virtual work. Describe the FEM formulation for 1D bar element.
  • Using a variational approach (potential energy), describe FE formulation for 1D bar element.

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Finite Elements Methods UNIT – II

  • Explain the elimination method and the penalty method for imposing specified displacement boundary conditions
  • Derive the strain displacement matrices for a triangular element of
    revolving body.
  • Differentiate among Bar element, Truss element and Beam element indicating D.O.F and geometry characteristics.

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Finite Elements Methods UNIT-III

  • Derive the stiffness matrix for
    1
    a 2D truss Element.
  • Derive the Stiffness matrix for a 3D truss Element.

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Finite Elements Methods UNIT-IV

  • Derive the Hermite shape functions for beam element.
  • Derive the Hermite shape functions for beam element.
  • Draw beam element in a global and intrinsic coordinate system.

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Finite Elements Methods UNIT – V

  • Write short notes on Gaussian quadrature integration techniques
  • Derive the strain displacement matrix for a triangular element.
  • Explain Iso-parametric, sub-parametric and super-parametric element

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Finite Elements Methods UNIT – VI

  • for the Isoparametric quadrilateral element shown in fig, determine the local coordinates of the point P whose Cartesian co=ordinatesas(6,4)
  • Explain the concept of numerical integration and its utility in generating Isoperimetric finite element matrices.
  • Derive the a)shape function and b) strain displacement matrices for a triangular element of a revolving body

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Finite Elements Methods UNIT – VII

  • Derive the Strain displacement Matrix for a 2D-Thin plate. Consider the temperature field within the triangular element is given by T= N1T1 + N2T2 + N3T3.

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Finite Elements Methods UNIT – VIII

  • corresponding eigenvectors and mode shapes. take EI=FLEXURALRIGIDITY and density =ρ .A=AREA and LENGTH= L.
  • State the properties of Eigen Values.
  • Evaluate natural frequencies for the CANTILEVER beam shown in fig USING ONE ELEMENT.

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