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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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