3.1) Name few 2-D elements along with a neat sketch.
3.2) State the differences between 2D element and 1D element.
3.3) Define Lagrange’s interpolation.
3.4) What is geometric Isotropy? [AU, May / June – 2013]
3.5) Write the Lagrangean shape functions for a 1D, 2 noded elements.
[AU, Nov / Dec – 2008]
3.6) Obtain the shape function for a 1D quadratic Isoparametric element.
3.7) Write the relation to obtain the size of the stiffness matrix for a linear quadrilateral element having Ux and Uy as dof.
3.8) Why is the 3 noded triangular element called as a CST element?
[AU, Nov / Dec – 2010]
3.9) Write down the interpolation function of a field variable for three-node triangular
element. [AU, April / May – 2010]
3.10) What is a CST element? [AU, April / May – 2011]
3.11) Draw the shape functions of a CST element. [AU, Nov / Dec – 2010]
3.12) Explain the important properties of CST elements. [AU, Nov / Dec – 2008]
3.13) Write a note on CST element. [AU, May / June – 2011]
3.14) Write briefly about LST and QST elements.
3.15) What are CST and LST elements? [AU, Nov / Dec – 2009]
3.16) Define LST element. [AU, Nov / Dec – 2012]
3.17) Write the displacement function equation for CST element.
3.18) Write the strain – displacement matrix for CST element.
3.19) Differentiate CST and LST elements. [AU, Nov / Dec – 2007, April / May – 2009]
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 38
3.20) Evaluate the following area integrals for the three node triangular element
∫ [AU, May / June – 2012]
3.21) A triangular element is shown in Figure and the nodal coordinates are expressed in mm. Compute the strain displacement matrix. [AU, Nov / Dec – 2012]
3.22) What do you mean by the terms : c0,c1 and cn continuity?
[AU, April / May – 2010]
3.23) Distinguish between C0, C1 and C2 continuity elements.
3.24) What are the different problems governed by 2D scalar field variables?
3.25) Use various number of triangular elements to mesh the given domain in the order of increasing solution refinement.
3.26) Define Pascal triangle.
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 39
3.27) Write the significance of Pascal triangle in developing triangular elements.
3.28) Distinguish one from the other of the following
a) Linear and quadratic triangular elements. b) Linear and quadratic Lagrange elements.
3.29) What do you mean by area co-ordinate method?
3.30) State the advantage of serendipity element.
3.31) What do you mean by wrapping?
3.36) State the condition for plane stress problem.
3.37) Give one example each for plane stress and plane strain problems.
[AU, Nov / Dec – 2008]
3.38) Distinguish between plane stress and plane strain problems. [AU, Nov / Dec – 2009]
3.39) Distinguish plane stress and plane strain conditions. [AU, Nov / Dec – 2010]
3.40) Define plane strain with suitable example. [AU, Nov / Dec – 2012]
3.41) Define plane strain analysis. [AU, Nov / Dec – 2011]
3.42) Define a plane stress problem with a suitable example. [AU, May / June – 2013]
3.43) Explain plane stress problem with an example. [AU, April / May – 2011]
3.44) Explain plane stress conditions with example. [AU, May / June – 2011]
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 40
3.45) Write down the strain displacement relation. [AU, April / May – 2011]
3.46) State whether plane stress or plane strain elements can be used to model the following structures. Justify your answer. [AU, Nov / Dec – 2012]
(a) A wall subjected to wind load
(b) A wrench subjected to a force in the plane of the wrench.
3.47) Write the assumptions used to define the given problem as plane stress problem.
3.48) Write the assumptions used to define the given problem as plane strain problem.
3.49) Using general stress - strain relation, obtain plane stress equation.
3.50) Beginning with general elastic stress-strain relation, derive the plane strain condition.
3.51) What are the differences between 2 Dimensional scalar variable and vector variable
elements? [AU, Nov / Dec – 2009]
3.52) What are the ways by which a three dimensional problem can be reduced to a two dimensional problem?
3.53) How to reduce a 3D problem into a 2D problem? [AU, Nov / Dec – 2012]
3.54) Give the stiffness matrix equation for an axisymmetric triangular element.
3.55) What is axisymmetric element?
3.56) Give examples of axisymmetric problems. [AU, May / June – 2012]
3.57) What is an axisymmetric problem? [AU, April / May – 2011]
3.58) Write short notes on axisymmetric problems.
[AU, Nov / Dec – 2007, April / May – 2009]
3.59) What is meant by axi-symetric field problem? Given an example.
[AU, Nov / Dec – 2009]
3.60) State the situations where the axisymmetric formulation can be applied.
[AU, April / May – 2011]
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 41
3.61) Give four applications where axisymmetric elements can be used.
[AU, April / May – 2011]
3.62) State the applications of axisymmetric elements. [AU, Nov / Dec – 2010]
3.63) Write down the constitutive relationship for axisymmetric problem.
[AU, April / May – 2009]
3.64) Write down the constitutive relationship for the plane stress problem.
[AU, Nov / Dec – 2010]
3.68) Give a brief note on static condensation.
3.69) Prove that 2 0 for plane strain condition.
3.70) Differentiate axi – symmetric and cyclic –symmetric structures.
3.71) Differentiate axi-symmetric load and asymmetric load with examples.
3.72) State the condition for axi-symmetric problem.
3.73) List the required conditions for a problem assumed to be axisymmetric.
[AU, April / May – 2010]
3.74) What are the four basic sets of elasticity equations? [AU, May / June – 2012]
3.75) Give examples for the following cases.
a) plane stress problem b) plane strain problem c) axi-symmetric problem 3.76) Define the following terms with suitable examples [AU, April / May – 2010]
i) Plane stress, plane strain ii) Node, element and shape functions iii) Axisymmetric analysis iv) Iso – parametric element
3.77) Define the term initial strain.
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 42
3.78) State the effect of Poisson’s ratio in plane strain problem.
3.79) How will the stress field vary linearly?
3.80) Compare the changes in the D matrix evolved out of plane strain, plane stress and axi-symmetric problem.
3.81) What do you mean by Isoparametric formulations?
[AU, Nov / Dec – 2007, April / May – 2009]
3.82) Express the shape functions of four node quadrilateral element.
[AU, May / June – 2012]
3.86) What are the advantages of natural coordinates over global co-ordinates?
[AU, Nov / Dec – 2008]
3.87) Give a brief note on natural co-ordinate system.
3.88) Write the natural co-ordinates for the point “P” of the triangular element. The point
‘P’ is the C.G. of the triangle. [AU, Nov / Dec – 2008]
3.89) Show the transformation for mapping x-coordinate system onto a natural coordinate system for a linear spar element and for a quadratic spar element.
[AU, Nov / Dec – 2012]
3.90) Define a local co – ordinate system. [AU, Nov / Dec – 2011]
3.91) What is area co – ordinates? [AU, Nov / Dec – 2011]
3.92) What do you understand by area co – ordinates? [AU, April / May – 2011]
3.93) State the basic laws on which Isoparametric concept is developed.
[AU, April / May – 2008]
3.94) Differentiate: local axis and global axis. [AU, April / May – 2008]
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 43
3.95) Define super parametric element. [AU, April / May – 2009]
3.96) Explain super parametric element. [AU, Nov / Dec – 2010]
3.97) Define Isoparametric elements? [AU, Nov / Dec – 2008]
3.98) Define Isoparametric elements with suitable examples [AU, April / May – 2010]
3.99) Define Isoparametric element formulations. [AU, Nov / Dec – 2012]
3.100) What do you mean by Isoparametric formulation? [AU, April / May – 2011]
3.101) What is the purpose of Isoparametric elements?
3.102) What are the applications of Isoparametric elements? [AU, April / May – 2011]
3.103) Differentiate x – y space and - space.
3.104) Write the advantages of co-ordinate transformation from Cartesian co-ordinates to natural co-ordinates.
3.105) What is a Jacobian? [AU, Nov / Dec – 2010]
3.106) What is the need of Jacobian? [AU, April / May – 2011]
3.107) Write down the Jacobian matrix. [AU, Nov / Dec – 2010]
3.108) Write about Jacobian transformation used in co-ordinate transformation.
3.109) What is the significance of Jacobian of transformation? [AU, May / June – 2012]
3.110) Differentiate between sub-parametric, iso- parametric and super – parametric elements.
3.111) Represent the variation of shape function with respect to nodes for quadratic elements in terms of natural co-ordinates.
3.112) Compare linear model, quadratic model and cubic model in terms of natural co-ordinate system.
3.113) Write a brief note on continuity and compatibility.
3.114) Write down the element force vector equation for a four noded quadrilateral element.
3.115) Write down the Jacobian matrix for a four noded quadrilateral element
FINITE ELEMENT ANALYSIS QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 44
3.116) Write the shape function for the quadrilateral element in , space.
3.117) Why is four noded quadrilateral element is preferred for axi-symmetric problem than three noded triangular element?
3.118) Sketch a four node quadrilateral element along with nodal degrees of freedom.
[AU, April / May – 2011]
3.119) Write down the stiffness matrix for four noded quadrilateral elements.
[AU, May / June – 2011]
3.120) Distinguish between essential boundary conditions and natural boundary
conditions. [AU, Nov / Dec – 2009]
3.121) Write the advantages of higher order elements in natural co – ordinate system.
3.122) What are the types of non-linearity?
[AU, Nov / Dec – 2007, April / May – 2009, May / June – 2012]
3.123) State the advantage of Gaussian integration.
3.124) State the four-point Gaussian quadrature rule.
3.125) Briefly explain Gaussian quadrature. [AU, April / May – 2011]
3.126) What are the advantages of Gaussian quadrature? [AU, Nov / Dec – 2012]
3.127) What are the weights and sampling points of two point formula of Gauss
quadrature formula? [AU, May / June – 2012]
3.128) Why numerical integration is required for evaluation of stiffness matrix of an
Isoparametric element? [AU, Nov / Dec – 2011]
3.129) Write the Gauss points and weights for two point formula of numerical integration.
[AU, April / May – 2011]
3.130) Write down the Gauss integration formula for triangular domains.
[AU, April / May – 2009]