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PRIST UNIVERSITY(Estd. u/s 3 of UGC Act, 1956)

Vallam, Thanjavur -613403 _______________________________________________________________________

_

M.Tech. STRUCTURAL ENGINEERING

QUESTION BANK

Course Details

Course Code & Title :12255H22&12255H22P /F inite Element A nalysis

Regulation : 2012 R

Semester : II

H.O.D. Staff-In-

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12255H22&12255H22P FINITE ELEMENTANALYSIS

AIM and OBJECTIVES:The finite element method is the most powerful structural analysis tool for the civil engineers. The basic formulation and programming technique areintroduced. According to the same procedures, the different elements such astruss, beam, plate and shell are easily formulated.

UNIT I INTRODUCTION: 12Differential equilibrium equations - strain displacement relation - linear

constitutive relation - special cases. Principle of stationary potential energy -application to finite element methods. Some numerical techniques in finiteelement Analysis

UNIT II ANALYSIS OF PLATE BENDING; 12Two Dimensional problems - Plane Stress, Plain Strain andAxisymmetric Problems - Triangular and beam element -. Analysis of plate

bending- Basic theory of plate bending - displacement functions - plate bending Elements.

UNIT III MODELS AND FUNCTION OF ELEMENT: 10

Displacement models - convergence requirements. Natural coordinatesystems Shape function. Interpolation function. Linear and quadraticelements - Lagrange & Serendipity elements.

UNIT IV ANALYSIS OF NONLINEAR AND VIBRATION PROBLEMS: 12

Strain displacement matrix - Material and Geometric Nonlinearity -Methods of Treatment -Dynamic condensation-Eigen value extraction

UNIT V ASSEMBLAGE OF ELEMENT: 10Assemblage of elements Direct stiffness method. Special characteristics of stiffness matrix - Boundary condition & reaction - Gauss elimination Basic steps in Finite element analysis.

REFERENCE1. Krishnamoorthy, C.S, Finite Element Analysis Theory & Programming , McGraw- Hill2. Desai C.S and Abel, J.F., Introduction to the finite element Method,Affiliated East west Press Pvt. Ltd. New Delhi 1997.3. Bathe , K.J., Finite Elements Procedures in Engineering analysis,

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Prentice Hall Inc., 1995.

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UNIT-1

PART-A1. What is the basis of finite element method?2. State generalized Hookes law?3. Clearly point out the situations in which FEM is preferred over other methods.4. What is meant by finite element?5. What is meant by a node or joint?6. What are the three types of nodes?7. Distinguish between potential energy function and stationary potential energy

function.8. What is the correct solution for a linearly elastic problem?9. State the principle of stationary potential energy10. Write the applications of finite element analysis.

PART-B

1. Briefly explain the advantages and disadvantages of finite element analysis?

2. Find the nodal displacements, displacement at 1200 mm and 3200 mm from theleft hand support and element stresses for the stepped bar shown in figure.

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3. Find the nodal displacements and element stresses for the stepped bar shown inFig.

4. Explain about the applications of Finite element analysis.5. Explain the concept of FEA briefly and outline the procedure.

6. Write a brief note on some numerical techniques in finite element analysis.

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UNIT-II

PART-A

1. Distinguish between plane strain and plane stress problems

2. Write the use of triangular plate bending elements.3. Define the term Anisotropic

4. Define the terms Orthotropic and Isotropic

5. Give constitutive laws for plane stress problems.

6. What do you meant by plane stress problems?

7. What do you meant by plane strain problems?

8. What do you meant by Axis symmetric problems?

9. Distinguish between orthotropic and isotropic materials.

10. Write the relation between stress and strain.

PART-B

1. Explain about the basic theory of plate bending.

2. Formulate element Stiffness matrices and global load vector for the truss shown

in fig and also state the boundary conditions=200 GPa; A=100mm 2; P=10 kN

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3. Calculate the nodal displacements and element stresses for the truss shown in

fig.3.4 E=70GPa.Cross sectional area A=2 cm 2 for all truss members.

4. Obtain the element stiffness matrix for a pin jointed truss element.

5. Explain the term plane stress and give constitutive laws for such problems.

6. Explain the term Axi symmetric problems and give constitutive law for such

problems

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UNIT-III

PART-A

1. Define shape function2. What is meant by higher order element?3. Differentiate between global and local axis.4. What is the difference between natural coordinate and simple natural

coordinates?5. What is scalar or homogeneous degree of freedom? Give examples6. What are the advantages of using shape functions for setting up element stiffness

matrix for an element?7. How inter element compatibility requirement is met in finite element

dissertation?8. What is meant by isoparametric element?

9. Define clearly the following termsa) Local coordinates b) Global coordinates

10. Define clearly the following termsa) Simple natural coordinates and natural coordinatesb) Generalized coordinates

PART-

1. Determine the shape function for a two nodded bar element using Cartesian

coordinate system.

2. Using generalized coordinate approach, determine shape functions for a twonodded beam element and apply necessary checks.

3. Determine the shape functions for a CST element.

4. A shaft is supported in a long bearing at the left end and another bearing at the

end right side which has vertical stiffness Ks.Shaft is subjected to a distributed

load whose intensity is a p equal to 5000 N/m and appoint load P of 2500 N as

shown in fig. The flexural rigidity EI of the shaft is 50 X 10 3 Nm 2.The shaft is

made of steel with modulus of elasticity E equal to 200 GPa.Find i) the slope

and deflection at the ends and midspan of the shaft ii) the moment and shear

force at the middle of the distributed load.

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5. Determine the deflection and slope at 2m from the left end of shaft mounted in

bearings. A load 1 kN and a moment of 2 kN-m act on the shaft. Model the

bearings as fixed supports. G=200 GPa ;I 1=4 X 10 -6 m4 ; I2=2 X 10 -6 m4

5. Determine the deflection and slope under the point load for the beam

shown in fig. . G=200 GPa ;I 1=4 X 10 -6 m4 ; I 2=2 X 10 -6 m4

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H.O.D. Staff-In-

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UNIT-IV

PART-A

1. What is meant by static condensation?

2. Distinguish between essential (forced or geometric) and non-essential (natural)

boundary conditions.

3. Mention the methods available for handling material non-linear problems

4. Mention the methods available for handling geometric non-linear problems

5. What do you meant by material non-linearity?

6. What do you meant by geometric non-linearity?

7. Mention the various non-linearity in finite element analysis

8. Distinguish between linear and non-linear analysis.

9. What do you meant by Non-linearity?

10. State the incremental procedure to handle material non-linear problems.

PART-B

1. Explain the different type of non-linearitys encountered in structural analysis.

2. Explain midpoint runge-kutta incremental scheme and discuss its advantages and

disadvantages over the incremental procedure.

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3. Explain the iterative procedure of handling geometric non-linearity problems in

structural mechanics.

4. Explain about the reversible non-linearity.

5. Discuss in detail about the general procedure for solution of non-linear discrete

problems by direct iterations.

6. Explain iterative procedure and modified iterative procedure for the analysis of

materials non-linearity problems.

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UNIT-V

PART-A

1. What is the effect of using nonconforming elements in an assemblage?

2. Define stiffness matrix.

3. What are the properties of stiffness matrix?

4. What are the complete requirements?

5. What do you meant by inter element compatibility?

6. Mention different types of elements give example.

7. What is the use of pascals triangle?

8. What is Gauss elimination method?9. Write the steps involved in finite element analysis

10. Distinguish between primary, secondary and internal nodes.

PART-B

1. Explain about the boundary condition in finite element method.

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2. Explain in detail about the Gauss elimination method.

3. Explain briefly the steps involved in Finite Element Analysis.

4. What are the factors considered in the selection of displacement function?

Explain in detail.

5. Write short note on stiffness method.

6. Write short note on

a) Compatibility

b) Boundary condition and reaction

H.O.D. Staff-In-

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