144900329 Ansys Lab Procedure and Viva q s

VIDYASAGAR.R

MECHANICAL ENGINEERING

ANSYS LAB EXAM KIT

2

CONTENTS

SIGN CONVENTIONS & DISPLACEMENTS IN ANSYS SOFTWARE……. 03

PROCEDURE TO WRITE IN THE EXAM…………………………………………… 03

GUI PATHS FOR BARS…………………………………………………………………… 04

GUI PATHS FOR TEMPERATURE STRESS PROBLEMS……………………… 06

GUI PATHS FOR TRUSSES……………………………………………………………… 08

GUI PATHS FOR BEAMS………………………………………………………………… 10

GUI PATHS FOR COMPOSITE WALLS…………………………………………….. 13

GUI PATHS FOR PLATE WITH HOLES…………………………………………….. 15

GUI PATHS FOR MODAL ANALYSIS………………………………………………. 17

GUI PATHS FOR HARMONIC ANALYSIS…………………………………………. 19

SOLVED PROBLEMS …………………………………………………………………….. 21

VIVA QUESTIONS WITH ANSWERS……………………………………………….. 55

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1. SIGN CONVENTIONS IN ANSYS SOFTWARE

1. FORCES -- --- A) FX direction, Positive value

B) FX direction, Negative value

C) FY direction, Negative value

D) FY direction, Positive value

2. MOMENTS ------ A) Clockwise, Negative value

B) Anti-clockwise, Positive value

2. TYPE OF DISPLACEMENTS

1. Δ – UY – fix the end in UY direction

2. Or - Fix in both direction – ALL DOF

3. - Fix in both direction – All DOF

4. - UY – fix the end in UY direction (Used in SFD and BMD)

3. PROCEDURE TO WRITE IN THE EXAM

1. AIM/QUESTION

2. GUI PATH/PROCEDURE( IF ASKED TO WRITE ONLY)

3. DIAGRAM OF GIVEN MODEL

4. FEM MODEL

5. THEORITICAL SOLUTION

6. CONNECTIVITY TABLE (ONLY FOR BARS)

7. ANSYS SOLUTION

8. CONCLUSION

4

1. ANSYS LAB PROCEDURE FOR BARS [GUI PATH]

(Q1) To find the nodal displacements, stress in the elements and reaction forces for a bar element.

1. Preferences -> structural ->h-method->ok

2. Preprocessor ->element type-> Add/edit/delete->Add->Link->2D spar 1->ok

->close

3. Preprocessor->Real constants->Add/edit/delete->Add->ok->Enter the cross

sectional area in the space provided for area(in mm2)->ok(note:- if the bar is

stepped bar then after entering the area->apply->In the space provided

against “REAL CONSTANT SET NO.” Enter the next number (i.e. 2 for 2nd area,3

for 3rd area)->type the next cross-sectional area->ok) ->close

4. Preprocessor->Material props->Material models->Structural->Linear->Elastic

->Isotropic->Enter the value of young’s modulus(in N/mm2) in the space

provided for ”EX”, Enter the value of POISSON’S ratio in the space provided

against ”PRXY” ->close(Note:- If there are 2 or more materials then on top of

the window select ->material->New model and follow the same procedure)

5. Preprocessor->Modeling->Create->Nodes->In active cs->Enter the node no,

co-ordinates at which they are located(Note:- For bars, co-ordinates are only

in either x-direction or y-direction and hence values must be entered in the

first or second boxes of the location box and other two boxes must be entered

zero or leave it blank) ->apply-> enter the next node number and follow the

same procedure till the last node ->ok(Note:- The values of co-ordinates must

be entered in mm)

6. Preprocessor->Modeling->Create->Elements->Elem attributes->Check for

material number and real constant set number->ok

7. Preprocessor->Modeling->Create->Elements->Auto numbered->Thru nodes

->Select the 2 nodes to be joined ->ok

5

8. If there are more than 1 material or real constants Repeat step no.6 and step

no.7 varying suitable material and real constant set number in “Elem

Attributes”.

9. Preprocessor->Loads->Define loads->Apply->Structural->displacement->on

nodes->select the node on which you want to apply the boundary conditions

->ok->select the type of boundary condition(Note:- If there is a gap b/w the

node and boundary condition then enter the gap distance in the space

provided against “VALUE Displacement value”)->ok

10. Preprocessor->Loads->Define loads->Apply->Structural->Force/moment->on

nodes->Select the node on which you want to apply the force->Direction of

force must be FX->Enter the value of force(in Newton’s) ->ok

11. Repeat step no.10 if you want to apply loads on other nodes.

12. Solution->Solve->current Ls->ok->close->close the solution window

13. General Postproc->Element table->Define table->Add->In the space provided

against “use label for Item” type any word(e.g.:-Stress) ->ok->close

14. General Postproc->Element Table->List elem table->Select the word you had

typed(e.g.:-Stress)->By sequence num->LS,1 ->ok(A window pop-ups showing

the values of stress in each element)

15. General postproc->List results->Nodal solution->Under nodal solution select

DOF solution-> X-component of displacement->ok( A window pop-ups

showing the nodal displacements)

16. General postproc->List results->Reaction solutions->All items->ok( A window

pop-ups showing the reaction solution at each node, if the node no is not

shown then there is no reaction force on that node)

17. Close all the windows after noting down the values->File->clear and start new

->Do not read file->ok->yes

CONCLUSION: - The given model is analyzed and correct solutions were found and

tabulated

6

2. ANSYS LAB PROCEDURE FOR

TEMPERATURE STRESS BARS [GUI PATH]

(Q2)To find the nodal displacements, stress in the elements and reaction forces for a bar element initially at a given temperature and then raised to another temperature.



->close



stepped bar then after entering the area->apply->type the next cross-sectional

area->ok) ->close




against ”PRXY” ->close(Note:- If there are 2 or more materials then, on top of


5. Preprocessor->Material props->Material models->Structural-> Thermal

expansion->Secant coefficient->Isotropic-> in the space provided against

“ALPX” enter the value of coefficient of thermal expansion value(α)->ok

->Close


co-ordinates at which they are located(Note:- For bars, co-ordinates are only

in x-direction and hence values must be entered in the first box of the location

box and other two boxes must be entered zero or leave it blank) ->apply-

>enter the next node number and follow the same procedure till the last

node->ok(Note:- The values of co-ordinates must be entered in mm)







Attributes”.

7



->ok->select the type of boundary condition(Note:- If there is a gap b/w the

node and boundary condition then enter the gap distance in the space

provided against “VALUE Displacement value”)->ok



force must be FX->Enter the value of force(in Newton’s) ->ok


13. Preprocessor->Loads->Define loads->Apply->Structural->Temperature->On

elements->select the elements->ok->In the space provided against

“TEMPERATURE AT LOCATION N” enter the temperature difference given

(e.g. If the initial temperature is 20°C and raised temperature is 60°C then

enter 40)->ok





typed(e.g.:-Stress) ->By sequence num->LS,1 ->ok(A window pop-ups showing



DOF solution-> X-component of displacement->ok( A window pop-ups







*Note: - Bolded step indicates the change compared to previous problems.


tabulated

8

3. ANSYS LAB PROCEDURE FOR TRUSSES

[GUI PATH]

(Q3)To find the nodal displacements, stress in the elements and reaction forces in each member subjected to loads as given for the truss setup.



->close



stepped bar then after entering the area->apply->In the space provided

against “REAL CONSTANT SET NO.” Enter the next number (i.e. 2 for 2nd area,3

for 3rd area)->type the next cross-sectional area->ok) ->close




against ”PRXY” ->close(Note:- If there are 2 or more materials then on top of



co-ordinates at which they are located(Note:- For trusses, co-ordinates are

only in x-direction and y-direction and hence values must be entered in the

first & second box of the location box and other box must be entered zero or

leave it blank) ->apply-> enter the next node number and follow the same

procedure till the last node ->ok(Note:- The values of co-ordinates must be

entered in mm)







Attributes”.



->ok->select the type of boundary condition->ok

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force may be may in FX or FY ->Enter the value of force(in Newton’s) ->ok






typed(e.g.:-Stress) ->By sequence num->LS,1 ->ok(A window pop-ups showing



DOF solution-> Displacement vector sum->ok( A window pop-ups showing

the nodal displacements)






*Note: - Bolded step indicates the change compared to previous problems.


tabulated.

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4. ANSYS LAB PROCEDURE FOR BEAMS

[GUI PATH]

(Q4)To find the reaction solution,nodal displacements, shear force and bending moments at each node of the given beam and to draw the shear force diagram(SFD) and Bending moment diagram (BMD)


2. Preprocessor ->element type-> Add/edit/delete->Add->Beam->2D elastic 3-

>ok ->close

3. Preprocessor->Sections->Beam->Common sections->Sub type is the type of

cross section of the beam(e.g. circular, rectangular, etc)->offset to centroid

->Enter the value of h and b(for rectangle ) or enter the radius R (for circle

) or enter the values similarly for I section also->preview->Close


sectional area in the space provided for area(in mm2)->Enter the value of Izz

which is present on the screen->enter height of the beam->ok ->close




against ”PRXY” ->close


co-ordinates at which they are located(Note:- For beams, co-ordinates are

only in x-direction and hence values must be entered in the first box of the

location box and other two boxes must be entered zero or leave it blank) -

>apply-> enter the next node number and follow the same procedure till the

last node ->ok(Note:- The values of co-ordinates must be entered in mm)

11


->Select the first 2 nodes->apply->select the next 2 nodes->apply(repeat till all

the nodes are joined)->ok



->ok->select the type of boundary condition->ok



force must be FY->Enter the value of force(in Newton’s) ->ok


nodes->Select the node on which you want to apply the moment->ok->in the

options provided against “Direct of force/moment” select Mz-> Enter the

value of moment(in Newton-mm) in the value box ->ok

11. To apply UDL(uniformly distributed load) apply the following procedure:

preprocessor->loads->define loads->apply->structural->pressure->on beam-

>select the element on which you want to apply UDL->ok->In the box provided

against “PRESSURE VALUE AT NODE I” Enter the UDL load in KN/m(e.g. If the

load is 6KN/m, enter as 6)->Leave all other boxes empty->ok

12. To apply UVL(uniformly Varying load) apply the following procedure:

preprocessor->loads->define loads->apply->structural->pressure->on beam-

>select the element on which you want to apply UDL->ok->In the box provided

against “PRESSURE VALUE AT NODE I” Enter the load at that node and against

“PRESSURE VALUE AT NODE J” enter the load at the next node in KN/m(e.g. If

the load varies from 0KN/m to 10KN/m, At node I enter “0” and at node J

enter”10”)->Leave all other boxes empty->ok

13. Repeat step no.10, 11, 12 if you want to apply loads and moments on other

nodes.


12

15. General Postproc->Element table->Define table->Add->select By sequence

number->Select SMISC and Type 2 next to it->apply->Select SMISC and Type 8

next to it ->apply->select SMISC and Type 6 next to it ->Apply->Select SMISC

and Type 12 next to it ->ok->close

16. General Postproc->Element Table->List elem table->Select SMIS2,SMIS8,SMIS6

and SMIS12->ok(A window pop-ups showing the values of shear force and

bending moment)

17. General postproc->plot results->contour plot->line elem Res->Select SMIS2 in

the first box and SMIS8 in the second box to get SHEAR FORCE DIAGRAM->ok

18. General postproc->plot results->contour plot->line elem Res->Select SMIS6 in

the first box and SMIS12 in the second box to get BENDING MOMENT

DIAGRAM->ok


DOF solution-> Y-component of displacement->ok( A window pop-ups



pop-ups showing the reaction solution at each node, if the node no. is not





the shear force and bending moment diagrams are plotted.

13

5. ANSYS LAB PROCEDURE FOR

COMPOSITE WALLS [GUI PATH]

(Q5)To determine the heat flux and temperature distribution of the given composite wall

1. Preferences -> Thermal ->h-method->ok

2. Preprocessor ->element type-> Add/edit/delete->Add->Link->2D conduction

32->apply->Link->Convection 34->ok ->close

3. Preprocessor->Real constants->Add/edit/delete->Add->select Type 1 Link 32

->Enter the cross sectional area in the space provided for area(in m2)->ok -

>Add-> Select Type 2 Link 34-> Enter the cross sectional area in the space

provided for area(in m2)(Note:-Leave other boxes blank)->ok) ->close

4. Preprocessor->Material props->Material models->Thermal->Convection or

film coef->Enter the value of HF of inner surface->ok->on top of the window

select ->material ->New model->ok->Select conductivity->Isotropic->Enter the

value of thermal conductivity of 1st material in the box provided against

“KXX”->ok(Note:- Repeat the conductivity if there are more than 1 material)-

>on top of the window select ->material ->New model->Ok->Select

Convection or film coef->Enter the value of HF of outer surface->ok->Close


co-ordinates at which they are located(Note:- For composite wall, co-

ordinates are only in either x-direction and hence values must be entered in

the first box of the location box and other two boxes must be entered zero or

leave it blank) ->apply-> enter the next node number and follow the same

procedure till the last node ->ok(Note:- The values of co-ordinates must be

entered in m)(Note:-If the length of convection is not given assume it as

0.001m)

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element type number(i.e. link 32 for conduction and link 34 for

convection),material number and real constant set number->ok





Attributes”.

9. Solution->Analysis type->New analysis->Steady state->ok

10. Solution->Define loads->Apply->Thermal ->temperature->on nodes->select

the node on which you want to apply the Temperature->ok->Select Temp-

>Enter the value of temperature ->ok

11. Repeat the above step to apply temperatures on other nodes.


13. In the above there are options like file, select, list plot etc->Select->Plot Ctrls

-> Style->Size and shape->Display of element √ On->ok

14. General Postproc -> plot results->Contour plots->Nodal solution->DOF

solution->Nodal temperature->ok

15. General Postproc->Element table->Define table->Add->by sequence Number -

>SMISC->Type 1 next to that->ok->close

16. General Postproc->Element Table->List elem table->SMIS 1 ->ok(A window

pop-ups showing the values of stress in each element)

17. General Postproc->List results->Nodal solution->Under nodal solution select

DOF solution->Nodal temperature->ok( A window pop-ups showing the nodal

Temperatures)




tabulated

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6. ANSYS LAB PROCEDURE FOR PLATE

WITH HOLES [GUI PATH]

(Q5)To determine the maximum stress for a rectangular plate with hole and which is loaded


2. Preprocessor ->element type-> Add/edit/delete->Add->Solid->Quad4node 42

->ok->Options->in the box provided against “K3” select “plane strs w/thk”

->ok->close

3. Preprocessor->Real constants->Add/edit/delete->Add->Type 1 plane 42->

Enter the Thickness in the space provided for THK(in mm2)->ok ->close




against ”PRXY” ->close

5. Preprocessor->Modeling->Create->Key points->In active cs->Enter the node

no, co-ordinates at which they are located ->apply-> enter the next node

number and follow the same procedure till the last node ->ok(Note:- The

values of co-ordinates must be entered in mm)

6. Preprocessor->Modeling->Create->Areas->Arbitrary->Through KP’s ->Select

the nodes you want to join->ok

7. Preprocessor->Modeling->Create->Areas->Circle->Solid circle->Enter the

distance of the centre of the circle in X- direction from the extreme left end in

the box provided against “WP X”-> Enter the distance of the centre of the

circle in Y- direction from the bottom end in the box provided against “WP Y”

->Enter the radius of the circle->ok

8. Preprocessor->Modeling->Operate->Booleans->Subtract->areas->Select the

rectangular area->select ok in the bottom left box->Select the circular area-

>click next in the top left box->ok in the bottom left box

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9. Preprocessor->Meshing->Mesh tool-> Select √ Smart size-> reduce it to size 2

->Mesh->Select the area ->ok


lines->select the line on which you want to apply the boundary conditions -

>ok->select the type of boundary condition->ok


nodes->Select Box-> Select the nodes on which you want to apply the force-

>Select the Direction of force ->Enter the value of force(in Newton’s)(Note:-

When you select box, you will select many no of nodes so when the load is

applies you should apply the load divided by no. of nodes selected, E.g. If the

load is 10000N and no of selected nodes is 23,apply load as 10000/23) ->ok



14. General Postproc->Plot results ->Contour plot->Nodal Solution->Stress->Von

mises stress->ok

15. General Postproc->List results->nodal solution->Stress-> von mises stress->ok


tabulated

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7. ANSYS LAB PROCEDURE FOR MODAL ANALYSIS [GUI PATH]

(Q5)To carry out the modal analysis for the given beam and to plot the mode shapes.



>ok ->close



->Enter the value of h and b(for rectangle ) or enter the radius R (for circle )

or enter the values similarly for I section also->preview->Close(All values in m)







against ”PRXY” ->ok->Select Density->Enter the value of density in the space

provided against “DENS”->ok->Close

6. Preprocessor->Modeling->Create->Key points->In active cs->Enter the Key

point no, co-ordinates at which they are located(Note:- For beams, co-

ordinates are only in x-direction and hence values must be entered in the first

box of the location box and other two boxes must be entered zero or leave it

blank) ->apply-> enter the next key point number and follow the same

procedure till the last key points ->ok(Note:- The values of co-ordinates must

be entered in m)

7. Preprocessor->Modeling->Create->lines->Lines->Straight line->Select the key

points to be joined->ok

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8. Preprocessor->Meshing->Mesh tool ->Under size control, Lines, Select set

->Select the line->ok-> Enter no of divisions as100-> Mesh->Select the line->ok

9. Solution->Analysis type->new analysis->Modal->ok->Analysis options->in the

space provided against “No of modes to extract” type 3->ok->ok

10. Solution->Define loads->Apply->Structural->Displacement->On nodes->Select

the nodes to apply the boundary conditions->Select the type of boundary

condition->ok

11. Solution->Solve->Current LS->ok->Done

12. General Postproc-> Results summary( A window pops-up Showing the natural

frequencies)

13. General Postproc->Read result->First set

14. General Postproc-> Plot results->Deformed shape->Def+undeformed->ok(The

screen shows the 1st modal shape)

15. General Postproc->Read result->Next set

16. Repeat step 14 (The screen shows the 2nd modal shape)

17. Repeat steps 15 & 16 for other mode shapes


tabulated

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8. ANSYS LAB PROCEDURE FOR HARMONIC ANALYSIS [GUI PATH]

(Q5)To carry out the harmonic analysis for the given beam subjected to cyclic loads for a given frequency range



>ok ->close



->Enter the value of h and b(for rectangle ) or enter the radius R (for circle )

or enter the values similarly for I section also->preview->Close(All values in m)







against ”PRXY” ->ok->Select Density->Enter the value of density in the space

provided against “DENS”->ok->Close

6. Preprocessor->Modeling->Create->Key points->In active cs->Enter the Key

point no, co-ordinates at which they are located(Note:- For beams, co-

ordinates are only in x-direction and hence values must be entered in the first

box of the location box and other two boxes must be entered zero or leave it

blank) ->apply-> enter the next key point number and follow the same

procedure till the last key points ->ok(Note:- The values of co-ordinates must

be entered in m)

7. Preprocessor->Modeling->Create->lines->Lines->Straight line->Select the key

points to be joined->ok

20

8. Preprocessor->Meshing->Mesh tool ->Under size control, Lines, Select set

->Select the line->ok-> Enter no of divisions as100-> Mesh->Select the line->ok

9. Solution->Analysis type->new analysis->harmonic->ok

10. Solution->Analysis type->analysis options->ok->ok

11. Solution->Define loads->Apply->Structural->Displacement->On nodes->Select

the nodes to apply the boundary conditions->Select the type of boundary

condition->ok

12. Solution->Define loads->Apply->Structural->Force/moment->On nodes-

>Select the nodes to apply the Force->Type the value of force in newton->ok

13. Solution->Load step opts->Time/Frequency->Frequency and sub steps-> In the

box provided against “Harmonic frequency range” enter the range given (e.g.,

frequency range maybe from 0 to 100) ,in the box provided against “no. of sub

steps” enter the given sub steps-> Stepped->ok

14. Solution->Solve->Current LS->ok->Done

15. TimeHistPostporc-> Time history variable->Add data ->Nodal solution->DOF

solution->Y-component of displacement->Type the node no on which load is

applied->ok

16. TimeHistPostporc-> Time history variable->graph data->Nodal solution->DOF

solution->Y-component of displacement->ok( Graph appears)


tabulated

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SOLVED PROBLEMS STEPPED BARS

22

23

24

25

26

27

28

29

30

31

32

33

34

35

TRUSSES

36

37

38

BEAMS

39

40

41

42

43

44

45

COMPOSITE WALLS( THERMAL ANALYSIS)

46

47

48

49

PLATE WITH HOLE

50

51

MODAL ANALYSIS

52

53

54

HARMONIC ANALYSIS

55

VIVA QUESTIONS WITH ANSWERS

1. What are the different approximate solution methods?

Finite Element method, Finite difference method and quadrature method.

2. What do you mean by continuum?

A continuous sequence in which adjacent elements are not perceptibly different from each other, although the extremes are quite distinct.

A continuous extent, succession, or whole, no part of which can be distinguished from

neighboring parts except by arbitrary division.

3. Define term node?

In the FEM, the structural system is modeled by a set of appropriate finite elements

interconnected at points called nodes

A node is a specific point in the finite element at which the value of the field variable is

to be determined.

Nodes are the selected finite points at which basic unknowns (displacements in elasticity problems) are to be determined in the finite element analysis

4. Define term element?

In a continuum, unknowns are many. The FE procedure reduces such unknowns to a

finite no. by diving the solution regimes into small parts called elements

5. What is convergence?

Convergence refers to how close the FEM solution is to the exact solution

6. What are the types convergence?

h – method and p-method

7. What is p-convergence?

Large elements and complex shape functions are used in p-method problems. In order to increase the accuracy of the solution, the complexity of the shape function must be increased. The mesh does not need to be changed when using the p-method.

Increasing the polynomial order increases the complexity of the shape function. As an initial run, the solution might be solved using a first order polynomial shape function. A solution is obtained. To check the solution the problem will be solved again using a more complicated shape function. For the second run, the solution may be solved using a third order polynomial shape function. A second solution is obtained. The output from the two runs is compared. If there is a large difference between the two solutions, then the solution should be run using a third order polynomial shape function. This process is repeated until the solution is not changing much from run to run.

8. What is h convergence?

Simple shape functions and many small elements are used in h-method problems. In order to increase the accuracy of the solution, more elements must be added. This means creating a finer mesh.

56

As an initial run, a course mesh is used to model the problem. A solution is obtained. To check this solution, a finer mesh is created. The mesh must always be changed if a more accurate solution is desired. The problem is run again to obtain a second solution. If there is a large difference between the two solutions, then the mesh must be made even finer and then solve the solution again. This process is repeated until the solution is not changing much from run to run. When using an h-method finite element program (such as ANSYS), the user must run two or more solutions to ensure that the solution has converged. The user runs the solution with one mesh and then changes the mesh and reruns the solution.

9. What is higher order elements?

If the interpolation polynomial is of the order two or more, the element is known as

Higher order elements.

10. Give example for higher order elements.

Quadratic bar element, cubic bar element etc..

11. What do you mean by compatible elements?

The elements which deform without causing openings, overlaps or discontinuities b/w

the adjacent elements are known as compatible elements

12. What is geometric invariance?

Displacement shapes will not change in local coordinate system. This property is known

as geometric invariance.

13. Why do we use Pascal’s triangle in FEA?

In order to achieve geometric invariance the polynomial should contain terms that do

not violate symmetry; this is achieved by the use of Pascal triangle for 2Dcases and

Pascal tetrahedron for 3D cases.

14. What are the steps involved in FEA?

Discretization of the continuum, Selection of displacement models, Deriving element

stiffness matrix, assemblage of elemental equations to obtain overall equilibrium

equations, Applying boundary conditions, Solution for unknown nodal displacements

and Computation of strain, stress and reaction solution.

15. What is stiffness matrix?

For an element, Stiffness matrix is a matrix such that { f } = [K] {Q}, [K] relates nodal

displacements to nodal force of a single element.

16. How to obtain stiffness matrix?

Using the formula for particular element.

17. What are the properties of stiffness matrix?

Non negative diagonal elements, Symmetry and sparsity.

57

18. What is displacement function?

The displacement function, uniquely defines strain within an element in terms of

nodal displacements.

19. How to identify order of elements?

The maximum power of the variable in the interpolation polynomial gives the order or

the order can be obtained by no. of nodes present.

20. Mention different types of elements.

Simplex elements,complex elements and multiplex elements; Based on their geometry

they are classified as 1D,2D,3D and axis symmetric elements.

21. Mention some application of FEA.

Stress analysis of bars, beams, trusses, buckling problems, Heat transfer problems, fluid

flow problems, bio medical areas etc.

22. What is connectivity?

Connectivity is a term used when a matrix or a table connects the stress,reactions

,displacements etc

23. What are the methods to improve problem solution?

Use of higher order elements in order to get exact solutions

24. Define symmetry in matrix.

A symmetric matrix is a square matrix that is equal to its transpose

25. What is plane stress?

Plane stress is defined to be a state of stress in which the normal stress and shear stress

directed perpendicular to the plane are assumed to be zero e.g. thin plate with hole

26. What is plane strain?

Plane strain is defined to be a state of strain in which normal strain and shear strain

normal to the XY plane are assumed to be zero.

27. Compare FEA with solid mechanics.

Finitie element analysis can be applied to any continous matter where you can divide

the situation into small elements (usually triangular) and apply a set of edge constraints

and then use a computer to solve for the area of concern for whatever the value under

investigation is e.g. temperarture, flow rate, stress, shear, bending moment etc.

So Solid mechanics is the study of things as shear, stress, etc. and they use FEA as a tool

but FEA can be applied to many other fields e.g fluid mechanics thermodynamics, etc.

28. What are the packages available for FEA?

STAAD-PRO, GT-STRUDEL, NASTRAN, NISA and ANSYS

58

29. Define potential energy.

Potential energy is energy which results from position or configuration

30. Define minimum potential energy.

Deformation and stress analysis of structural systems can be accomplished using the

principle of Minimum Potential Energy (MPE), which states that “For conservative

structural systems, of all the kinematically admissible deformations, those

corresponding to the equilibrium state extremize (i.e., minimize or maximize) the total

potential energy. If the extremum is a minimum, the equilibrium state is stable.

31. Write potential energy equation for cantilever beam.

32. Mention 2 different methods to approach the model of physical system.

FEM and FDM

33. Difference between global coordinate and local coordinate?

34. What is local coordinate?

For the convenience of deriving element properties, in FEM many times for each element a separate coordinate system is used known as local coordinate system

35. What is global coordinate?

The coordinate system used to define the points in the entire structure is called global

coordinate system.

36. What is shape function?

Function which relates the field variable at any point within the element to the field variables of nodal points is called shape function.

37. What are two general natural coordinate?

Zeta ξ and neta ή

38. Mention the range of natural coordinate.

-1 to +1

39. Number of shape function in CST

3

40. Number of shape function in quadrilateral.

4

41. Explain one point formula and Explain two point formula.

1 point formula ∫ ( )

w1f(ξ), w1 = 2, ξ= 0

2 point formula ∫ ( )

w1f(ξ1)+w2f(ξ2), w1= 1,ξ1 = 1/√3, w2= 1, ξ2 = -1/√3

42. Why we are using polynomial equation in FEA?

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It is easier to formulate and computerize the finite element equations with polynomial-type interpolation functions. Specifically, it is easier to perform differentiation or integration with polynomials.

It is possible to improve the accuracy of the results by increasing the order of the polynomial.

43. Mention two schemes to represent band width?

Node numbering along longer edge and shorter edge.

44. What are forces involved in work potential?

Body forces and traction forces

45. What are anisotropic elements?

The property of the material is not same along all the directions; such materials are

called anisotropic elements.

46. What are isotropic elements?

The property of the material is same along all the directions; such materials are called

isotropic elements.

47. What are the 2 different approaches to study elasticity?

Elimination and penalty approach method

48. List the properties of shape functions.

Shape function at a specified point is unity and other than the specified point it is zero.

Sum of shape functions is unity.

The differentiation of shape function is a constant

49. Define truss.

A framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge,

or other structure

50. What is weighted residual methods?

The weighted residual method is a technique that can be used to obtain approximate solutions to linear and nonlinear differential equations. If we use this method the finite element equations can be derived directly from the governing differential equations of the problem without any need of knowing the “functional.” We first consider the solution of equilibrium, eigenvalue, and propagation problems using the weighted residual method and then derive the finite element equations using the weighted residual approach.

51. Different methods to solve weighed residual problem.

Galerkin method, Collocation method, Sub domain method

52. Explain the principle of virtual work.

The principle of virtual work (PVW) states that the stress, body force and traction are in

equilibrium if and only if the IVW equals the EVW for every virtual displacement field.

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53. Mention some advantages of FEA over solid mechanics.

In classical methods exact equations are formed and exact solutions are obtained where as in finite element analysis exact equations are formed but approximate solutions are obtained.

Solutions have been obtained for few standard cases by classical methods, where as solutions can be obtained for all problems by finite element analysis.

Whenever the following complexities are faced, classical method makes the drastic assumptions’ and looks for the solutions: Shape, Boundary conditions, Loading

To get the solution in the above cases, rectangular shapes, same boundary condition along a side and regular equivalent loads are to be assumed. In FEM no such assumptions are made. The problem is treated as it is.

When material property is not isotropic, solutions for the problems become very difficult in classicalmethod. Only few simple cases have been tried successfully by researchers. FEM can handle structures with anisotropic properties also without any difficulty.

If structure consists of more than one material, it is difficult to use classical method, but finite element can be used without any difficulty.

Problems with material and geometric non-linearities can not be handled by classical methods.There is no difficulty in FEM.

54. Define Young’s Modulus and Poisson’s Ratio.

Within the limits of elasticity, the ratio of the linear stress to the linear strain is termed

the modulus of elasticity or Young's Modulus and may be written Young's Modulus, or E

=(Stress/Strain) It is this property that determines how much a bar will sag under its own

weight or under a loading when used as a beam within its limit of proportionality. For

steel, Young's Modulus is of the order of 205000 N/mm2.

Ratio of decrease in the thickness (lateral contraction) of a body being pulled (under a

tensile load) to its increase in length (longitudinal extension). It is constant for

a material, around 0.28 for ordinary steels. Named after its discoverer, the French

mathematician Siméon-Davis Poisson (1781-1840).

55. Mention different types of elastic constants.

(i)Modulus of Elasticity or Young’s Modulus (E)

Modulus of Elasticity is the ratio of direct stress to corresponding linear strain within

elastic limit. If p is any direct stress below the elastic limit and e the corresponding linear

strain, then E = p / e.

(ii)Modulus of Rigidity or Shear Modulus (G)

Modulus of Rigidity is the ratio of shear stress to shear strain within elastic limit. It is

denoted by N,C or G. if q is the shear stress within elastic limit and f the corresponding

shear strain, then G = q / f.

(iii) Bulk Modulus (K)

Bulk Modulus is the ratio of volumetric stress to volumetric strain within the elastic limit.

If pv is the volumetric stress within elastic limit and ev the corresponding volumetric

strain, we have K = pv / ev.

56. Which is the most accepted form of numerical integration in FEM?

Gaussian quadrature

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57. List the different approaches to derive integral equation.

Gaussian quadrature, Simpson’s 1/3 rule etc

58. What are the different types of errors in FEA?

Modeling Error, User error, bugs, Discretization error, Rounding error, manipulation

error, Numerical error

59. Define Beam & Its types.

A bar subjected to forces and couples that lie in a plane containing its longitudinal axis is

called a beam

Types include Cantilever beam,simply supported beam and over hanging beam

60. Define Conduction, Convection and radiation.

Conduction is the transfer of energy from the more energetic particles of a substance to

the adjacent less energetic ones as a result of interactions b/w particles.

Convection is the mode of heat transfer b/w a solid surface and the adjacent fluid that is

in motion and it involves the combined effects of conduction and fluid motion.

Radiation is the energy emitted by matter in the form of electromagnetic waves as a

result of the changes in the electronic configurations of the atoms or molecules.

61. Define Heat flux, Heat flow & Heat generation

Heat flux is defined as the rate of heat transfer per unit area.\

Heat flow means transfer of heat energy.

Heat generation means heat developed in the body.

62. Define adiabatic surfaces.

Adiabatic surfaces are surfaces which do not allow the flow of heat either into the body

or out the body.

63. Define Density, film coefficient.

Density is defined as mass per unit volume.

For a fluid confined in a vessel, the rate of flow of heat out of the fluid, per unit area of

vessel wall divided by the difference between the temperature in the interior of the fluid

and the temperature at the surface of the wall. Also known as convection coefficient.

64. Define Thermal gradient & Thermal conductivity.

The rate of temperature change with distance

Thermal conductivity is defined as the rate of heat transfer through a unit thickness of

the material per unit area per unit temperature difference.

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65. Define Specific heat .

It is a measure of a material’s ability to store thermal energy

66. Define Dynamic Analysis and its types

Dynamic analysis is analysis done if loading is of higher frequency or is applied suddenly.

Types are modal analysis, harmonic analysis etc

67. Define Modal & Harmonic Analysis with its application.

Modal analysis is the study of the dynamic properties of structures under vibrational

excitation

Harmonic analysis is analysis done when a structure is subjected to cyclic loading

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