COMPUTER AIDED DESIGN

Question Bank

UNIT I

INTRODUCTION TO CAD

1. Explain two main processes through which the product goes from idea conceptualization

to finished product. (7m) (RTMNU Summer 2004)

2. Suppose a computer with 32 bits per word and a transfer of 1 mips (one million

instructions per second). How long would it take to fill the frame buffer of a 300 dpi (dots

per inch) laser printer with a page size of 8½ inches by 11 inches? (6m) (RTMNU Summer

2004)

3. Explain graphics, application and programming software modules with reference to any

commercial available CAD software. (9m) (RTMNU Summer 2004)

4. Assuming that a certain full-colour (24-bit per pixel) RGB raster system has a 512-by-512

frame buffer, how many distinct colour choices (intensity levels) would we have available?

How many different colours we display at any one time? (4m) (RTMNU Summer 2005)

5. Varieties of CAD software’s are available for different applications. Explain how CAD

software’s help for Education and Training applications. (4m) (RTMNU Summer 2005)

6. Consider two raster systems with resolutions of 640 by 480 and 1280 by 1024. How many

pixels could be accessed per second in each of these systems by a display controller that

refreshes the screen at a rate of 60 frames per second? What is the access time per pixel in

each system? (4m) (RTMNU Summer 2005)

7. What is computer aided design process? Explain how computer aids designer? (5m)

(RTMNU Summer 2005)

8. Explain the various steps which are used in Computer Aided Design process. (7m)

(RTMNU Summer 2006, 2007)

9. Discuss the working principles of following graphic terminals:-

i. DVST

ii. Raster Scan

iii. Vector refresh (RTMNU Summer 2006)

10. Explain with examples role of CAD in following areas of design:

i. Geometric Modelling

ii. Engineering Analysis

11. What is the conventional design process? How this process is modified when we use

CAD process? (7m) (RTMNU Summer 2009)

12. What are the benefits of CAD over conventional Design process? (3m) (RTMNU Summer

2009)

13. Explain product cycle. (3m) (RTMNU Summer 2009)

14. List the benefits of CAD/CAM Techniques. (5m) (RTMNU Summer 2010)

15. What do you mean by Geometric modelling? (4m) (RTMNU Summer 2010)

16. What are the types of graphics input devices? (2m) (RTMNU Summer 2010)

17. List the software used for Geometric modelling and for analysis. (2m) (RTMNU Summer

2010)

18. List the software modules and its capabilities related to CAD. (7M) (RTMNU Winter

2004)

19. Consider three different raster systems with resolution of 640 by 480, 1280 by 1024 and

2560 by

20. What size frame buffer (in bytes) is needed for each of these systems to store 12 bits per

pixel? How much storage is required for each system if 24 bits per pixel are to be stored?

(6m) (RTMNU Winter 2004)

20. What is the conventional design process? How this process is modified when we use

CAD process? (7m) (RTMNU Winter 2005)

21. Suppose a computer with 16 bits per word and a transfer rate of 1 mip (one million

instructions per second). How long would it take to fill the frame buffer of a 600 dpi (dots

per inch) laser printer with a page size of 8½ inches by 14 inches? (6m) (RTMNU Winter

2005)

22. Explain CAD software models and its capabilities related to CAD. (6m) (RTMNU Winter

2006)

23. Differentiate raster scan and random scan display systems. (7m) (RTMNU Winter 2006)

24. How CAD is used in designing Machine Element? Explain with suitable example. (7m)

(RTMNU Winter 2007)

25. What is Frame Buffer? Explain. (6m) (RTMNU Winter 2007)

26. What does the term 16-bit or 32-bit machine or computer mean? (2m) (RTMNU Winter

2007)

27. What is meant by single or double precision? How does that affect engineering and

design calculations? (4m) (RTMNU Winter 2007)

28. What is reasonable resolution of an eight-plane display refreshed from a bit map of 256

k bytes of RAM? (4m) (RTMNU Winter 2007)

29. An eitht-plane raster display has a resolution of 1280 horizontal × 1024 vertical and a

refresh rate of 60 Hz non-interlaced, find:

i. The RAM size of the bit map (refresh buffer).

ii. The time required to display a scan line and a pixel.

iii. The active displays area of screen if the resolution is 78pixels (dots) per inch.

iv. The optimal design if the bit map size is to be reduced by half. (4m) (RTMNU Winter

2007)

30. Explain the components of a CAD system. Why is geometric modelling component

considered important? (6m) (RTMNU Winter 2008)

31. List the input devices used in CAD. Explain any two. (3m) (RTMNU Winter 2008)

32. Explain the working DVST display. Why is it not popularly used today? (4m) (RTMNU

Winter 2008)

33. Explain Raster Refresh Graphic Displays. (7m) (RTMNU Winter 2009)

34. Explain the different softwares used for computer Aided Modelling and Analysis. ( 6m)

(RTMNU Winter 2009)

35. Explain the components of CAD system. (6m) (RTMNU Winter 2010)

36. Explain working of Raster Display System. Why is it popularly used today? (4m) (RTMNU

Winter 2010)

37. Explain about simple color frame buffer. (4m) (RTMNU Winter 2010)

UNIT-II

TWO DIMENSIONAL TRANSFORMATIONS

1. Explain how pixels are selected in Bresenham’s line algorithm. Write equation for decision

parameter. (7m) (RTMNU Summer 2004)

2. A triangle with vertices at A(0,0), B(8,0), C(0,8) is scaled by 1.2 units in X-direction. It is

translated by 3.5 units in Y-direction and two units in X-direction. Find the final position of

the triangle. Show the total transformation on graph paper stepwise. (7m) (RTMNU Summer

2004)

3. Prove that successive decision parameter Pk for midpoint circle generation algorithm is

Pk+1=Pk + 2xk+1 + 1 – 2yk+1 when Pk ≥ 0. Initial value of decision parameter is P0 = 5/4 – r

Where k = 0,1,2,3,4,…………. (7m) (RTMNU Summer 2005)

4. A point P has co-ordinates (10,5) with reference to XY Cartesian system. What will be the

coordinates of point P with reference to X’Y’ cartesian system. Two cartesian systems are

shown in

Figure

Write the steps and matrix for transformation between Cartesian co-ordinate systems. (6m)

(RTMNU Summer 2005)

5. Show that transformation matrix for a reflection about the line Y= -X is equivalent to a

reflection relative to the Y- axis followed by a counter clockwise rotation of 900. (7m)

(RTMNU Summer 2005).

6. Show the nature of two dimensional Bezier curves for three, four, five and six control

points. (6m) (RTMNU Summer 2005)

7. Write DDA Algorithm for a straight line and hence vectorize a line to be drawn from

(10,20) to (18,30). Plot the points on graph-paper. (9m) (RTMNU Summer 2006)

8. Explain the concept of homogeneous co-ordinates in graphics transformations. (4m)

(RTMNU Summer 2006, 2007)

9. Figure shows a circle with radius r = 5 cm. center ‘A’ (5,8) is to be converted into an ellipse

with major axis r1 = 8cm, minor axis r2 = 5 cm. find the total transformation matrix. (6m)

(RTMNU Summer 2006)

10. Write Bresenham’s circle generating algorithm. (7m) (RTMNU Summer 2006)

11. Explain and write Bresenhaem’s midpoint algorithm to draw circle of radius ‘R’ at centre

(Xc, Yc). (7m) RTMNU Summer 2007, Winter 2007, 2008, 2010) OR Write an algorithm to

draw circle with radius (R). (7m) (RTMNU Summer 2009)

12. Write Bresenhem’s line generating algorithm. (6m) (RTMNU Summer 2007)

13. The triangle having vertex (2,2), (10,2) and (6,4) is first translated by 3 units in x-

direction. Then it is rotated by 200 in C. W. about origin direction and then it is scaled by 4

unit in Y-direction. Find out final position of the triangle about origin. (6m) (RTMNU Summer

2007)

14. Develop DDA algorithm to draw a straight line with slope ‘m’, ∞ < m < -1, generalize this

algorithm for line with any slope. (6m) (RTMNU Summer 2009, Winter 2008) OR Write DDA

Algorithm for line. (5m) (RTMNU Summer 2010, Winter 2010)

15. Explain shear transformation. (3m) (RTMNU Summer 2009)

16. Find out the final position of line having end points (2,2) and (10,4), when it is translated

by 5 units in y direction. Then scaled 2 units in x-direction and then rotated by 450 in

clockwise direction. (7m) (RTMNU Summer 2009)

17. Show that two rotations are cumulative. (3m) (RTMNU Summer 2009)

18. Show that rotation about origin by 2700 is equivalent to reflection about two axes. (3m)

(RTMNU Summer 2009)

19. Write an algorithm to draw an arc in clockwise sense. Input is centre, radius, start angle

zero and end angle 900. (5m) (RTMNU Summer 2010)

20. What do you mean by concatenation? (5m) (RTMNU Summer 2010)

21. Obtain the reflection of a figure defined by the coordinates A(-1,0), B(0,-1), C(1,0) and

D(0,2) about the following axis. (i) y = 2 (ii) x = 2 (iii) y = x + 2

24. Write short note on shear transformation. (3m) (RTMNU Summer 2010)

25. A triangle having coordinates A (3,3), B(6,3) and C(4,7) is translated by 2 units in X-

direction and 3 units in Y-direction then it is scaled by factor 1.5 units with respect to point

(4,4). Find the final position of triangle. (9m) (RTMNU Summer 2010)

26. Derive the decision parameter for the midpoint circle algorithm assuming the start

position is (o.ry) and points are to be generated in clockwise order. (7m) (RTMNU Winter

2004)

27. A part drawing of a sub-assembly is printed on A4 size paper (210 × 300 mm) in position

A as shown in figure. It is desired to print the part drawing in position B. find the final

transformation matrix. (7m) (RTMNU Winter 2004)

28. A line PQ was transformed to P’Q’. P’(10,10), Q’(20,20). Transformation carried out

were:

(i) Scaling about origin by 2 units.

(ii) Rotation about origin by 450.

Find out the co-ordinates of end points of original line PQ. (7m) (RTMNU Winter 2004)

29. Determine the form of transformation matrix for a reflection about an arbitrary line with

equation Y = mX + C. (6m) (RTMNU Winter 2004)

30. In a midpoint ellipse generation algorithm, the first quadrant of ellipse is divided in two

regions as shown in figure. Derive the decision parameter to select pixels for region I.

explain why the same decision parameter cannot be used for region II. Calculate pixels for

region I. (7m) (RTMNU Winter 2005)

31. A triangle having vertices (2,3), (6,3) and (4,8) is reflected about the line having equation

Y = 3X + 4. Find

the final position of the triangle using 2D transformation. (6m) (RTMNU Winter 2005)

32. The figure ABC is to be transformaed to A’B’C’. find the transformation. (7m) (RTMNU

Winter 2005)

33. Explain and write Bresenhem’s algorithm for generation of line with slope less than one?

(9m) (RTMNU Winter 2006)

34. Rasterize a quarter circle using Bresenham’s midpoint algorithm in positive quadrant

with (3,3) as centre as Radius = 5. (5m) (RTMNU Winter 2006)

35. What do you mean by homogenous transformation and what is its need in concatenated

transformation, in case of 2-D transformation? (4m) (RTMNU Winter 2006)

36. Find the transformation which converts the figure defined by vertices A(3,2), B(2,1) and

(C(4,1) into another figure which is defined by vertices A’(-3,-1), B’(-4,-2) and C’(-2,-2). (9m)

(RTMNU Winter 2006)

37. Find the final position of a rectangle defined by point A(2,2), B(4,2), C(2,4), D(4,4) when

reflected about a line defined by the equation y=2x+10. (7m) (RTMNU Winter 2007)

38. Why is DDA algorithm to draw a line not preferred over Bresenham’s algo? (5m)

(RTMNU Winter 2007)

39. State and explain the essential characteristics of line drawing algorithms. (5m) (RTMNU

Winter 2009)

40. Write note on Homogeneous coordinates system. (4m) (RTMNU Winter 2009)

41. Show that rotation about origin by 2700 is equivalent to reflection about two axes. (3m)

(RTMNU Winter 2009)

42. Determine 3×3 homogeneous transformation matrix to transform a square ABCD into

another square A’B’C’D’ as shown in figure. The side of square ABCD is 2 unit and coordinate

of point A is (20,10). Depict the final transformation on graph paper. (6m) (RTMNU W2010)

43. A triangle ABC is to be reflected about its side BC. Explain the steps required and

determine the resultant transformation matrix. A(2,3), B(10,8) and C(-1,10). (7m) (RTMNU

Winter 2010).

UNIT III

THREE DIMENSIONAL TRANSFORMATIONS

1. Explain the concept of homogeneous co-ordinate system. If homogeneous co-ordinate h

is 0.5 and 2, what will be the co-ordinates of point P(2,4,8). (5m) (RTMNU Summer 2004)

2. Consider a region defined by the position vectors

Relative to the global XYZ axis system. It is rotated by +300 about the X’ axis parallel to X axis

and passing through point (1.5,1.5,1.5,1). Find the final transformation matrix and final

positions of the region. (8m) (RTMNU Summer 2004)

3. Should topology and geometry of solid model inter-related? If not, what will happen?

(3m)

4. What are the primitives used in CSG? (6m)

5. How 3D solid is represented in CSG method? Explain with suitable example. (4m) (RTMNU

Summer 2010)

6. What is Bezier curve? How is it defined? How is it used? (4m) (RTMNU Summer 2010)

7. What are the properties of Bezier curve? (RTMNU Summer 2004,Winter 2008)

8. Explain Bezier curve and write its basic properties. (6m) (RTMNU Winter 2006)

9. Explain the characteristics of Bezier Curves. (7m) (RTMNU Summer 2006)

10. Show the exact B-rep model of a cylinder and sphere. (5m)

11. Compare the two techniques of solid modeling C.S.G. and B-rep techniques. (6m)

(RTMNU Summer 2006)

12. Explain with example CSG and B.rep. techniques. (3m) (RTMNU Winter 2004)

13. How is 3-D solid represented in CSG method? Explain with suitable example. (5m)

(RTMNU Winter 2010)

14. Show the nature of two dimensional Bezier curves for three, four, five and six control

points. (6m) (RTMNU Summer 2005)

15. A cone with its base in X, Y plane and centre of base circle at (0,0) has radius 5 and axis

along Z axis of height 10 is rotated about a line A passing through L(0,0,0), A(20,10,10) by

450 clockwise. What are the co-ordinates of centroid of the cone before and after

transformation of all transformation matrix. (9m) (RTMNU Summer 2005)

16. Prove that the multiplication of three-dimensional transformation for two successive

scaling operations is commutative. (5m) (RTMNU Summer 2005)

17. Compute 3D-homogeneous transformation matrix to carry out a transformation

comprising a translation of 20 mm in the Z direction together with a rotation of 350 about a

line parallel to the Z-axis through (20,20,0). (8m) (RTMNU Summer 2007)

18. Write necessary steps and transformation matrix for a rotating a point in 3-D space

about a given 3-D line. (8m) (RTMNU Winter 2010)

19. What are blending functions? Explain the blending functions for Bezier curve and Bezier

surface. (6m) (RTMNU Summer 2007)

20. Write short note on-

I. 3D modeling (Summer 2006,2007)

II. Zeroth order continuity (Summer 2004,2007)

21. A cube of 6 mm having one point at (0,0,0) is translated 3 mm in x-direction and scaled

twice in all direction. Find the final position of cube. (10m) (RTMNU Summer 2009, Winter

2009)

22. Explain and write the series of transformations required to rotate a point P(x,y,z) about

an arbitrary line in 3D space. [Sequence and individuate transformation matrices are

expected, total resultant transformation is not expected]. (14m) (RTMNU Summer 2009)

23. A cube of length 10 units is having one of its corner at the origin (0,0,0) and three edges

along the three principle axes. If the cube is to be rotated about Z-axis by an angle 450 in

counter clockwise direction. Calculate the new position of cube. (10m) (RTMNU Winter

2004, Summer 2010)

24. A point P(3,4,5) is defined in space in absolute co-ordinate system. Define the point in

cylindrical and spherical co-ordinate system. Locate the point on graph paper. (4m) (RTMNU

Winter 2004)

25. Calculate the three dimensional homogeneous transformation matrix to carry out a

transformation comprising a translation of 20 mm in the z-direction together with a rotation

of 300 about a line parallel to the z-axis through (20,20,0). (10m) (RTMNU Winter 2005)

26. Explain the Boolean operations required to model a cone pulley. From the solid primitive

cylinder, shown in figure. (7m) (RTMNU Winter 2005)

27. A point P(6,9,12) is defined in space in absolute co-ordinate system. Define the point in

cylindrical and spherical co-ordinate system. Locate the point on graph paper. (6m) (RTMNU

Winter 2005)

28. Create a CSG model of solid shown in figure (without dimensions) using set theory. (7m)

(RTMNU Winter 2006)

29. Explain the concept of surface of revolution and generate the solids, cylinder, cone and

sphere using various types of surfaces. (6m) (RTMNU Winter 2006)

30. Write down the parametric form of the quadratic Bezier curve B(t) with central points

b0(-1,5), b1(2,0) and b2(4,6). Evaluate B(0.75) and B(1.25). Also draw a plot of curve

obtained by evaluating B(t) at a sequence of parameter values in the interval [0,1]. (9m)

(RTMNU Winter 2007)

31. Compare the transformation matrix of the rotation through an angle θ about the line

through the points P(2,1,5) and Q(4,7,2). (13m) (RTMNU Winter 2006)

UNIT IV

FINITE ELEMENT METHOD

1. For the figure shown below find displacement of each node and reaction at support

E=210Gpa. All dimensions are in mm. (RTMNU Summer 2004)

2. Explain the principle of Minimum Potential Energy. (RTMNU Summer 2004, Winter 2006,

Winter 2008, Winter 2010)

3. What do you mean by plane stress and plane strain conditions? Explain each with suitable

example. (RTMNU Summer 2004, Winter 2009)

4. Explain why shape functions are required in FEM? Write at least one shape function for

linear and quadratic bar equations. (RTMNU Winter 2004)

5. Explain plain stress and strain compatibility condition. Write the stress and strain matrix

for the same. (RTMNU Winter 2004)

7. Define minimum potential energy principle. Write the generalized mathematical

expression for potential energy in terms of stress, strain and forces acting on the element.

(RTMNU Winter 2004)

8. Explain the significance of Bandwidth in FEM. (RTMNU Winter 2004, Summer 2005)

9. “Finite Element Method” is best for engineering analysis problems. Comment. (RTMNU

Summer 2005)

10. Discuss different types of elements used in finite element method along with their

characteristics. (RTMNU Summer 2005, Summer 2009, Winter 2009, Summer 2010, Winter

2011)

11. The stepped shaft shown in figure is fully restrained against rotation at supports about

its axis. Twisting moment of 15 kN is applied at the point of changing section. J1 = 3 × 107

mm4 , J2 = 2 × 107 mm4

a) Calculate the rotation of the bar about its axis at point where torque is applied.

b) Determine reaction twisting moment at the end of the bar.

cDistribution of torque along the bar. (RTMNU Summer 2005, Winter 2012)

12. Consider the bar in fig. having cross sectional area Ae = 625 mm2 and Young’s modulus =

200 x 105 N/mm2. If q1 = 0.6 mm and q2 = 0.8 mm; do the following:

a) Find displacement at point P

b) Stress and strain in the element

c) Find element stiffness matrix

d) Strain energy in the element (RTMNU Summer 2005)

13. Explain how Bandwidth effects the size of a stiffness matrix? What are the properties of

stiffness matrix? (RTMNU Summer 2005)

14. What considerations are taken into account while discritizing the domain for FEM?

(RTMNU Winter 2005)

15. Explain with examples plane stress and plane strain problems. (RTMNU Summer 2005)

16. Explain the difference between plane stress and plane strain problems. (RTMNU Winter

2005)

17. What are shape functions? How would you determine shape functions for one

dimensional cubic model? (RTMNU Winter 2005)

18. What are isoparametric elements? Determine the shape functions for a triangular

isoparametric element. (RTMNU Winter 2005)

19. List the applications where finite element method is used. (RTMNU Summer 2006)

20. Give the difference between finite element method and finite difference method.

(RTMNU Summer 2006)

21. For the linear elastic spring subjected to a force of 1000 KN shown in figure evaluate the

total potential energy for various displacement value, Starting deformation x = -4 mm to

Ending deformation x = 5 mm with increment at one mm and hence show that the minimum

potential energy also corresponds to the equilibrium position of the spring. Also draw

variation at potential energy with spring deformation. (RTMNU Summer 2006)

22. Figure shows one dimensional elements subjected to load at the end P = 10 KN.

Determine nodal displacement and support reaction. (RTMNU Summer 2006)

23. Explain the shape function for 1-D quadratic bar element along with their salient

features (RTMNU Winter 2006, Winter 2010, Winter 2012)

25. Explain the steps of finite element method. (RTMNU Summer 2007)

26. Derive the relation for principle of minimum potential energy. (RTMNU Summer 2007)

27. Figure shows a composite bar carrying force P = 60KN. Esteel = 200 GPa EAl = 70 GPa

connection plate and walls are rigid, treating each member as one dimensional linear

element. Determine,

a) Stresses in each member.

b) Displacement of a load point

c) Reactions at wall. (RTMNU Summer 2007)

28. Consider the bar in figure. Determine the nodal displacement, element stresses and

support reactions. (RTMNU Winter 2007, Winter 2008)

29. Derive equation for element strain displacement matrix {B} for two dimensional

constant strain triangle. (RTMNU Winter 2007)

30. Figure shows a one dimensional two node element. Displacement function in terms of

polynomial equation is u(x) = A + Bx. Where ‘A’ and ‘B’ are constants. Derive equation for

shape function. (RTMNU Winter 2007)

31. Explain the steps carried out in finite element analysis. (RTMNU Winter 2008, Winter

2010)

32. What do you understand by shape functions? (RTMNU Winter 2008, Winter 2009)

33. A horizontal step bar consists of two steps and made of steel material. An axial load P =

5 KN is applied as shown in figure. Using elimination method, calculate: (RTMNU Summer

2009)

a) Global stiffness matrix.

b) Displacement at nodal point

c) Stresses in each element.

d) Reactions at support.

34. The nodal co-ordinates of the triangular element as shown in Fig. 7. At the interior point

P, the x coordinate is (7, 4) and N1 = 0.3. Determine N2, N3 and the y-co-ordinate of point P.

(RTMNU Summer 2009)

35. Write the steps used to solve the numerical by F.E.M. Techniques. (RTMNU Winter 2009)

36. For the one-dimensional steel bar fixed at each end as shown in figure, determine the

reactions, nodal displacement, and stress in the element. Let E = 210 GPa and A = 1 x 10-2

m2. (RTMNU Winter 2009)

38. For a plane stress condition of a CST elements shown in figure, determine Element

Stiffness matrix and the Principle stress and the Principle Plane angle (Op). Assume: E = 200

GPa; t = 10 mm; r = 0.3. (RTMNU Summer 2010)

39. Derive an expression of element stiffness matrix for two dimensional constant strain

triangular element using shape function. (RTMNU Winter 2010)

40. Figure shows a thin plate having uniform thickness t = 25 mm. modulus of elasticity E = 2

x 105 N/mm2. In addition to self weight it is subjected to two point loads as shown. The

density ρ = 7.86 x 10-6 gm/mm3. Model the plate with one-dimensional elements and

determine stresses in each member. (RTMNU Winter 2011)

41. Explain in brief the various approaches used to formulate element matrices. (RTMNU

Summer 2012)

42. For the spring assemblage shown in figure obtain

a) the assembled stiffness matrix

b) the displacement of node 2 and 3

c) the reaction forces at node 1 and 4

d) the forces in each spring. (RTMNU Summer 2012)

43. For the three stepped bar shown in figure, the bars fit snugly between the rigid walls at

room temperature. The temperature is then raised by 400C. Determine the displacements

at 2 and 3 and the stresses in the three sections. (RTMNU Summer 2012)

44. What do you understand by shape function ? Name the various shape functions used for

one dimensional

finite element modelling. (RTMNU Summer 2012)

45. What are the various steps involved in FEM? (RTMNU Winter 2011, Winter 2012)

UNIT V

TWO DIAMENSIONLA FINITE ELEMENT METHOD1. For the truss shown in fig., find the displacement of node 1 and reactions at support A

and B. Area of cross-section of each link = 200 mm2 and Modulus of Elasticity E = 200 Gpa.

(RTMNU Summer 2004, Summer 2007, Winter 2010)

2. Explain the shape function for CST element. (RTMNU Summer 2004)

3. A helical compression spring of a Cam mechanism is subjected to an initial preload of 50

N. The maximum operating force during the load cycle is 150 N. The wire diameter is 3 mm,

while mean coil diameter is 18 mm. The spring is made of oil hardened and tempered Valve

spring wire of grade VW (Sut = 1430 N/mm2). Factor of safety = 1.25. Do the following:

(RTMNU Summer 2004)

a) Discritize the spring in 1D element.

b) Calculate length of element.

c) Calculate polar moment of inertia.

d) Calculate mean and amplitude torque in element. Torque = Force x Spring diameter/2

e) Deflection of spring.

f) Check if direct shear stress in element is less than design stress. Take shear stress

correction factor as 1.1. Direct shear stress = 0.5 of torsional shear stress.

4. Derive the element strain matrix B for constant strain triangle. (RTMNU Winter 2004)

5. Derive the co-ordinates at point P if the shape function

N1 = 0.25, N2 = 0.3 and N3 = 0.45 (RTMNU Winter 2004) Find displacement (u, v) at point P

if qT = [0.1, 0.2, 0.15, 0.1, 0.1, 0.2].

7. A helical tensile spring with wire diameter d = 3 mm and mean coil diameter D = 18 mm

having number of turns N = 10 is fixed at one end and a load of F = 100 N is applied at other

end. Modulus of rigidity G is 81370 N/mm2. (RTMNU Summer 2005)

a) Discritize the spring into one element defined by two node having shape functions:

b) Prove that deflection obtained by FEM is same as that given by the formula:

8. Fig. shows a truss consisting of three elements. Cross-sectional area of each bar = 200

mm2, E = 200 GPa Calculate deflection of nodes, stress and strain in each element and

Reaction at supports. (RTMNU Summer 2005)

10. Explain the terms pre-processing and post-processing with reference to FEM. (RTMNU

Winter 2005)

11. Consider the rod (a robot arm) in figure which is rotating at constant angular velocity ω =

30 rad/s. Determine the axial stress distribution in the rod using two linear finite elements.

Plot the stress distribution (ignore bending, consider only centrifugal force). (RTMNU Winter

2005) A = 375 mm2, E = 8 x 104 MPa Weight density ρ = 9 gm/cm2

12. Suppose a plate as shown in figure is discretized by triangular elements into four

elements. Find

a) Degree of freedom.

b) No. of element matrix.

c) Size of global stiffness matrix

d) Bandwidth of global stiffness matrix.

e) Area of element 2 using Jacobian.

f) Element strain matrix for element 2.

g) Can the bandwidth be reduced by changing node numbers? (RTMNU Winter 2005)

13. Derive an individual element stiffness matrix for two dimensional CST element starting

with stretch energy of the triangular element. (RTMNU Summer 2006)

14. Fig shows a triangular element with thickness f = 15 mm. If load P = 15 KN is applied as

shown in figure determine nodal displacement. Young’s Modulus E = 210 GPa, Poisson’s

Ratioν = 0.3. (RTMNU Summer 2006)

15. Analyze the truss shown in figure to determine the nodal displacement stresses in

members and the reactions at the supports. (RTMNU Summer 2006)

16. Find the simultaneous equations for the nodal displacement of a Beam having two C.S.T.

elements as shown in figure. Assume plane stress condition. Take f = 0.25, E = 2 x 105

N/mm2, Thickness = 15mm. (RTMNU Winter 2007)

17. Derive expression for shape functions of one dimensional linear element in natural co-

ordinates. (RTMNU Winter 2008)

18. Derive an expression for strain displacement transformation matrix‘B’ for two

dimensional constant strain triangular element. (RTMNU Winter 2008)

UNIT VI

OPTIMIZATION

1. Define the following terms with reference

(i) Design Variables

(ii) Constraints

(iii) Objective Functions

(iv) Variable Bounds. (RTMNU Summer

2. Write the algorithm for Golden section Summer 2007)

3. State the optimality criteria used in multi-variable optimization. (RTMNU Summer 2004)

4. State and explain Duality principle. (RTMNU Summer 2004)

5. Write short note on Bisection Method and Simplex Method. (RTMNU Winter 2004,

Summer 2007)

6. Write short note on Penalty approach in FEM. (RTMNU Winter 2004, Summer 2007)

7. Use four iterations of the golden section search method in order to maximize the

function: f(x) = 10 + x3 – 2x – 5 exp (x) in the interval (-5, 5). (RTMNU Summer 2005)

8. Explain with example Single Variable Optimization Problem. (RTMNU Summer 2005)

9. What is Compatibility ? Derive compatibility equation in teo-dimensions. (RTMNU Winter

2005)

10. Explain the“Simplex search method” for multivariable optimization. Also write the

algorithm for the same. (RTMNU Summer 2006, Winter 2007, Winter 2009, Winter 2011,

Winter 2012)

11. Using Bisection Method Minimize, F(x) = x2 + 54 / x bracketed in the interval (a, b) where

a = 2, b = 5, select small number = 10-3. (RTMNU Summer 2006)

12. Write the Golden Section Search Algorithm for single variable optimization problem.

(RTMNU Winter 2006, Winter 2008, Summer 2010)

14. Discuss“Optimal problem formulation.” Give a flow chart of the optimal design

procedure. (RTMNU Winter 2007)

15. Using Bisection method, minimize f(x) = x2 + 40/x in interval (a, b) a = 1 to b = 4solve

upto 3 iterations. (RTMNU Winter 2008, Winter 2012)

16. Explain Golden Search Method. (RTMNU Summer 2009)

17. Explain steps used in formation of“Optimal Problem Formulation.” (RTMNU Summer

2009)

18. Explain with suitable example Bisection method for single variable optimization.

(RTMNU Winter 2009, Winter 2011)

19. Using Bisection method, minimize: F(x) = ex – x3 (RTMNU Winter 2010)

20. Write short notes on:

a) Golden search method

b) Penalty function method

c) Bisection method

d) Hermite shape functions for beam element. (RTMNU Summer 2012)

21. Explain the“Simplex search method” for one variable optimization. (RTMNU Summer

2010)

22. Explain Golden Section Search method for single variable optimization problem.

(RTMNU Winter 2010)

Subject Teacher

Prof. P.V.Lande

VI (A)