ASSIGNMENT 1 INTRODUCTION TO CAD

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1 Computer Aided Design( ) ASSIGNMENT 1 INTRODUCTION TO CAD Theory 1. Discuss the reasons for implementing a CAD system. 2. Define computer aided design. Compare computer aided design and conventional design with a neat sketch/block diagram. 3. List and explain the important parameters to be considered while selecting CAD systems. List the different application of CAD in mechanical engineering. 4. State the different applications of CAD in an engineering field. Justify the need of CAD in engineering area. 5. Prepare the detailed specifications for a typical CAD workstation with latest hardware. 6. State the different CAD software commercial available and explain the features of CAD software in detail. (Any two software.) 7. What are the advantages of CAD in design? Explain application of Computers to the design process. 8. Explain DDA algorithm for generation of line and identify the pixel locations that will be chosen by the DDA algorithm while scan converting a line from screen coordinate (10,30) to (19,36). 9. Write Bresenham s algorithm for generation of line with suitable example. 10. What is graphics standards? 11. Give your Comments on the need for standardization in Computer Graphics. Briefly discuss about various graphics standards available. Darshan Institute of Engineering and Technology, Rajkot 1

2 ASSIGNMENT 2 CURVES AND SURFACES Theory 1. Write down differences between Analytic curves and Synthetic curves. 2. Develop the parametric equations for i) line ii) Circle iii) Ellipse. 3. Explain Hermite cubic spine curve with neat sketch also write its characteristics and obtain the parametric equation for the same. 4. With neat sketch explain the characteristics of Bezier curve, properties of Bezier curve and mention its advantages. 5. Explain B-spline curve and mention its advantages. Examples 1. A line having length 20 unit, passes through the point P1 (1,2). It makes an angle 60 with X- axis. Determine the parametric equation of line. 2. The end points of a cubic spline curve are P0(1,2), and P1(7,1). The tangent vector for end P0 is given by line joining P0 and point P2(-2,1). The tangent vector for end P0 is given by line joining P3(9,-2) and point P1. i. Determine the parametric equation of Hermite cubic spline curve. ii. iii. Determine the parametric equation for tangent vector. Plot the Hermite cubic curve. 3. A Bezier curve is to be constructed using control points P0(35, 30), P1(25, 0), P2(15, 25) and P3(5,10). The Bezier curve is anchored at P0 and P3. Find the equation of the Bezier curve and plot the curve for u= 0, 0.2, 0.4, 0.6, 0.8 and Generate a Bezier curve using the following control points: (2, 0), (4, 3), (5,2), (4, -2), (5, -3), and (6, -2). Darshan Institute of Engineering and Technology, Rajkot 1

3 ASSIGNMENT 3 MATHEMATICAL REPRESENTATION OF SOLIDS Theory 1. Write down differences between Analytic curves and Synthetic curves. 2. What are different types of geometric technique available? Describe the common facilities available in a solid modeling package. 3. Discuss about Constructive solid modelling (C-Rep) and Boundary representation (B- Rep) approaches. 4. What do you mean by 2D and 3D wireframe modeling? Differentiate between wireframe modeling and solid modeling technique for CAD. 5. Explain the feature based modeling with suitable examples in detail. 6. Explain the concept of half spaces. Darshan Institute of Engineering and Technology, Rajkot 1

4 Computer Aided Design( ) ASSIGNMENT 4 GEOMETRIC TRANSFORMATION Theory 1. What is a geometric transformations? Define and explain the following With respect to 2-D transformations: (i) Translation (ii) rotation (iii) scaling (iv) reflection. 2. Write a short note on orthographic and perspective projection. 3. Explain 2-D and 3-D shearing in brief. 4. Explain the concept of window to View-port transformation. Examples 1. Using transformation matrix determine the new coordinates of triangle A(0,0), B(3,2) and C(2,3) after it is rotated 45 clockwise about origin. 2. A rectangle ABCD has vertices A(1,1), B(2,1), C(2,3) and D(1,3). It has to be rotated by 30 0 CCW about point P(3,2). Determine the new coordinates of rectangle. 3. A triangle ABC with vertices A(30,20), B(90,20) and C(30,80) is to be scaled by factor 0.5 about a point X(50,40). Determine the coordinates of the vertices for a scaled triangle. 4. A rectangle is formed by the four point ABCD, whose co-ordinates are: A = (25,25), B = (25,125), C = (75, 125) and D = (75, 25) Calculate the new co-ordinates: (i) If it is changed by scaling factors Sx = 0.4 and Sy = 0.6 (ii) When after scaling centre is remained at same position and scaling factor is The coordinates of the triangle are P(50,20), Q(110,20) and R(80,60). Determine the coordinates of the vertices for the new reflected triangle, if it is to be reflected about :Xaxis and (ii) line y = x. 6. A rectangle ABCD having vertices A(10,15), B(25, 15), C(25, 25) and D(10, 25) is to be reflected about a line passing through points P(25, 20) and Q(10, 30). Determine the vertices of the reflected rectangle. 7. A triangle ABC with vertices A(0,0), B(4,0) and C(2,3). Perform the following operations for it. (i) Translation through 4 and 2 units along X and Y directions respectively. (ii) Rotation through 90 incounterclockwise direction about new position of point C. Darshan Institute of Engineering and Technology, Rajkot 1

5 Computer Aided Design( ) 8. Reflect the diamond shape polygon whose vertices are A(- 2,0), B(0,-1), C(2,0), D(0,1) about an arbitrary line L which is represented by equations y = 0.5x A rectangle parallel piped block ABCDEFGH has position vectors Obtain the transformed position vectors after rotation (i)about X axis θ = -90 and then (ii)about Y axis φ = 90. Darshan Institute of Engineering and Technology, Rajkot 2

6 ASSIGNMENT 5 Finite Element Analysis (Part 1) 1. Explain various steps for FEA. Theory 2. State and describe various types of elements used in FEA. Examples 1. A stepped shaft is as shown in fig. Determine the stresses and deflections in each of the sections. Assume uniform material for the complete shaft having a modulus of elasticity as 200 GPa and the axial force F as 35 KN. 2. By using a finite element method for the bar in fig. loaded as shown, determine the nodal displacements, element stresses and support reactions using minimum number of elements. Assume E = 200 x 10 9 N/m A rectangular section steel bar is suspended vertically from the top edge. First four meter length of the bar is 100 mm x 100 mm in cross section, while the lower 1 meter is 50 mm x 50 mm in cross section, the axis of the two cross sections being coincident. Model this as two linear elements and find the assembled stiffness matrix. Evaluate extension of the bar under self weight. Assume modulus of elasticity as 2.1 x 10 5 Mpa and specific gravity of steel as 8. Also determine the reaction forces and the stresses developed. Darshan Institute of Engineering and Technology, Rajkot 1

7 4. The stepped shaft as solved earlier in Q-5 is to be solved by penalty approach. Determine the deflections and reaction forces in each of the sections. Assume F = 35 KN and E = 200 GPa. 5. Solve the following example by penalty approach. Determine the displacements and support reaction. Assume modulus of elasticity as 80 x 10 3 N/mm 2. Darshan Institute of Engineering and Technology, Rajkot 2

8 6. For the compound section shown in fig. fixed at both ends, estimate reactions at both ends and stresses when a force of 1600 N is applied at the change of cross-section. Use penalty approach. 7. Consider the bar as shown in fig. Determine the nodal displacements, element stresses and reactions, if the temperature rises by 60 C. Assume modulus of elasticity for the complete bar as 200 GPa and coefficient of thermal expansion as 12 x 10-6 per C. Darshan Institute of Engineering and Technology, Rajkot 3

9 ASSIGNMENT 5FINITE ELEMENT ANALYSIS (Part 2) Theory 1. Derive the equation of element stiffness matrix by potential energy approach. 2. Explain pre processing & post processing related to FEA. 3. Explain natural coordinate system. 4. Explain shape function in natural coordinate system. Examples 1. Temperature at Node 1 is l00 C and at Node 2 is 40 C. The length of the element shown in Fig. 1 is 200 mm. Evaluate the shape function associated with Node 1 and Node 2. Calculate the temperature at point 'P' situated at 150 mm from Node 1. Assume a linear shape function. Figure 1 2. A 1D spar element having a linear shape function is as shown in Fig. 2. If the temperature at node 1 is 50 C and at node 2 is -20 C, find the temperature at point P. Figure 2 3. Consider an element having a linear shape function as shown in Fig. 3. Evaluate the natural coordinate and the shape functions for point P. If the displacement at node 1 and node 2 are 2mm and -1mm respectively, determine the value of the displacement at point P. Also determine in global terms, the point where the displacement would be zero. Also determine the shape functions at zero displacement point. Darshan Institute of Engineering and Technology, Rajkot 1

10 Figure 3 4. Determine the temperature at x = 40 mm, if the temperature at nodes φi = 120 C, φj= 80 C, and xi = 10 mm, xj = 60 mm. Figure 4 5. A system of springs is as shown in Fig. 5. Determine the overall stiffness matrix and determine the deflections of each of the springs. Figure 5 Darshan Institute of Engineering and Technology, Rajkot 2

11 6. Fig.6 shows a cluster of four springs. One end of the assembly is fixed and a force of 1000 N is applied at the end. Using the finite element method, determine: a. The deflection of each spring. b. The reaction forces at support. Figure 6 7. Fig. 7 shows a cluster of 5 springs. One end of the assembly is fixedand a force of 800 N is applied at the end. Using the finite element method, determine : a. The deflection of each spring. b. The reaction forces at support. Figure 7 8. For the two bar truss as shown in Fig. 8, determine the displacements ofand the stresses in the bars. Assume E = 70 GPa and A = 200 mm 2 for both members. Figure 8 Darshan Institute of Engineering and Technology, Rajkot 3

12 9. Fig. 9 shows a truss consisting of three elements whose AE/L value is1000 N/mm. Calculate the deflection at node 2. Figure 9 Darshan Institute of Engineering and Technology, Rajkot 4

Chapter 1 Introduction

Chapter 1 Introduction GTU Paper Analysis (New Syllabus) Sr. No. Questions 26/10/16 11/05/16 09/05/16 08/12/15 Theory 1. What is graphic standard? Explain different CAD standards. 2. Write Bresenham s