gtu paper analysis (new syllabus) chapter 1 introduction...the temperature rises from 20 'c to...

GTU Paper Analysis (New Syllabus)

COMPUTER AIDED DESIGN (2161903) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Chapter 1 –Introduction

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Theory

1. What is graphic standard? Explain different CAD standards. 07 07

2. Write Bresenham’s line algorithm. Determine intermediate pixels for line starting from (1, 1) to (8, 5). 07

3. Explain DDA algorithm for line generation with its limitations. 07

4. Write a Breshnham’s algorithm for line having slop more than 45° 07 07

5. Explain IGES graphic standard in detail with structure. 07 07

6. State different commercial CAD software available and explain the features of any two CAD software in detail.

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Examples

1.

Determine following for an 8-plane raster display with resolution of 1280 x 1024 and a refresh rate of 60Hz (non-interlaced):

i. The size of graphical memory (refresh buffer memory).

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

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

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Chapter 2– Curves and Surfaces

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1. With the help of neat sketches explain various types of surfaces. 07

2. Derive general parametric equation for Hermits cubic spline curve in matrix form. 07 07 07

3. Two Bezier curve sections A and B have order of 3 and 4 respectively. Derive the condition for 1st order (C1) continuity between these two sections.

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4. What is parametric representation? 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.

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5. Explain the following surfaces 1. Plane surface 2. Bezier surface 3. B-spline surface 4. Coons surface 07

6. Write parametric equation for Bezier curve. Briefly discuss its characteristics. 07

7. Explain analytic curves and synthetic curves with example. 07 04



Examples

1. 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 1.

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2. Coordinates of four data points P0, P1, P2 and P3 are (2, 2, 0), (2, 3, 0), (3, 3, 0) and (3, 2, 0) respectively. Find the equation of Bezier curve and determine the coordinates of points on curve for u = 0, 0.25, 0.5, 0.75 and 1.0.

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3.

A line is represented by the end points P1 (2, 4, 6) and P2 (-3, 6, 9). If the value of parameter u at P1 and P2 is 0 and 1 respectively, determine the tangent vector for the line. Also determine the coordinate of a point represented by; u equal to 0, 0.25, -0.25, 1 and 1.5. Also find the length and unit vector of line between two points P1 and P2.

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Chapter 3 – Mathematical representation of solids

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Theory

1. Explain constructive solid geometry (CSG). 05

2. Write limitations of a wire frame model. 02

3. Write short note on Constructive Solid Geometry (CSG) for solid modeling. 07

4. What do you understand by 2 ½ D model? Clearly distinguish it from 3-D model. 07

5. Compare CSG and B-rep techniques of solid modeling. 07

6. Differentiate between wireframe modeling and solid modeling technique. 07

7. Enlist the various methods of geometric modeling. Discuss wire frame modeling in detail. 07 07

8. Discuss steps involved in feature based modeling. List most commonly used feature operations in CAD systems.

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Chapter 4 – Geometric Transformations

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Theory

1. Explain two dimensional geometric transformations in details. Also give transformation matrix for each 07

2. Explain orthographic and oblique projections in details with suitable sketch. 07

3.

Write 3x3 transformation matrix for each of the following effects; (i). Scale the image to be twice as large and then translate it 1 unit to the left. (ii). Scale x direction to be half as large and the n rotate anticlockwise by 90O about origin. (iii). Rotate anticlockwise about origin by 90O and then scale the x direction by half as large. (iv). Translate down 0.5 unit, right 0.5 unit, and then rotate anticlockwise by 45O.

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Examples

1.

A triangle PQR has its vertices at P (0, 0), Q (4, 0) and R (2, 3). It is to be translated by 4 units in X

direction, and 2 units in Y direction, then it is to be rotated in anticlockwise direction about the new

position of point R through 90o. Find the final position of the triangle.

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2. A triangle ABC has vertices as A (2, 4), B (4, 6) and C (2, 6). It is desired to reflect through an arbitrary line L whose equation is y=0.5X+2. Calculate the new vertices of triangle and show the result graphically.

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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 (i) the composition matrix and (ii) the coordinates of the vertices for a scaled triangle.

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4.

A triangle ABC with vertices A(0,0), B(4,0) and C(2,3) is Translated through 4 and 2 units along X and Y directions respectively and then Rotated through 90o in counterclockwise direction about the new position of point C. Find: (1) The concatenated transformation matrix and (2) The new position of triangle

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Chapter 5 – Finite Element Analysis

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1. What is shape function? Derive linear shape functions for 1-dimensional bar element in terms of natural coordinate. Also plot variation of shape functions within this element.

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2. With the help of suitable examples explain condition of plane stress and plane strain. 07

3. List properties of global stiffness matrix [K]. 04 03

4. Write element stiffness matrix and element load vectors for a beam element. 03

5. What are the different types of elements used in FEA? Explain in brief. 07

6. Explain the concepts of FEM. Discuss the different steps involved in FEA in detailed. 07 07

7. Explain Penalty approach and Elimination approach for FEA. 07

8. What do you mean by primary and subsidiary design equation? Explain with example. 07

9. Explain Johnson method of optimum design with an example. 07

10. Discuss the advantages of finite element analysis. 03

11. With reference to finite element analysis, discuss the treatment of boundary condition using elimination approach.

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Examples

1.

Consider the bar shown in figure-1. An axial load F=35 kN is applied as shown. Using penalty approach for handling boundary conditions, determine nodal displacements and support reactions. Take E=200 GPa. for all elements. Length of each element is in mm.

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2.

Consider the bar as shown in figure-2. Determine the nodal displacements and element stresses, if the temperature rises from 20'C to 60oC. Take P=300kN, E1=70GPa, A1=900 mm2, Coefficient of thermal expansion, α1=23 x 10-6 per 'C ; E2=200GPa, A2=1200 mm2, Coefficient of thermal expansion, α2=11.7 x 10-6 per 'C.

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3. Evaluate the shape functions N1, N2 and N3 at the interior point P (3.85, 4.8) for the triangular element shown in figure-3. Also determine Jacobean of the transformation J for the element.

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4.

A stepped shaft is shown in figure-1. Using Elimination Approach, determine the stresses and nodal displacements for each element. Assume uniform material for the complete shaft having a modulus of elasticity as 200 GPa and axial force F as 35kN. Length of each element is in mm.

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5 A four bar truss is as shown in figure-4. Assuming that for each element, the cross-sectional area is 400 mm2 and modulus of elasticity is 200 GPa, determine the nodal displacements. Length of each element is in mm.

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6

A stepped metallic bar with circular cross section consists of two segments. Length & cross section area of first segment is 350 mm & 275 mm2 respectively. Length & cross section area of second segment is 250 mm & 175 mm2 respectively. Assume modulus of elasticity is 200 GPa. If one end of the bigger segment is fixed and if an axial tensile force acting on the free end of the smaller segment is 700 kN, find: (1) Nodal displacements, using global stiffness matrix. (2) Elemental Stresses, (3) Support Reaction.

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A two-step as shown in figure is subjected to thermal loading conditions. The length of left step is 250 mm & length of right step is 350 mm. An axial load P = 200 x 103 N applied 20°C to the end. The temperature of the bar is raised by 50°C. Calculate: (i) Element stiffness matrix (ii) Global stiffness matrix Consider E1 = 70 x 103 N/mm2, E2 = 200 x 103 N/mm2, A1 = 700mm2, A2 = 1000 mm2, α1 = 23 x 10-6 per °C and α2 = 11.7 x 10-6 per °C.

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8

Fig.1 shows the compound section fixed at both ends. With the help of FEA estimate the reaction forces at the supports and the stresses in each material when a force of 200 KN is applied at the change of cross section.

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9

A system of a rigid cart connected by three linear springs as shown in Fig.2. The force of 60 N is acting on cart as shown in figure. Determine the following: (1) Use finite element concept to assemble the elemental stiffness matrices of three linear springs into global stiffness matrix. (2) Write global load vector. (3) Find Nodal solution.

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10 For one dimensional element shown in Figure 1, temperature at node 1 is 100 0C and at node 2 is 40 0C. Evaluate shape function associated with node 1 and node 2. Calculate temperature at point P. Assume linear shape function.

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A stepped metallic bar, made of aluminum (E1 = 70 x 103 N/mm2) and steel (E2 = 200 x 103 N/mm2), is subjected to the axial force of 5000 N, as shown in figure 2. It is attached to rigid wall at node 1. Determine nodal displacements using finite element analysis.

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12

Figure 3 shows two springs connected in series, having stiffness 12 and 8 N/mm respectively. One end of the assembly is fixed and a force of 60 N is applied at the end. Using finite element method; (i). Derive global stiffness matrix (ii). Derive global load vector (iii). Find displacement of all the nodes

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gtu paper analysis (new syllabus) chapter 1 introduction...the temperature rises from 20 'c to...

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