## Computer Aided Design - May 2016

### Mechanical Engineering (Semester 6)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Explain DDA algorithm for line generation with its limitations.(7 marks)
**1 (b)** What is graphic standard? Explain different CAD standards.(7 marks)
**2 (a)** 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.(7 marks)

### Solve any one question from Q2(b) & Q2(c)

**2 (b)** Explain two dimensional geometric transformations in details. Also give transformation matrix for each.(7 marks)
**2 (c)** Explain orthographic and oblique projections in details with suitable sketch.(7 marks)

### Solve any two question from Q3(a), Q3(b), Q3(c) & Q3(d), Q3(e), Q3(f)

**3 (a)** What is parametric representation? A line having length 20 unit, passes through the point P_{1} (1, 2). It makes an angle 60° with X-axis. Determine the parametric
equation of line.(7 marks)
**3 (b)** Explain B-spline curve and mention its advantages.(7 marks)
**3 (c)** Explain the following surfaces

1. Plane surface

2. Bezier surface

3. B-spline surface

4. Coons surface(7 marks)
**3 (d)** A Bezier curve is to be constructed using control points P_{0} (35, 30), P_{1} (25, 0),
P_{2} (15, 25) and P_{3} (5, 10). The Bezier curve is anchored at P_{0} and P_{3}. Find the
equation of the Bezier curve and plot the curve for u= 0, 0.2, 0.4, 0.6, 0.8 and 1.(7 marks)

### Solve any two question from Q4(a), Q4(b) & Q4(c), Q4(d)

**4 (a)** Write short note on Constructive Solid Geometry (CSG) for solid modeling.(7 marks)
**4 (b)** What do you understand by 2 1/2 D model? Clearly distinguish it from 3-D
model.(7 marks)
**4 (c)** What are the different types of elements used in FEA? Explain in brief.(7 marks)
**4 (d)** Enlist the various methods of geometric modeling. Discuss wire frame modeling in detail with neat sketch.(7 marks)

### Solve any two question from Q5(a), Q5(b) & Q5(c), Q5(d)

**5 (a)** Explain the concepts of FEM. Discuss the different steps involved in FEA in detailed.(7 marks)
**5 (b)** A stepped metallic bar with circular cross section consists of two segments.
Length & cross section area of first segment is 350 mm & 275 mm^{2} respectively.
Length & cross section area of second segment is 250 mm & 175 mm^{2}
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.(7 marks)
**5 (c)** Explain Penalty approach and Elimination approach for FEA.(7 marks)
**5 (d)** 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=200×10^{3} 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 E_{1}=70×10^{3} N/mm^{2}, E_{2}=200×10^{3} N/mm^{2}, A1=700mm^{2}, A2= 1000 mm^{2}, α_{1}=23×10^{-6} per °C and α_{2}=11.7×10^{-6} per °C.