3RD YEAR SEMESTER 1 SUPPLEMENTARY JUNE 2010 JNTU B.TECH ENGINEERING QUESTION PAPER- FINITE ELEMENT METHOD

Code No:  RR311403                     RR           Set No.   2

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

FINITE ELEMENT METHOD Mechatronics

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1. A spring system has two linear springs connected  in series with spring stiffness k1 and k2.  The left hand  end is fixed rigidly and a force F is acting in the right end of the system.  Solve the physical system by using Finite  Element method.        [16]

 

2. Establish  Jacoban  matrix  for a Hexahedron  element.                                            [16]

 

3. For the truss  structure shown in figure 3 is subjected  to a horizontal  load of 4 kN

in positive x-direction at node 2. Calculate

 

(a)  stiffness matrix  and

 

(b)  stresses.                                                                                                           [10+6]

 

 

4. A simply supported  beam of l m length carries a single point load P at the center of the span.  Descritize the span into two elements, find the value of central deflection using FEM?                                                                                                                 [16]

 

5. The coordinates  of the  nodes 1, 2 and 3 of a triangular element are (1, 1), (8, 4)

and (2, 7) in mm.  The displacements  at the nodes are u1  = 1 mm, u2  = 3 mm, u3

= -2 mm, v1  = -4 mm , v2  = 2 mm and v3  = 5 mm.  Obtain  the strain-displacement

relations,  matrix  B and determine  the strains  εx, εy  and γxy .                               [16]

 

6.   (a)  From first principles, derive the general equation  for elemental mass matrix? (b)  Derive the elemental mass matrix  for 2-D triangular element?                 [8+8]

7. Derive the  conductivity  matrix  and  vector  for the  2-D element  when one of the faces is exposed to a heat  transfer  coefficient of h at  T∝ and  with  internal heat generation  of q W/m3.                                                                                     [16]

 

 

  

8. Explain  the  mathematical interpretation of finite element method  for one dimen- sional field problems.                                                                                                 [16]

 

Code No:  RR311403                     RR           Set No.   4

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

FINITE ELEMENT METHOD Mechatronics

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1. For the truss  structure shown in figure 3 is subjected  to a horizontal  load of 4 kN

in positive x-direction at node 2. Calculate

 

(a)  stiffness matrix  and

 

(b)  stresses.                                                                                                           [10+6]

 

Figure 3

 

2. Derive the  conductivity  matrix  and  vector  for the  2-D element  when one of the faces is exposed to a heat  transfer  coefficient of h at  T∝ and  with  internal heat generation  of q W/m3.                                                                                     [16]

 

3. Establish  Jacoban  matrix  for a Hexahedron  element.                                            [16]

 

4. The coordinates  of the  nodes 1, 2 and 3 of a triangular element are (1, 1), (8, 4)

and (2, 7) in mm.  The displacements  at the nodes are u1  = 1 mm, u2  = 3 mm, u3

= -2 mm, v1  = -4 mm , v2  = 2 mm and v3  = 5 mm.  Obtain  the strain-displacement

relations,  matrix  B and determine  the strains  εx, εy  and γxy .                               [16]

 

5. A spring system has two linear springs connected  in series with spring stiffness k1 and k2.  The left hand  end is fixed rigidly and a force F is acting in the right end of the system.  Solve the physical system by using Finite  Element method.        [16]

 

6. Explain  the  mathematical interpretation of finite element method  for one dimen- sional field problems.                                                                                                  [16]

 

7.   (a)  From first principles, derive the general equation  for elemental mass matrix? (b)  Derive the elemental mass matrix  for 2-D triangular element?                 [8+8]

 

 

 

8. A simply supported  beam of l m length carries a single point load P at the center of the span.  Descritize the span into two elements, find the value of central deflection using FEM?                                                                                                                [16]

 

 

Code No:  RR311403                     RR           Set No.   1

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

FINITE ELEMENT METHOD Mechatronics

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1. A spring system has two linear springs connected  in series with spring stiffness k1 and k2.  The left hand  end is fixed rigidly and a force F is acting in the right end of the system.  Solve the physical system by using Finite  Element method.        [16]

 

2. Explain  the  mathematical interpretation of finite element method  for one dimen- sional field problems.                                                                                                  [16]

 

3. The coordinates  of the  nodes 1, 2 and 3 of a triangular element are (1, 1), (8, 4)

and (2, 7) in mm.  The displacements  at the nodes are u1  = 1 mm, u2  = 3 mm, u3

= -2 mm, v1  = -4 mm , v2  = 2 mm and v3  = 5 mm.  Obtain  the strain-displacement

relations,  matrix  B and determine  the strains  εx, εy  and γxy .                               [16]

 

4.   (a)  From first principles, derive the general equation  for elemental mass matrix? (b)  Derive the elemental mass matrix  for 2-D triangular element?                 [8+8]

 

5. For the truss  structure shown in figure 3 is subjected  to a horizontal  load of 4 kN

in positive x-direction at node 2. Calculate

 

(a)  stiffness matrix  and

 

(b)  stresses.                                                                                                           [10+6]

 

Figure 3

 

6. Derive the  conductivity  matrix  and  vector  for the  2-D element  when one of the faces is exposed to a heat  transfer  coefficient of h at  T∝ and  with  internal heat generation  of q W/m3.                                                                                     [16]

 

7. A simply supported  beam of l m length carries a single point load P at the center of the span.  Descritize the span into two elements, find the value of central deflection using FEM?                                                                                                                 [16]

 

  

8. Establish  Jacoban  matrix  for a Hexahedron  element.                                           [16]

 

Code No:  RR311403                     RR           Set No.   3

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

FINITE ELEMENT METHOD Mechatronics

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1. The coordinates  of the  nodes 1, 2 and 3 of a triangular element are (1, 1), (8, 4)

and (2, 7) in mm.  The displacements  at the nodes are u1  = 1 mm, u2  = 3 mm, u3

= -2 mm, v1  = -4 mm , v2  = 2 mm and v3  = 5 mm.  Obtain  the strain-displacement

relations,  matrix  B and determine  the strains  εx, εy  and γxy .                               [16]

 

2. Explain  the  mathematical interpretation of finite element method  for one dimen- sional field problems.                                                                                                  [16]

 

3. For the truss  structure shown in figure 3 is subjected  to a horizontal  load of 4 kN

in positive x-direction  at node 2. Calculate

 

(a)  stiffness matrix  and

 

(b)  stresses.                                                                                                           [10+6]

 

 

4. A spring system has two linear springs connected  in series with spring stiffness k1 and k2.  The left hand  end is fixed rigidly and a force F is acting in the right end of the system.  Solve the physical system by using Finite  Element method.        [16]

 

5.   (a)  From first principles, derive the general equation  for elemental mass matrix? (b)  Derive the elemental mass matrix  for 2-D triangular element?                 [8+8]

 

6. Establish  Jacoban  matrix  for a Hexahedron  element.                                            [16]

 

7. A simply supported  beam of l m length carries a single point load P at the center of the span.  Descritize the span into two elements, find the value of central deflection using FEM?                                                                                                                 [16]

 

 

  

 

8. Derive the  conductivity  matrix  and  vector  for the  2-D element  when one of the faces is exposed to a heat  transfer  coefficient of h at  T∝ and  with  internal heat generation  of q W/m3.