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PSNA COLLEGE OF ENGINEERING & TECHNOLOGY, DINDIGUL – 624

622

DEPARTMENT OF MECHANICAL ENGINEERING

FINITE ELEMENT ANALYSIS

TWO DIMENSIONAL PROBLEMS

(UG and PG

Pa!" – A

1. List the types of nodes with examples.

2. What is CST Element?3. What is LST Element4. Write a displacement fnction e!ation for CST element.". Write a strain#displacement matrix for CST element.$. What is meant %y plane stress and plane strain analysis?&. Write down the expression for the shape fnctions for a CST element.'. What is axisymmetric element?(. )i*e the strain#displacement matrix e!ation for an axisymmetric

trian+lar element.1,. What are the assmptions sed in thic- plate element?

Pa!" –B

1. eri*e the shape fnction for the CST element.2. eri*e the stain#displacement for the CST element.3. etermine the sti/ness matrix for the CST element co#ordinates are

102, 3, 20', 3, and 30",12, are +i*en in nits of millimeters.

ssme plane stress conditions. Ta-e E 21, )5a 6,.2" and t 1,

mm.4. 7or the plain strain element as shown in 8+re. The nodal

displacements are9 1  ,.,," mm: *1  ,.,,2 mm: 2  , mm: *2  ,

mm: 3  ,.,," mm: *3  , mm. etermine the element stress ;x ;y

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". eri*e the thermal sti/ness matrix for two dimensional heat transfer

pro%lems.$. Calclate the element e!ations for the element shown in 8+re which

experiences con*ection on the die >- and its pper face.

&. Compte the element matrices and *ectors for the element shown in

8+re when the ed+es 2#3 and 1#3 experience con*ection heat loss.

'. 7or the axisymmetric element as shown in 8+re. etermine the

stresses. Ta-e E 2.1 x 1," @mm2 and 6,.2". The nodal

displacements are9 1  ,.,," mm: w1  ,.,,2 mm: 2  , mm: w2  ,

mm: 3  ,.,," mm: w3  , mm. The co#ordinates are in millimeters.

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(. 7ind the natral fre!encies of lon+itdinal *i%ration of the

nconstrained stepped %ar as shown in 8+re.

1,. etermine the natral fre!encies of the system in 8+re.