Finite Element Analysis

Define :

i) Isoparametric 

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Finite representation of infinite bodies.

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Pascal's triangle and its applications

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Hermitian polynomials

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Software's used in finite element analysis

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Brief history of finite element method

(05 Marks)Obtain the shape function for all the nodes shown in Fig Q7(b) and for all the element using natural co-ordinates. Apply Lagrange interpolation function approach.

Mention the five conditions to be satisfied by the general shape function, explain any one.

Derive the shape function in natural coordinate for a CST element from fundamentals. Use the concept of parent element in natural coordination. Also plot the variation of shape function for all the nodes in CST element. 

Define "shape function" plot the same for

i) 3 noded bar element-one node at mid point

ii) 3 noded CST element

iii) 4 noded Quadrilateral element

[No derivation required, only plot]

Determine Cartesian co-ordinates for the point shown in Fig Q5(b). , 

Define :

iii) super parametric elements.

Define :

ii) sub parametric

What are plane stress and plane strain problem? Explain with examples.

Determine the direction cosines, element displacement and elemental stress for the turn element shown in Fig Q4(c) Fig. 

@CC For Fig Q4(c), E = 300x10³ N/mm', A = 100mm²

Element displacement 

Mention the steps involved in finite element analysis.

Mention the advantages and disadvantages of finite element analysis.

Define local global and natural co-ordinates. Give exemples.

With usual notation prove that

Apply virtual work principle. 

Prove that , with usual notation.

 Determine displacement at loading point and the corresponding stress using Rayleigh Ritz method for a fixed bar at both ends as shown in Fig Q2(n).

Assume 

 Assume second order polynomial function.

Explain briefly the steps involved Galerkin's method. Mention its application.

 Explain briefly

iv) Body and Traction forces.

 Explain briefly

iii) The Functional

 Explain briefly

ii) The principle of minimum potential energy

 Explain briefly

i) Constitutive law