CE1018 – FINITE ELEMENT TECHNIQUES

CE1018  –   FINITE ELEMENT TECHNIQUES

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UNIT I           INTRODUCTION – VARIATIONAL FORMULATION                     9
General field problems in engineering – Modelling – Discrete and continuous models –
Characteristics – Difficulties involved in solution – The relevance and place of the finite
element method – Historical comments – Basic concept of FEM – Boundary and initial
value problems – Gradient and divergence theorems – Functionals – Variational calculus
–  Variational  formulation  of  VBPS  –  The  method  of  weighted  residuals  –  The  Ritz
method.

UNIT II          FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL             
    PROBLEMS                                                                                               9
One  dimensional  second  order  equations  –  Discretisation  of  domain  into  elements  –
Generalised  coordinates  approach  –  Derivation  of  elements  equations  –  Assembly  of
elements  equations  –  Imposition  of  boundary  conditions  –  Solution  of  equations  –
Cholesky method – Post processing – Extension of the method to fourth order equations
and their solutions – Time dependant problems and their solutions – Example from heat
transfer fluid flow and solid mechanics.

UNIT III        FINITE    ELEMENT    ANALYSIS    OF    TWO    DIMENSIONAL               
              PROBLEMS                                                                                               9
Second  order  equation  involving  a  scalar  –  Valued  function  –  Model  equation  –
Variational  formulation  –  Finite  element  formulation  through  generalised  coordinates
approach  –  Triangular  elements  and  quadrilateral  elements  –  Convergence  criteria  for
chosen models – Interpolation functions – Elements matrices and vectors – Assembly of
element matrices – Boundary conditions – Solution techniques.

UNIT IV        ISOPARAMETRIC ELEMENTS AND FORMULATION                   9                      
Natural  coordinates  in  1,  2  and  3  dimensions  –  Use  of  area  coordinates  for  triangular
elements  in  –  Two  dimensional  problems  –  Isoparametric  elements  in  1,2  and  3
dimensional  –  Largrangean  and  serendipity  elements  –  Formulations  of  elements
equations in one and two dimensions  –Numerical integration.

UNIT V          APPLICATIONS TO FIELD PROBLEMS IN TWO                  
    DIMENSIONALS                                                                                      9
Equations of elasticity – Plane elasticity problems – Axisymmetric problems in elasticity
– Bending of elastic plates – Time dependent problems in elasticity – Heat – Transfer in
two dimensions – Incompressible fluid flow.
      
  Total: 45 TEXT BOOKS
1.        Chandrupatla,  T.R.  and  Belegundu,  A.D.,  “Introduction  to  Finite  Element  in
Engineering”, 3rd Edition, Prentice Hall, 2003.
2.        Rao, S.S.,  “The Finite Element Method in Engineering”, Pergaman Press, 2003.

REFERENCES
1.         Reddy, J.N., “An Introduction to Finite Element Method”, McGraw-Hill, 1985.
2.         Desai,  C.S.  and  Abel,  J.F.,  “Introduction  to  the  Finite  Element  Method”,
Affiliated East West Press, 1972.
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