CE1033 FINITE ELEMENT TECHNIQUES 3 1 0 100
OBJECTIVE
At the end of this course the student shall have a basic knowledge of finite element method and shall be able to analyse linear elastic structures, that he has studied about in core courses, using finite element method.
1. INTRODUCTION – VARIATIONAL FORMULATION 8
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.
2. FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL PROBLEMS 8
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.
3. FINITE ELEMENT ANALYSIS OF TWO DIMENSIONAL PROBLEMS 8
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.
4. ISOPARAMETRIC ELEMENTS AND FORMULATION 7
Natural coordinates in 1, 2 and 3 dimensions – use of area coordinates for triangular elements in - 2 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.
5. APPLICATIONS TO FIELD PROBLEMS IN TWO DIMENSIONALS 7
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.
6. INTRODUCTION TO ADVANCED TOPICS (NOT FOR EXAMINATION PURPOSE) 7
Three dimensional problems – Mixed formulation – use of software packages like NISA, ANSYS OR NASTRAN.
TOTAL : 45
TEXT BOOK
1. Chandrupatla, T.R., and Belegundu, A.D., “Introduction to Finite Element in Engineering”, Third Edition, Prentice Hall, India, 2003
REFERENCES
1. J.N.Reddy, “An Introduction to Finite Element Method”, McGraw-Hill, Intl. Student Edition, 1985.
2. Zienkiewics, “The finite element method, Basic formulation and linear problems”, Vol.1, 4/e, McGraw-Hill, Book Co.
3. S.S.Rao, “The Finite Element Method in Engineering”, Pergaman Press, 2003.
4. C.S.Desai and J.F.Abel, “Introduction to the Finite Element Method”, Affiliated East West Press, 1972.
OBJECTIVE
At the end of this course the student shall have a basic knowledge of finite element method and shall be able to analyse linear elastic structures, that he has studied about in core courses, using finite element method.
1. INTRODUCTION – VARIATIONAL FORMULATION 8
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.
2. FINITE ELEMENT ANALYSIS OF ONE DIMENSIONAL PROBLEMS 8
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.
3. FINITE ELEMENT ANALYSIS OF TWO DIMENSIONAL PROBLEMS 8
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.
4. ISOPARAMETRIC ELEMENTS AND FORMULATION 7
Natural coordinates in 1, 2 and 3 dimensions – use of area coordinates for triangular elements in - 2 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.
5. APPLICATIONS TO FIELD PROBLEMS IN TWO DIMENSIONALS 7
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.
6. INTRODUCTION TO ADVANCED TOPICS (NOT FOR EXAMINATION PURPOSE) 7
Three dimensional problems – Mixed formulation – use of software packages like NISA, ANSYS OR NASTRAN.
TOTAL : 45
TEXT BOOK
1. Chandrupatla, T.R., and Belegundu, A.D., “Introduction to Finite Element in Engineering”, Third Edition, Prentice Hall, India, 2003
REFERENCES
1. J.N.Reddy, “An Introduction to Finite Element Method”, McGraw-Hill, Intl. Student Edition, 1985.
2. Zienkiewics, “The finite element method, Basic formulation and linear problems”, Vol.1, 4/e, McGraw-Hill, Book Co.
3. S.S.Rao, “The Finite Element Method in Engineering”, Pergaman Press, 2003.
4. C.S.Desai and J.F.Abel, “Introduction to the Finite Element Method”, Affiliated East West Press, 1972.
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