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An introduction to FEM V.S.S.Srinivas
Plan ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A glance at Finite Difference Method ,[object Object],[object Object],[object Object],q
Illustration by example 1 2 3 4 q
Solution of FDM
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object]
Finite Element Method ,[object Object],[object Object],[object Object]
Finite Element Method-Galerkin Weighted Residuals ,[object Object],[object Object],[object Object],[object Object],[object Object]
FEM-Galerkin Weighted Residuals
Analytical solution and comparison ,[object Object],[object Object]
Other Weighted Residual Methods ,[object Object],[object Object],[object Object]
Concept of assembly ,[object Object],[object Object],1 2 3 1 2 3 4
Concept of Assembly Assembled matrix
Contd.. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Revisiting interpolation functions Element point of view  ,[object Object],[object Object],[object Object],[object Object],[object Object]
Interpolation functions from an element point of view
FEM-Standard Procedure ,[object Object],[object Object],[object Object],[object Object],[object Object]
Element shape functions ,[object Object],[object Object]
FEM Standard Procedure- Coordinate Transformation  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Pictorial representation-coordinate transformation ,[object Object],Jacobian
Assembly of element matrices nodal connectivity-1D 1 2 3 4 1 2 3 1 2 Local node no. Global node no. 1 - 3, 2 – 4 3 1 - 2, 2 – 3 2 1 - 1, 2 - 2 1 Local to global Element
Nodal Connectivity-2D Global node no. Local node no. (i,j) entry in every element conductivity matrix goes to (I,J) entry in global conductivity matrix (i,j)—local node nos, (I,J)—Global node nos. 1 2 3 4 1 5 6 7 8 9 2 3 4 1 2 3 4 1 – 4, 2 – 5,3 – 8, 4 – 7 3 1 – 5, 2 – 6, 3 – 9, 4 – 8 3 2 – 2, 2 – 3,3 – 6,4 – 5, 2 1 – 1,2– 2, 3 – 5, 4 – 4 1 Local to global Element
Applying Boundary Conditions ,[object Object],[object Object],[object Object],[object Object]
Contd.. ,[object Object],[object Object],[object Object],[object Object]
Contd.. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
References ,[object Object],[object Object],[object Object]
Interpolation functions

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Introduction to FEM V.S.S.Srinivas Plan Day 1