The document outlines the 10 general steps of the finite element method (FEM) for analysis: 1) Discretize the structure into elements, 2) Number nodes and elements, 3) Select displacement functions, 4) Define material behavior, 5) Derive element stiffness matrices, 6) Assemble into a global stiffness matrix, 7) Apply boundary conditions, 8) Solve for unknown displacements, 9) Compute element strains and stresses, and 10) Interpret results. FEM breaks a structure into small pieces (elements) and models them individually to obtain an approximate solution for the whole structure.

1. Finite Element Method
(FEM)
UNIT 2
Mr. M. Sasi Kumar
Assistant Professor
Department of Aeronautical Engineering
Kalaignarkarunanidhi Institute of Technology
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2. Syllabus
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3. General Steps of the FEM/FEA
• STEP 1 : Discretization of Structure
• STEP 2 : Numbering of Nodes & Elements
• STEP 3 : Selection of Displacement Function
• STEP 4 : Define the Material Behavior
• STEP 5 : Derivation of Element stiffness matrix
• STEP 6 : Derivation of Global stiffness matrix
• STEP 7 : Applying Boundary Condition
• STEP 8 : Solution for the unknown displacements
• STEP 9 : Computation of the element strains and stresses
• STEP 10: Interpret the Results
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4. STEP 1 : Discretization of Structure
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5. STEP 1 : Discretization of Structure
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6. STEP 2 : Numbering of Nodes & Elements
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7. STEP 3 : Selection of Displacement Function
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8. STEP 4 : Define the Material Behavior
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9. STEP 5 : Derivation of Element stiffness matrix
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10. STEP 6 : Derivation of Global stiffness matrix
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11. STEP 7 : Applying Boundary Condition
From the global stiffness matrix [K] is a singular matrix because its determinant is
Equal to zero. In order to remove this singularity problem, certain boundary
Conditions are applied.
STEP 8 : Solution for the unknown displacements
These equations can be solved and unknown displacements {u} are calculated
by using Gaussian Elimination method or Gauss Seidal method
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12. • From the solution of displacement vector {u}, stress and strain value can be calculated.
STEP 9 : Computation of the element strains and stresses
STEP 10: Interpret the Results
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