The document outlines the 10 general steps of the finite element method (FEM) for analyzing structures: 1) Discretize the structure into elements and nodes, 2) Number the nodes and elements, 3) Select displacement functions, 4) Define material behavior, 5) Derive the element stiffness matrix, 6) Assemble the global stiffness matrix, 7) Apply boundary conditions to remove singularities, 8) Solve the equations for unknown displacements, 9) Compute element strains and stresses, and 10) Interpret the results. The 10 steps provide the overall process for using FEM to model a structure and calculate its response to loading.

1. Finite Element Method
(FEM)
UNIT 2
Mr. M. Sasi Kumar
Assistant Professor
Department of Aeronautical Engineering
KIT-Kalaignarkarunanidhi Institute of Technology
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2. 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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3. STEP 1 : Discretization of Structure
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4. STEP 1 : Discretization of Structure
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5. STEP 2 : Numbering of Nodes & Elements
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6. STEP 3 : Selection of Displacement Function
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7. STEP 4 : Define the Material Behavior
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8. STEP 5 : Derivation of Element stiffness matrix
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9. STEP 6 : Derivation of Global stiffness matrix
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10. 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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11. • 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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