Engineering reference for Indian students

Tools & software

FEA

5 self-contained study topics — notes, diagrams, formulas, and worked examples for exams and GATE.

Topics

Finite Element Formulation
FEA discretises a continuum into elements and solves the global system [K]{u} = {F} for nodal unknowns. The stiffness matrix comes from energy/weighted-residual methods, per FEA texts.
1D and 2D Elements
1D bar/beam elements and 2D triangular/quadrilateral elements have characteristic stiffness matrices; the bar element is [K]ᵉ = (AE/L)[[1,−1],[−1,1]]. Element choice affects accuracy and cost, per FEA texts.
Meshing and Convergence
Meshing divides the domain into elements; refining the mesh (h-refinement) or raising element order (p-refinement) reduces error toward the exact solution. Convergence is checked by mesh-independence studies, per FEA texts.
Boundary Conditions
Boundary conditions constrain the FEA model: essential (Dirichlet) BCs prescribe displacements, natural (Neumann) BCs prescribe forces/tractions. Correct constraints prevent rigid-body motion and singular [K], per FEA texts.
$Symmetry: u_{n} = 0 on symmetry plane$
Post Processing of Stress Results
Post-processing recovers and interprets stresses from the nodal displacements; the von Mises stress σ_vm = √(σ₁² + σ₂² − σ₁σ₂ + 3τ²) is compared to yield. Stress averaging and singularity awareness are key, per FEA texts.