Skip to main content

Basic steps in finite element analysis

Short answer

FEM steps: discretise the body into elements and nodes; assume displacement shape functions; form strain and stress relations; derive element stiffness and load vectors; assemble global equations; apply boundary conditions; solve for nodal displacements; compute strains, stresses and reactions.

Describe the basic steps in finite element analysis.

The finite element method replaces a continuum by a finite number of elements and solves the resulting algebraic equations. The basic steps are:

  1. Discretisation: divide the body into finite elements joined at nodes (select element type and mesh).
  2. Select interpolation (shape) functions: assume displacement within an element as u=[N]{d}u = [N]\{d\}.
  3. Strain-displacement and stress-strain relations: {ε}=[B]{d}\{\varepsilon\} = [B]\{d\}, {σ}=[D]{ε}\{\sigma\} = [D]\{\varepsilon\}.
  4. Element stiffness matrix and load vector: [k]=∫[B]T[D][B] dV[k] = \int [B]^T[D][B]\,dV and equivalent nodal loads {f}\{f\}.
  5. Assembly: combine element matrices into the global equations [K]{U}={F}[K]\{U\} = \{F\}.
  6. Boundary conditions: apply supports (known displacements) and loads.
  7. Solve for nodal displacements.
  8. Post-processing: compute strains, stresses, reactions and plot results.
 Body -> Mesh -> [k] each -> [K]{U}={F} -> U -> stress

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Computational Techniques in Civil Engineering chapter 1 questions →