FEA in three phases#

Every finite-element simulation, regardless of the solver, decomposes into three phases. femorph-solver’s user guide is organised around them because that organisation is the mental model of the subject and the library’s API mirrors it directly.

1. Pre-process

Describe the physics: geometry, discretisation, materials, loads, and constraints. The output is a system of equations ready to solve.

2. Solve

Turn the handle. A direct or iterative algorithm converts the equations into numbers — displacements for a static solve, eigenpairs for modal, a time history for transient.

3. Post-process

Interpret. Compute derived quantities (stress, strain energy, reactions), visualise mode shapes, compare against a reference, write artefacts for downstream tools.

Pre-process#

The pre-processing phase asks one question:

Given what I want to model, what system of equations describes it?

That question decomposes into sub-problems:

Geometry & discretisation. Meshing happens upstream of femorph-solver — you arrive with a pyvista.UnstructuredGrid or a mapdl_archive.Archive already in hand. See The Model.
Element choice. Which class of element interpolates the field? femorph-solver registers a kernel for each MAPDL-style element name; see Element library.
Constitutive laws. What material behaviour? Today linear elastic only; see Materials.
Element data. Cross-sections for BEAM / LINK / SHELL; see Real constants and sections.
Constraints & loads. Dirichlet displacements and nodal forces; see Boundary conditions and loads.

The output of pre-processing is a Model with a fully-stamped grid, a material table, and the constraint / load records. From it the library can assemble the global sparse matrices K and M on demand (Model.stiffness_matrix() and Model.mass_matrix()).

Solve#

The solve phase is where all the heavy compute lives. The API is deliberately small:

solve_static() — K u = F with Dirichlet BCs.
solve_modal() — K ϕ = ω² M ϕ.
solve_transient() — M ü + C u̇ + K u = F(t) with Newmark-β.
solve_cyclic_modal() — sector modal with harmonic-index phase constraints.

Every solver accepts a thread_limit kwarg and dispatches internally to a pluggable linear / eigen backend — see Solvers and Performance.

Post-process#

The solve returns a lightweight dataclass (ModalResult, StaticResult, etc.). From there the workflow is conventional Python:

Index into result.displacement / result.mode_shapes to get per-DOF values.
Feed result.frequency into a Campbell diagram.
Call Model.eel() for elastic strain at every element node.
Attach result arrays to the model’s grid and hand the grid to pyvista for rendering or to VTK / Paraview for further analysis.

See Post-processing for the catalogue of recipes.

Why this structure?#

The three-phase decomposition is not femorph-solver’s invention. It’s the organising principle of every FEM textbook (Bathe §1.2, Zienkiewicz ch. 1-2, Cook §1.1) and of every industrial solver — MAPDL’s /PREP7 → /SOLU → /POST1 split is the same shape. We mirror it because it makes the library easier to learn: you already know the structure, and the API method names line up with each phase.