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LowLevelFEM

LowLevelFEM is a Julia package for finite element analysis with an engineering-first workflow. It exposes each phase of the workflow as simple functions (mesh → matrices → loads/BCs → solve → postprocess → visualize), so you can customize, combine, or inspect any step. Typical tasks such as strain energy or resultants are one-liners (for example, U = q' * K * q / 2).

Requirements

  • Julia 1.x
  • Gmsh C API is bundled via gmsh_jll and re-exported as gmsh from this package; no separate Gmsh.jl installation is required.

Capabilities

  • Geometry and meshing: integrates with gmsh for 2D/3D geometry, meshing, and physical groups.
  • Problem types: 3D solids, 2D plane stress/plane strain, axisymmetric; 3D/2D heat conduction and axisymmetric heat conduction.
  • Elements and order: standard line/triangle/quad/tetra/hex/pyramid/wedge with Lagrange order up to 10.
  • Materials: linear elastic (Hooke) and large deformation laws (St. Venant–Kirchhoff, compressible Neo-Hooke).
  • Matrices: stiffness K, mass M (lumped or consistent), proportional damping C (Rayleigh/Caughey), heat conduction/capacity, latent heat, and convection matrices/vectors.
  • Loads and constraints: nodal and distributed loads on physical groups; function-based loads and temperature BCs; elastic supports; initial displacement/velocity/temperature.
  • Thermal–structural coupling: thermal expansion, thermal stresses, and heat generated by elastic deformation.
  • Solvers: static and transient dynamics (central difference and HHT-α from the Newmark family).
  • Eigenproblems: modal analysis (frequencies and mode shapes, optionally prestressed) and linear buckling (critical factors and modes).
  • Field operators and results: gradient/divergence/curl; stress/strain and heat flux as element or nodal fields; smoothing at nodes with field jumps; user-defined scalar/vector/tensor FE fields.
  • Visualization and plots: Gmsh-based views for displacements, stresses, strains, heat flux, with animation for dynamics; plot results along user-defined paths; show results on surfaces.
  • Coordinate systems: rotate nodal DOFs with constant or function-defined local coordinate systems (incl. curvilinear).

Installation

using Pkg
Pkg.add("LowLevelFEM")

Quick Start

using LowLevelFEM

# `gmsh` is exported by LowLevelFEM
gmsh.initialize()
gmsh.open("your_model.geo")

mat = material("body", E=2e5, ν=0.3)
prob = Problem([mat], type=:PlaneStress)  # :Solid, :PlaneStrain, :AxiSymmetric, :HeatConduction, ...

bc   = displacementConstraint("supp", ux=0, uy=0)
force = load("load", fy=-1)

q = solveDisplacement(prob, [force], [bc])
S = solveStress(q)

showDoFResults(q, :uvec)
showStressResults(S, :s)

openPostProcessor()
gmsh.finalize()

Note: physical group names in your geometry (created in Gmsh) must match the strings used above (e.g., "body", "supp", "load").

An alternative solution (instead of q = ..., S = ...)

K = stiffnessMatrix(prob)
f = loadVector(prob, [force])
applyBoundaryConditions!(K, f, [bc])
q = K \ f

E = mat.E
ν = mat.ν

A = (u ∘ ∇ + ∇ ∘ u) / 2
I = unitTensor(A)
S = E / (1 + ν) * (A + ν / (1 - 2ν) * trace(A) * I)

More end-to-end examples are available under examples and in the documentation.

Documentation

Planned features

  • Other material laws (incompressible Neo-Hooke, Mooney-Rivlin, etc.)
  • Truss, beam, shell elements
  • Contact problems (penalty, Lagrange multiplier)
  • Multithreading

Any suggestions are welcome. In case of any issue, please send a bug report.

License

This project is licensed under the MIT License — see LICENSE for details.