TopOpt.jl Documentation

Introduction

TopOpt is a topology optimization package written in Julia. It supports both structural mechanics (linear elasticity) and heat transfer (heat conduction) problems, on either continuum or truss ground meshes, in 2D and 3D. Optimization is carried out through Nonconvex.jl, which provides MMA, IPOPT, TOBS, Juniper, and other solvers.

Installation

To install TopOpt.jl, run:

using Pkgpkg"add TopOpt"

To additionally load the visualization submodule of TopOpt, you will need to install Makie.jl using:

pkg"add Makie, GLMakie"

To load the package, use:

using TopOpt

and to optionally load the visualization sub-module as part of TopOpt, use:

using TopOpt, Makie, GLMakie

Quick start

A minimal 2D SIMP example — minimize the compliance of a cantilever beam subject to a volume-fraction constraint:

using TopOpt# Problem setup (2D)nels = (60, 20)problem = PointLoadCantilever(Val{:Linear}, nels, (1.0, 1.0), 1.0, 0.3, 1.0)# FEA solver with a power-law penaltysolver = FEASolver(DirectSolver, problem; xmin=1e-6, penalty=PowerPenaltyFun(3.0))# Differentiable objective and constraintcomp = ComplianceFun(solver)vol = VolumeFun(solver; fraction=true)filter = DensityFilterFun(solver; rmin=2.0)obj = x -> comp(filter(PseudoDensities(x)))constr = x -> vol(filter(PseudoDensities(x))) - 0.3# Optimize with MMAx0 = fill(0.3, length(solver.vars))model = Model(obj)addvar!(model, zeros(length(x0)), ones(length(x0)))add_ineq_constraint!(model, constr)result = optimize(model, MMA87(), x0)# Visualize the result (requires Makie)using Makie, GLMakiefig = visualize(problem; topology=result.minimizer)Makie.display(fig)

Problem types

TopOpt.jl provides several pre-defined problem types for common test cases:

Structural problems (linear elasticity)

• PointLoadCantilever — Cantilever beam with a point load at the free end (2D or 3D)
• HalfMBB — Half Messerschmitt-Bölkow-Blohm beam, a standard benchmark (2D or 3D)
• LBeam — L-shaped beam (2D only)
• TieBeam — Tie-beam test problem (2D only)
• InpStiffness — Import from Abaqus/FreeCAD .inp files for arbitrary meshes

Heat transfer problems

• HeatConductionProblem — Steady-state heat conduction with surface heat flux (2D or 3D)
• HeatTree — Tree-shaped heat conduction problem

Truss problems

• TrussProblem — General truss topology optimization with stress/buckling constraints
• PointLoadCantileverTruss — Truss cantilever with point load

See the TopOpt Tutorials section for complete, commented examples covering stress-constrained optimization, heat sinks, multi-material design, neural-network parametrization, trusses, and more.