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

Features

TopOpt.jl is organized around a small set of high-level building blocks: problem types define the design domain and physics, differentiable functions define objectives and constraints, filters regularize the design, and algorithms drive the optimization. Every feature links to its reference page.

Optimization domains

• Continuum structural (2D/3D linear elasticity): PointLoadCantilever, HalfMBB, LBeam, TieBeam, and arbitrary meshes imported from Abaqus/FreeCAD .inp files via InpStiffness (TopOptProblems)
• Truss (2D/3D): TrussProblem and PointLoadCantileverTruss, with stress and buckling constraints (TrussTopOptProblems)
• Heat transfer (2D/3D): HeatConductionProblem and HeatTree (TopOptProblems)
• Linear and quadratic triangle, quadrilateral, tetrahedron and hexahedron elements
• Concentrated and distributed loads, multi-load cases (MultiLoad), and fixed/non-design regions (FixedElementProjectorFun)

Optimization methods

• Density-based: SIMP and RAMP, with continuation
• BESO and GESO evolutionary algorithms (Algorithms)
• TOBS: binary topology optimization via sequential integer programming
• Level-set: 2D and 3D level-set topology optimization, with hole nucleation, stress minimization, and marching-cubes boundary discretization (OpenLSTO)
• Gradient-based optimization through Nonconvex.jl: MMA, Ipopt, NLopt, augmented Lagrangian, nonlinear SDP (buckling), and Juniper (mixed-integer)

Differentiable functions

Composable, Zygote-differentiable building blocks for objectives and constraints (guide, reference):

• Objectives: ComplianceFun, ThermalComplianceFun, VolumeFun, MeanComplianceFun, BlockComplianceFun
• Responses: DisplacementFun, TemperatureFun, StressTensorFun, von_mises_stress_function, epsilon_relaxed, TrussStressFun
• Buckling: ElementKFun, AssembleKFun, TrussElementKσFun
• Parametrization: NeuralNetworkFun, MaterialInterpolationFun, MultiMaterialVariablesFun, FixedElementProjectorFun

Filters and penalties

• DensityFilterFun, SensFilterFun, ProjectedDensityFilterFun (CheqFilters)
• Power, rational and hyperbolic-sine penalties, and Heaviside/sigmoid projections (Utilities)

Linear system solvers

• Direct sparse Cholesky/QR factorization (DirectSolver)
• Preconditioned conjugate gradient, with assembly and matrix-free (CGAssemblySolver, CGMatrixFreeSolver)
• Custom solver and preconditioner hooks (FEA)

Visualization and input/output

• Interactive and static (browser, camera-control) visualization with Makie.jl
• VTK export (save_mesh) and Abaqus/FreeCAD .inp import (InpStiffness)
• STL export of 3D level-set designs (write_stl)

Handling uncertainty

• Mean and per-scenario compliance under load uncertainty (MeanComplianceFun, BlockComplianceFun)
• Reliability-based topology optimization

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(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)

For an interactive camera-control app suitable for static HTML export, use visualize(problem; static=true, topology=result.minimizer) with WGLMakie and initialize Bonito with Bonito.Page(exportable=true, offline=true) first. This returns a Bonito.App.

Where to go next

The Tutorials walk through complete, commented examples — compliance and volume minimization, stress-constrained and buckling-constrained optimization, heat sinks, multi-material and neural-network parametrization, trusses, and level-set optimization. The sidebar lists the full API reference, grouped by module.