### Install TopOpt.jl Source: https://juliatopopt.github.io/TopOpt.jl Use the Julia package manager to add the TopOpt package. ```julia using Pkgpkg"add TopOpt" ``` -------------------------------- ### Install Makie.jl visualization Source: https://juliatopopt.github.io/TopOpt.jl Install the Makie and GLMakie packages to enable visualization capabilities. ```julia pkg"add Makie, GLMakie" ``` -------------------------------- ### Load TopOpt.jl with visualization Source: https://juliatopopt.github.io/TopOpt.jl Load the TopOpt package along with the Makie visualization sub-modules. ```julia using TopOpt, Makie, GLMakie ``` -------------------------------- ### Minimal 2D SIMP compliance minimization with TopOpt.jl Source: https://juliatopopt.github.io/TopOpt.jl Sets up a cantilever beam problem with 60x20 elements, uses a direct FEA solver with power-law penalty, defines compliance and volume fraction constraints, optimizes with MMA87, and visualizes the result with Makie. Requires Makie and GLMakie for visualization. ```julia 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) ``` -------------------------------- ### Load TopOpt.jl Source: https://juliatopopt.github.io/TopOpt.jl Load the TopOpt package into your Julia session. ```julia using TopOpt ``` === COMPLETE CONTENT === This response contains all available snippets from this library. No additional content exists. Do not make further requests.