Reliability-based topology optimization (RBTO)

[mohdibntarek]

Reliability-based topology optimization (RBTO) accounts for uncertainty in problem inputs — e.g. material properties or loads — by optimizing a function of the response distribution (mean plus a multiple of the standard deviation, or a reliability index) rather than a single deterministic compliance. It complements the stochastic (#31) and robust (#32) optimization themes.

PR #178 ("Rbto tutorial") implements a multimaterial RBTO example using ReliabilityOptimization.jl: the objective is wrapped in a RandomFunction with FORM(RIA()) over a lognormal distribution of the material moduli.

The PR predates several API changes and needs updating before it can land:

• Fun-suffixed names (ComplianceFun, DensityFilterFun, PowerPenaltyFun, MaterialInterpolationFun, MultiMaterialVariablesFun) — the non-suffixed aliases were removed in Remove non-Fun-suffixed aliases of Fun-suffixed names #276;
• the celltype keyword in place of the positional Val{:Linear};
• FEASolver(DirectSolver, ...) in place of the old Direct solver;
• the Quarto .qmd tutorial pipeline (docs/tutorials/) — the Literate docs/src/literate/ path was removed in Comprehensive docs overhaul: Literate→Quarto migration, dynamic CI, stress/buckling fixes #241;
• the ReliabilityOptimization dependency declared in the root and docs Project.toml.

This issue tracks RBTO support; #178 is the tutorial implementation to revive and bring up to date.

Prepared with assistance from deepseek-v4-pro via opencode.