IterSIMP-{\sigma}: Evaluating LLM-Assisted Spatial Interventions in Stress-Aware Topology Optimization

This paper studies whether multimodal large language models (LLMs) can serve as inspectable spatial proposal modules for stress-aware topology optimization. IterSIMP-{\sigma} keeps the SIMP optimizer as a compliance-minimizing finite-element solver and places a deterministic stress pass, gate evaluator, and hybrid LLM/rule interpreter around it. After each solve, density and von Mises stress fields are rendered; the interpreter proposes ranked spatial interventions; and deterministic safeguards accept, reject, or stop each action. The main action is a soft density seed, where selected elements are initialized at elevated density before the next solve but remain free under the optimality-criteria update. We evaluate the loop on a 16-problem 2D controller-policy benchmark, a six-problem exploratory 3D extension, passive-solid and input ablations, stress-threshold sensitivity, and a fixed-volume attribution study comparing LLM proposals with deterministic max-stress hotspot seeding, random stress-region seeding, and rule-based control. The 2D controller-policy benchmark shows a small retained-compliance difference (1.9% lower geometric mean for the soft-seed LLM), but this diagnostic is not statistically significant (W = 33, two-sided p = 0.382) and is not a fixed-volume feasible-final comparison. In the fixed-volume study, the LLM condition completed 44/48 attempted evaluations; 25/44 completed evaluations produced all-gate-passing retained states. Feasible-final scoring against rule-based control is split 4/4/1, and deterministic exact-hotspot seeding remains competitive. Accepted LLM spatial actions with per-step records have mean normalized seed-to-hotspot distance 0.221. The results support IterSIMP-{\sigma} as an inspectable LLM-assisted design-automation framework for spatial interventions, not yet as evidence that LLM visual reasoning improves stress-constrained optimization.