Submersible Hull Wall Stress: Lamé Solver

This is the 2D companion to the 3D Submersible Hull Collapse Depth simulator. Where the 3D version only checks whether hydrostatic pressure has exceeded the idealised thin-shell (Zoelly) elastic-buckling threshold, this simulator solves the exact Lamé thick-hollow-sphere elasticity equations for the radial and hoop stress at every point through the hull wall, from the crew-cabin surface to the outer skin. Stress concentrates at the inner wall — sometimes enough that the material yields long before the shell would ever buckle elastically, a genuinely different failure mode the 3D model cannot see at all. Descend toward the Challenger Deep while watching the wall cross-section colour-map by von Mises stress and the stress-versus-radius graph trace σ_r(r) and σ_θ(r) against the material's yield strength, and see which of the two independent failure criteria — material yield or elastic buckling — actually governs for your chosen geometry and material.