Multi-Objective Optimization of a High-Temperature Flange–Bolt–Gasket System Based on a Cyclic Symmetric Thermal–Structural Coupling Model

The high-temperature sealing reliability of flange–bolt–gasket systems is governed by the coupled gasket leakage, flange cracking, and bolt yielding. This study investigates a DN200 PN40 (nominal diameter 200 mm and nominal pressure 4.0 MPa) weld-neck flange assembly operating under 300 °C superheated steam at 4 MPa internal pressure. Exploiting the assembly’s 12-fold cyclic rotational symmetry, a 1/12 periodic-sector finite element model with steady-state thermal–structural sequential coupling was developed in ANSYS Workbench and validated against the Omiya–Sawa 3-inch weld-neck flange benchmark at two levels (Level 1: bolt load vs. experiment; Level 2: 250 °C gasket contact pressure vs. reference finite element method (FEM)), with maximum errors below 1.5% in both levels; the benchmark thus establishes the reliability of the modeling procedure rather than constituting a direct experimental validation of the DN200 PN40 configuration. Using a central composite design, second-order response surface models (RSM) and Kriging surrogate models were constructed and compared, followed by Sobol global sensitivity analysis, multi-objective optimization using the non-dominated sorting genetic algorithm II (NSGA-II), and decision-making using the technique for order preference by similarity to ideal solution (TOPSIS), with bolt preload F and gasket width b as design variables. Baseline analysis revealed a differential contact pressure distribution—lower at the inner radius and higher at the outer radius—driven by a −0.308° flange rotation, identifying the inner gasket edge as the critical sealing failure path. RSM outperformed Kriging for the primary objective (mean absolute percentage error (MAPE): 0.72% vs. 3.61%), and the Pareto front collapsed to b = 19 mm. The TOPSIS-recommended optimum (F = 59,942 N, b = 19.00 mm), verified by ANSYS back-substitution, increased the minimum gasket contact pressure by 31.01% while reducing the flange membrane-plus-bending stress by 2.26%, achieving a coordinated improvement of both sealing performance and structural safety.