THERMOELASTIC-PARAMETER INVERSION METHOD FOR THIN PLATES BASED ON HIGH-TEMPERATURE DIC FULL-FIELD DISPLACEMENT AND MEMBRANE WEAK-FORM EQUILIBRIUM CONSTRAINTS

In thermal buckling experiments of thin plates under nonuniform temperature rise and complex boundary constraints, stress fields cannot be measured directly, and the thermoelastic parameters cannot be inferred from full-field digital image correlation (DIC) displacements alone. This study proposes a structural-level equivalent thermoelastic-parameter inversion method that combines high-temperature DIC full-field displacements with membrane weak-form equilibrium constraints. First, the mid-plane membrane strain is calculated from the three-dimensional DIC displacement field, and the nonuniform temperature field is reconstructed by combining thermocouple measurements. Then, the elastic modulus and thermal expansion coefficient are expressed as continuous functions of a normalized thermal-loading state variable and are differentiably represented by a two-stage feedforward neural network. On this basis, a membrane thermoelastic trial stress field under the plane-stress condition is constructed from the observed membrane strain field and temperature field, and the weak-form equilibrium residual of effective internal nodes is taken as the minimization objective to invert the thermoelastic parameters varying with the thermal-loading state. A trend-consistency term is included, while the parameter functions are represented in a continuously differentiable form by tanh feedforward neural networks; no separate smoothness penalty is imposed. A nonuniform-heating thermal buckling experiment of a four-edge-clamped thin plate is conducted for method assessment. Loading steps 1-24 are used for parameter inversion, whereas loading steps 25-30 are reserved for assessment at subsequent loading states along the same monotonic heating path. Single-parameter-fixed ablation and local sensitivity analyses further show that the two parameters have clearly coupled but non-collinear effects on the equilibrium residual, while ten independent inversions demonstrate good numerical repeatability. The results show that, compared with the constant-parameter model, the identified parameter functions reduce the average membrane weak-form equilibrium residual over the considered loading process by 20.95% and 35.53% in the inversion interval and the subsequent-loading interval, respectively. The center-point deflection and full-field out-of-plane displacement morphology obtained based on the inverted parameters can reproduce the main evolutionary characteristics of the experimental thermal buckling process. The proposed method therefore provides a full-field-observation-based route for structural-level equivalent thermoelastic-parameter inversion without stress labels or boundary-reaction data.