A novel stability-preserving load regulation scheme for thermoelastic vibration optimization

Despite extensive studies on thermoelastic structural optimization, existing methods often fail to accurately capture the stability of frequency responses under nonuniform thermal effects, leading to inaccuracies in modeling coupled thermomechanical systems. Without proper stability control, intermediate designs may enter the post-buckling regime, resulting in unphysical configurations and inaccurate optimized outcomes. To address these issues, this study proposes a stability-preserving load regulation (SPLR) scheme, built upon the spectral correlation between buckling stability and vibrational behavior. SPLR maintains all designs within the prebuckling regime, ensuring real-valued and physically consistent frequencies that accurately represent the final optimized structures. Beyond addressing the core limitations of prior approaches, the proposed framework establishes a robust formulation for generalized frequency-based optimization by treating thermal frequencies as direct objectives rather than constraints. The method further extends to multimaterial and fully three-dimensional thermoelastic models. Analytical sensitivity analyses based on adjoint and auxiliary-vector formulations enhance computational efficiency, while a refined stabilization strategy suppresses localized vibration modes. Numerical validations demonstrate the accuracy, robustness, and versatility of the proposed methodology under complex coupled thermomechanical loading conditions.