A novel stability-preserving load regulation for coupled thermomechanical buckling optimization of shell structures

In realistic operating environments, thermal and mechanical fields interact in a highly complex manner, generating coupled responses that exert a profound influence on structural stability. Despite their practical importance, most existing topology optimization studies addressing stability have modeled thermal effects as uniform or independent, thereby overlooking the intrinsic coupling between temperature variation and mechanical deformation. Moreover, for decoupled buckling problems, a critical limitation that has received insufficient attention in prior research is the occurrence of complex eigenvalues resulting from the loss of spectral consistency. To overcome these issues, the present study introduces a comprehensive multimaterial topology optimization framework that directly incorporates coupled thermomechanical behavior into buckling design, wherein the temperature field is treated as a design-dependent load to fully capture its interaction with the evolving structural layout. In parallel, a novel stability-preserving load regulation (SPLR) scheme is proposed for decoupled buckling analysis to address the long-standing problem of numerical instability in conventional thermomechanical buckling formulations. The SPLR procedure maintains the positive definiteness of the baseline stiffness matrix and suppresses the emergence of complex-valued eigenmodes, ensuring reliable and physically meaningful buckling evaluation throughout the optimization process. Furthermore, the refined adaptive continuation method (RACM) is extended to coupled thermomechanical and multimaterial settings to enhance convergence and numerical robustness. The overall framework is subsequently formulated for curved shell structures using the mixed interpolation of tensorial components (MITC4) element, enabling the effective elimination of shear-locking effects, while a refined stabilization strategy is introduced to suppress artificial buckling modes frequently encountered in coupled stability analyses. Analytical sensitivities are derived through adjoint formulations employing auxiliary vectors, and the optimization problems are solved using the method of moving asymptotes (MMA). Numerical studies confirm the accuracy, robustness, and broad applicability of the proposed methodology under a wide range of complex coupled thermomechanical loading.