This study presents a higher-order nonlinear computational framework, implemented as a user element (UEL) subroutine in ABAQUS, for analyzing residual stress-induced configurational instability in multilayered plates. By integrating three-dimensional displacement field, higher-order plate theories, and process-induced eigenstrain model within the Carrera Unified Formulation, this framework eliminates the ad hoc approximations of a linear through-thickness displacement distribution inherent to classical approaches. Comparison with experimental results and solid element solutions for the stable configurations of cross-ply laminates validates the predictive accuracy of different plate theories, while their computational costs are also discussed. We thoroughly investigate the equilibrium paths of cross-ply laminates and film/substrate systems to compare classical plate theory with the proposed framework. Numerical results demonstrate that higher-order theories outperform linear theories in predicting bifurcation thresholds and post-bifurcation configurations. By enriching the degrees of freedom through the thickness direction, higher-order Equivalent Single Layer and Layer-Wise theories provide a more accurate characterization of through-thickness displacement distributions—particularly for thin film/substrate systems. Besides, higher-order plate theories reveal that in-plane geometric asymmetry leads to unequal strain energy in post-bifurcation configurations, a phenomenon that linear theory fails to capture. The transverse residual stress predicted by higher-order theories also aligns more closely with the requirement. This work delivers a robust computational framework that significantly enhances the analysis capability for residual stress-driven instabilities, offering valuable insights for the design and analysis of multi-stable plates.


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