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This study develops an efficient approach using the bubble-enriched smoothed finite element method (bES-FEM) combined with conic programming to compute the load-carrying capacity of structures under monotonic and variable repeated loads. The accumulative displacement field is enhanced with a cubic bubble function placed at the centroid of the element to improve accuracy and stability. All kinematic constraints are satisfied in an average sense at every smoothing domain associated with each edge, keeping the size of the problem small. The resulting optimization problem is formulated as second-order cone programming (SOCP), enabling using high-performance interior-point solvers. The shakedown loading factors can be accurately determined with the optimal computational cost. A series of numerical examples are investigated to validate the performance of the proposed method.