A novel topology optimization with load path capacity constraints for minimizing the peak stress control

To address the bottlenecks of traditional stress-constrained topology optimization, including stress singularities, the curse of dimensionality in computation, and high nonlinearity, this paper proposes a novel topology optimization framework based on the principle of load path equilibrium. By establishing a mechanical representation model of load path capacity S in continuum mechanics, the constitutive relationship between S and the stress tensor field is revealed, and an optimization objective function using S as a global criterion is constructed. A P-norm aggregation strategy is introduced to handle large-scale design variable constraints, and the analytical expression of sensitivity is derived. Numerical experiments on three typical stress concentration components—MBB (Messerschmitt-Bolkow-Blohm) beam, L-shaped bracket, and U-shaped structure—demonstrate the following significant advantages of the proposed method: (1) the maximum von Mises stress is reduced by 12.18%–23.69%, with stress at the inner corner of the L-shaped bracket reduced by 26.36% and convergence speed greatly improved; (2) the adaptability of the P-norm parameter is enhanced, maintaining structural symmetry and boundary smoothness within the range of P = 2–10, and the optimization results outperform traditional stress-constrained optimization. The experiments show that the load path capacity constraint effectively reduces the peak stress at key positions of the structure by optimizing the global load path, providing a parameter-robust solution for stress field structural design.