Abstract: In three-dimensional numerical manifold method, the problem of applying boundary displacement in arbitrary direction using penalty function is not yet clear, and multi-step loading would result in the accumulation of error. In view of this, the formulas in consideration of the boundary displacement conditions applied along a certain direction and the corresponding step loading conditions are derived by modifying the displacement boundary part of the governing equation of traditional three-dimensional numerical manifold method. The research is expected to expand the application of the governing equation in displacement boundary treatment and to reduce the cumulative effect of multi-step loading errors. Two typical examples are selected for numerical simulation and comparative analysis to verify the accuracy of the method. Results demonstrate that the calculation results of the proposed method are in good agreement with the analytical solutions, and the modified formula is applicable to the case of boundary displacement applied in different directions, and thus is strongly adaptable. The calculation accuracy with displacement boundary error correction is higher than that without error correction; with the increase of loading steps, the cumulative error with no error correction increases gradually, but that with error correction is unaffected.

Key words: three-dimensional numerical manifold method, essential boundary condition, penalty function method, multi-step loading, error correction