Essential Boundary Treatment of Three-dimensional Numerical Manifold Method

YANG Shi-kou; AI Hua-dong

doi:10.11988/ckyyb.20201243

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Journal of Changjiang River Scientific Research Institute ›› 2022, Vol. 39 ›› Issue (3) : 137-142. DOI: 10.11988/ckyyb.20201243

HYDRAULIC STRUCTURE AND MATERIAL

Essential Boundary Treatment of Three-dimensional Numerical Manifold Method

YANG Shi-kou, AI Hua-dong

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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

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YANG Shi-kou, AI Hua-dong. Essential Boundary Treatment of Three-dimensional Numerical Manifold Method[J]. Journal of Changjiang River Scientific Research Institute. 2022, 39(3): 137-142 https://doi.org/10.11988/ckyyb.20201243

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