基于三维数值流形法的位移边界处理方法

针对三维数值流形法中罚函数法施加任意方向边界位移和多步加载误差累积问题,通过修正传统三维数值流形法控制方程中的位移边界部分,推导出含沿着某一方向施加边界位移条件和相应的分步加载情况的计算公式,以期扩大控制方程在位移边界处理上的适用范围和减少多步加载误差累积效应。选取2个典型算例进行数值模拟和对比分析,验证该方法的准确性。计算结果表明:文中方法的计算结果与解析解相吻合,修正公式适用于不同方向施加边界位移的情况,具有较强的适应性;考虑位移边界误差修正比不考虑误差修正的计算精度高;随分步加载步数的增多,不考虑位移边界误差修正的累积计算误差逐渐增大,考虑位移边界误差修正的则影响不大。

Essential Boundary Treatment of Three-dimensional Numerical Manifold Method

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.