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在岩土工程分析中求解精度控制常常是必需的,在数值流形法中可以通过控制数学覆盖网格的稀疏和覆盖位移的阶数来达到精度的要求。提出了基于等几何分析的数值流形方法,定义了相应的数学覆盖的构造形式,推导了基于二次B样条的9节点数值流形方法分析格式;针对基于Lagrange插值函数的4节点数值流形方法提出了基于T样条思想的数学覆盖网格的局部加密方法。算例计算结果表明,相对于4节点的数值流形方法,基于非均匀有理B样条的9节点数值流形方法具有更高的精度;基于T样条思想的加密网格在保持计算精度的前提下降低了自由度的数量,表明T样条加密是一种自然的局部加密算法。
It is often necessary to solve the accuracy control in geotechnical analysis. In numerical manifold method, the precision can be achieved by controlling the sparsity of math coverage grid and the order of displacement. A numerical manifold method based on isometric geometric analysis is proposed, the corresponding mathematical coverage structure is defined, and a nine-node numerical manifold method based on quadratic B-spline is deduced. According to the four-node numerical flow based on Lagrange interpolation function Shaped method proposed a local encryption method based on T-spline idea of mathematical overlay grid. The results of numerical examples show that compared with the 4-node numerology method, the 9-node numerology method based on non-uniform rational B-splines has higher accuracy. The algorithm based on the T-spline idea The premise of reducing the number of degrees of freedom, indicating that T-spline encryption is a natural local encryption algorithm.