论文部分内容阅读
数值流形方法(NMM)中整体逼近函数是通过单位分解将局部逼近函数进行“粘结”而形成的,当将局部函数取为阶数不低于一阶的多项式时便形成了所谓的高阶流形方法。然而高阶流形方法会导致刚度矩阵亏秩,这种亏秩即使在施加完整的位移约束后仍然存在,从而会导致NMM方程组的多解,但是每个解所对应的位移是唯一的,只要能稳定地求得任何一个特解即可。该文根据刚度矩阵的性质提出了改进的LDLT算法,可快速稳定地求得一个特解。结合典型算例,与摄动解法、最小二乘法和二次规划法进行了对比分析。
The global approximation function in NMM is formed by “uniting” the local approximation function by unit decomposition. When the local function is taken as a polynomial of order no lower than one, then the so-called " The higher order manifold method. However, the higher-order manifold method leads to a loss of stiffness matrix. This disadvantage ranks even after imposing a complete displacement constraint, which leads to multiple solutions to the NMM equations. However, the displacement corresponding to each solution is unique. As long as any special solution can be obtained stably. According to the properties of the stiffness matrix, an improved LDLT algorithm is proposed to obtain a special solution quickly and stably. A typical example is compared with perturbation solution method, least square method and quadratic programming method.