STUDY ON LINEAR DEPENDENCE PROBLEM IN HIGH-ORDER NUMERICAL MANIFOLD METHOD

In the numerical manifold method (NMM), a global approximation function is built by “pasting together” the local approximation functions through the corresponding partition of unity. The high-order NMM is achieved by taking high-order polynomials with an order no less than one as the local approximation functions. However, the high-order NMM will be associated with a stiffness matrix of rank deficiency. Even if the complete displacement constraints are enforced, such rank deficiency remains and causes a non-uniqueness solution to the system of linear equations of NMM. Nevertheless, the displacement corresponding to each solution is unique. Hence it suffices to develop a procedure that is able to find efficiently and stably out a particular solution. Based on the properties of the stiffness matrix, this study proposes an improved LDLT decomposition algorithm which can be used to find a particular solution for the high-order NMM system. Using a typical example, we make comparisons with the perturbation algorithm, the least squares method and the quadratic programming.