Incompatible Numerical Manifold Method

The background of the researches is numerical simulation of particle-reinforced composites. Based on numerical manifold method, this paper improves and extends the method. A new numerical method named incompatible numerical manifold method is presented. To illustrate the feasibility and stability of the present approach, numerical examples are provided. The main contributions can be listed as follows:The covered displacement function expressed by the natural coordinate, the four-nodal quadrangular numerical manifold method is improved. It makes much easy the integration of the four-nodal quadrangular numerical manifold element in irregular covered mathematical mesh form. The results have been found more accurate than that of the finite element method.Using Common Plane techniques to detect and categorize contacts between three-dimensional blocks of any arbitrary shape, the contact detection method is reconstructed to reduce computation. The three-dimensional numerical manifold method is presented. The work enriches and extends the research domain of numerical manifold method.The incompatible displacement term is added to total displacement function, it makes displacement function tend to entire, establishes the improved manifold method named incompatible numerical manifold method. This method can greatly increase calculating accuracy and computing efficiency without adding generalized degrees of freedom.Wilson incompatible displacement function term is improved, generalized formula of incompatible displacement function is deduced. In order to apply this method to engineering, we give an explicit treatment of zero-order coved function and one-order coved function.In order to perfect theoretic system of incompatible numerical manifold method, its stability and convergence are analyzed. Some numerical examples are provided to illustrate this method. The conclusion shows that this method produces highly accurate and stable results.