Incompatible Numerical Manifold Method

This paper deduces the additional incompatible displacement terms on internal parameters for three-dimensional elasticity problems, establishes the improved incompatible numerical manifold method. Based on eliminating the internal parameters, the expressing formula of element strain matrix and element stiffness matrix are given. Calculating accuracy and computing efficiency can be greatly increased by incompatible numerical manifold method without adding generalized degrees of freedom. In order to apply this method to engineering, an explicit treatment of incompatible numerical method is provided. To illustrate the stability of the present approach, numerical examples are analyzed. It is shown that this method produces highly accurate and stable results.Keywords: numerical manifold method; incompatible element; additional displacement term; generalized degree of freedom; static concentration