Finite element method for incompatible meshes and propagating cracks

Abstract

Two-dimensional variable-node elements with linear or quadratic interpolation are developed using the moving least-square (MLS) approximation. The mapping from the parental domain to the physical element domain is implicitly obtained from MLS approximation, calculating and saving the shape functions and their derivatives only at the numerical integration points. The concept of these variable-node elements are further extended to develop crack elements, which allow discontinuity of crack faces and the singularity of crack tip within their integration domain. It is shown that the present variable-node elements meet the patch test if a sufficiently large number of integration points are employed for numerical integration. Furthermore, the accuracy of the crack elements is checked by calculating the stress intensity factor under mode I loading. The major applications of these variable-node elements include the treatment of the non-matching meshes occurring due to the partitioned finite element modeling and the construction of the crack elements. The crack elements turn out to be very efficient and accurate for simulating crack propagations, only with the minimal amount of element adjustment and node addition as the crack tip moves. Numerical results and comparison to the results from other works demonstrate the effectiveness and accuracy of the present scheme for each of the variable-node elements and the crack elements.