| A technique for modeling arbitrary discontinuities in finite elements is presented and implemented in the eXtended Finite Element Method (X-FEM), a computational methodology for solving solid mechanics problems. In the X-FEM, the finite element approximation is enriched by additional functions through the notion of the partition of unity. The geometries and interfaces can be independent of the mesh. Implementation of arbitrary strong and weak discontinuity in X-FEM is presented i.e. both discontinuities in the function and its derivatives. In all cases, the discontinuous approximation is constructed in terms of a signed distance functions, so level sets can be used to update the position of the discontinuities. The enrichment functions for tangential discontinuities for straight and circular lines in two dimensions are developed. For the approximation of a circular tangential discontinuity, three enrichment functions are tested. Correct rigid modes are obtained in the eigenvalue analysis. Material interfaces in three-dimensional space are modeled by implicit surface modeling. The implicit function is used for the definition of the domains occupied by the materials and to define the enrichment function. Numerical examples of the following applications are given: 2D circular inclusion, a spherical cavity, a spherical inclusion and 4D carbon/carbon composites material.; Adaptive methods for beam and shell finite element dynamic analysis are studied and presented. Adaptive projections for a beam which satisfies the governing equations are developed. Conservation of kinetic energy, conservation of momentum, conservation of angular momentum and kinetic conditions are considered. Also, a beam element kinematic solution recovery technique is developed. It can recover the exact displacement in the pure bending case. The adaptivity technique is applied to an elastoplastic beam buckling and a box beam buckling problem. Errors due to adaptivity projections are investigated. It is shown that these errors can cause unphysical behavior of the structure. |
