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This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.

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A reliable and cost effective two-phase methodology is proposed to predict crack propagation life in generic twodimensional structural components under complex fatigue loading. First, the usually curved fatigue crack path and its stress intensity factors are calculated at small crack increments in a specialized finite element software, using automatic remeshing algorithms, special crack tip elements and appropriate crack increment criteria. Then, the calculated stress intensity factors are transferred to a powerful general purpose fatigue design software based in the local approach, which has been designed to predict both initiation and propagation fatigue lives by all classical design methods. In particular, its crack propagation module accepts any K I expression and any da/dN rule, considering sequence effects such as overload-induced crack retardation to deal with one and two-dimensional crack propagation under complex loading. Non-trivial application examples compare the numerical simulation results with those measured in physical experiments.