REFINEMENT OF 3D MESHES AT SURFACE INTERSECTIONS

Refinement of curved boundaries is an important problem in the modelling of solid objects through the use of faceted triangular or quadrilateral elements. Finite element meshes of 3D solids frequently use faceted triangular and quadrilateral elements on their surfaces. Hence several techniques used in geometric modelling have wide ranging applications to finite element modelling. Large numbers of elements are required in finite element analysis in regions where solution variable gradients are high -regions such as corners, surface intersections and surface discontinuities. Creating finite element meshes for analysis can be time consuming, particularly for complex geometries. By employing an adaptive procedure to perform the finite element analysis, the rigorous task of accurately modelling the geometry using finite elements can be simplified, The paper presents an application of previously published work in surface and surface-surface intersection refinement techniques to h-adaptive finite element analysis. The algorithm presented in this paper refines a crude initial mesh on the basis of solution error indicators or other suitable error measures. The refinement procedure strictly maintains the integrity of the geometry by placing newly generated nodes on the true boundary of the solid and also maintains the physical conditions of the problem such as loads and boundary conditions. A geometric and numerical technique is used to refine tetrahedral element meshes in arbitrarily oriented intersecting cylindrical, spherical or conical surfaces. The transformation matrices are computed symbolically and are implemented in the program in order to reduce computational time. Extension of this procedure to surfaces that are other than cylindrical, spherical or conical can be achieved simply by employing an appropriate definition of the surface. The mesh refinement procedure presented in the paper utilizes data structures to store a comprehensive definition of the finite element model and the geometric model at all mesh levels. This allows the mesh density to be improved in any region of the solid, at any mesh level, without a mesh regeneration being required. Several examples are presented to show the meshes that are generated by adaptive refinement.