Adaptive constrained mesh generation: part 2 - accommodation of constraints

A novel algorithm for generating two-dimensional finite element meshes has been presented in Part 1. Herein, new methodologies of incorporating point and line constraints into an existing planar mesh are developed. Unlike the conventional method of applying local retriangulation to the areas affected by the constraints, the proposed method employs a combination of nodal repositioning and nodal insertion to accommodate the constraints so as to maximise the shape quality of the resulting mesh. The method has the major advantage that it is adaptive to the results of analysis and hence even new constraints emerging during the analysis may be incorporated. When new nodes are inserted, they are assigned node numbers close to those of the nodes connected to them to minimise the increase in bandwidth and, in order to avoid conflicting numbers, the nodes affected are renumbered by shifting their numbers upwards. After accommodating the constraints, mesh smoothing may be applied to further improve the shape quality. Applications of the method in computational mechanics are discussed and examples presented to illustrate its versatility and performance.