A NEW ELEMENT BISECTION ALGORITHM FOR UNSTRUCTURED ADAPTIVE TETRAHEDRAL MESH GENERATION

A new h-refinement adaptive tetrahedral mesh generation algorithm is p resented. Three-dimensional domains, to be analysed by the finite elem ent method, are initially modelled by a coarse background mesh of tetr ahedral elements. This mesh forms the input for finite element analysi s and error estimation by the Zienkiewicz-Zhu simple error estimator. Adaptive mesh refinement proceeds by selecting an element for remeshin g whose longest edge is shared by elements that also require refinemen t. This group of elements is refined by inserting a new node at the mi d-point of the shared edge thereby bisecting all elements within the g roup. Adaptive parameters are calculated for the new node and elements . Refinement then proceeds until no further group of elements can be f ound for refinement or no elements within the current mesh require fur ther refinement. The shape quality of the current mesh is then enhance d by the iterative application of nodal relaxation plus three topologi cal transformations. The entire refinement process is repeated iterati vely until the required degree of mesh refinement is reached. Ten-node d linear strain tetrahedral finite element meshes have been used for t he finite element and error estimation analyses. Four examples of adap tive tetrahedral mesh generation for linear elastic stress/displacemen t analysis are presented which show that this algorithm is robust and efficient in terms of reduction of the domain error with a minimum num ber of degrees of freedom being generated, number of iterations, and t herefore finite element analyses, required and computational time for refinement when compared to the advancing front method and Delaunay tr iangulation.