Mesh generation with adaptive finite element analysis E. Hinton, N.V.R. ILao and M. Ozakga Department of Civil Engineering, University College of Swansea This paper deals with key aspects of the coupling of automatic mesh generation with adap- tive analysis and shape optimisation of planar and surface structures. Adaptive analysis requires the design of nearly optimal meshes with varying element sizes to achieve a pre- scribed accuracy. In any shape optimisation process as the region to be discretised changes continuously and sometimes dreustically, mesh generation should ideally take place without intervention by the analyst and without any excessive distortion of elements. To carry out these processes in a fully automatic and efficient manner a highly robust, versatile and flex- ible mesh generator is required. A brief introduction to the features of one such automatic mesh generator, based on the advancing front method, is described. Several examples are presented exploiting the potential of this mesh generator for adaptive analysis and shape optimisation. The integration of the rnesh generator with these procedures is discussed as well as some issues which required special attention. Key Words: finite elements, adaptive analysis, error estimation, automatic mesh generation, advancing front method, structural shape optimisation. 1. INTRODUCTION I. I Preamble The finite element (FE) method is now firmly es- tablished as an engineering tool of wide applicabilil, y. When carefully used by experienced and diligent en- gineers, FE based models can provide much valuable insight into structural behaviour. However, designers who do not possess extensive expertise in numerical analysis, may unquestioningly believe that all FE re- sults are highly accurate or even exact. This has led to recent emphasis on adaptive analysis or adaptive mesh refinement (AMR) procedures to improve the reliabil- ity of the FE method and to ensure that the results produced are of appropriate accuracy. 1.2 Automatic mesh generation in AMR procedures A*IR procedures involve the design of nearly opti- mal meshes with varying element sizes to achieve a pre- scribed accuracy. The importance of AMR procedures in industrial applications has led to increased research on fully automatic mesh generators which require only the specification of the boundary and mesh size distri- bution over the domain. The success of AMR proce- dures depends to a large extent on the efficient coupling between the adaptive FE analysis and automatic mesh generation. Tile AMR procedure requires a convenient means of prescribing the mesh density over the domain, to gen- erate the so called optimal mesh; however, this type of feature is not commonly' available in most mesh gener- ators. A method for estimating the new element sizes is required in order to guide the generation of an en- tirely new mesh to achieve a prescribed accuracy. The new element sizes can be evaluated using an error es- timate from the results of a previous FE analysis and there are different ways of estimating this error based on residual or projection methods. Once information concerning the new element sizes has been estimated it has to be linked to the mesh generator to perform the desired discretisation by transferring the new element sizes to tile nodes of the current mesh or to the bound- ary of the domain to be discretised. The extension of this procedure for surface struc- tures further complicates the issue, as mesh generation and error estimation on curved surfaces are required coupled with accurate estimation of mesh parameters such as element size. Another aspect which requires attention in this case is the mapping of elements and @1991 Elsevier Science Publishers Ltd 238 Adv. Eng. Software, 1991, Vol. 13, No. 5/6 combined