Keywords: mesh generation, paving, constrained meshing, truss points, plates, structural analysis software, truss analysis.

This paper gives a solution to a meshing problem for a civil engineering application. The civil engineering application which is tackled is complete three-dimensional analysis of the roof of a building. The connection points where the roof meets the underlying supporting trusses are the points which must be connected with plates. The plates must also not violate the connectivity of the trusses. The complete 3-D analysis of the roof will give accurate results as the stiffness of the roofing material will be taken into account. The plates connect the trusses and also support some of the loads put on the roof. The nodal points of the roof are the connection points in the roof. These connection points if accurately modelled can increase the accuracy of the results.

The problem therefore is to mesh the roof surface for which all the nodes and some of the connectivities are pre-defined. Such problems are called constrained meshing problems. The nature of the problem is such that the ratio of already defined connectivities to connectivities that need to be formed is as high as 30 to 40 percent. The already existing solution for such problems is domain decomposition [1]. The reasons for not choosing the domain decomposition method are discussed in the paper.

An approach similar to the paving [2] algorithm for meshing is presented in this paper. This approach is based on laying the elements on top of nodes based on their connectivity status, the connectivity status of the nodes, previous and next to it and also on the angle that the nodes make with reference to nodes, previous and next to them. If there is a previously defined connectivity at a node, a truss point is said to exist for it. Some modifications to the paving algorithm are also presented in this paper. These modifications are in addition to modifications which have been accepted for the original algorithm [3,4]. The algorithm results in the formation of both quadrilateral and triangular plates.

The meshing results for a program using this algorithm are also presented in this paper. The meshing results are both in the form of example domains and time requirements. Towards the end some recommendations and conclusions are presented for the study. Although the algorithm is designed for a civil engineering applications, it is useful for other fields.

1

Lober, R.R., Tautges, T.J., Cairncross, R.A., "The Parallelization of an Advancing-Front, All-Quadrilateral Meshing Algorithm for Adaptive Analysis", Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.59-70, October 1995

2

Blacker T.D. and Stephenson M.B., "Paving: A new approach to automated quadrilateral mesh generation", IJNME, Vol 32, 811-847,(1991). doi:10.1002/nme.1620320410

3

White R.D. and Kinney P., "Redesign of paving algorithm: Robustness enhancements through element by element meshing", Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.323-335, October 1997.

4

A. Dixit, "Simplifying Improvements to the Paving Algorithm", in Proceedings of the Fourth International Conference on Engineering Computational Technology, B.H.V. Topping and C.A. Mota Soares, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 21, 2004. doi:10.4203/ccp.80.21

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