The Development Of The Regular Direct Boundary Element Method For The Analysis Of Plate Bending Problems

Abstract

The paper discusses the development of the Regular Direct Boundary Element Method for the analysis of plate bending problems. In the work, which is discussed in this paper, quadratic and cubic spline elements have been used to analyse plates having square and rhombic plan forms with different combinations of fixed, simply supported and free boundary conditions subjected to uniformly distributed loadings. The results of the deflection, slope, shear force and bending moment distributions from the analyses are presented in the paper and they indicate that the regular approach discussed in the paper, yields a considerable improvement in the results obtained at the corners, when compared with the corresponding results from the singular version of the Direct Method. The global results from the regular approach are also compared with the corresponding results from classical theory, where available, with results from the Singular Direct Boundary Element Method and with Finite Difference analyses and the Regular Method has generally been found to perform better than the Singular Method. INTRODUCTION The Boundary Element Method is now a well established numerical technique for the analysis of complex engineering problems and both the direct and the indirect versions of the method have been used extensively for the solution of a wide range of engineering field problems. Boundary integral techniques, on which modern boundary element methods are based were established by the work of such authors as Muskhelishvili [1] and Mikhlin [2]. The application of the Boundary Element Method for the solution of engineering problems gained prominence, however, in the 1970's and at the first International Conference on Boundary Element Methods (BEM-I), held in Southampton in 1978, it emerged as an alternative to the well established Finite Element Method for the analysis of engineering field problems. Since that initial conference there have been considerable developments in the use of the Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X