ABSTRACT:

The Numerical Manifold Method (NMM) has been developed based on finite triangular and quadrilateral covers. Using finite element covers. the weight functions in NMM can be the same as the shape functions in FEM. In this paper the Wilson non-conforming element is used in quadrangular covers. The corresponding matrices of equilibrium equations are given in detail in the present paper. A Fortran 95 program has been developed and applied to a cantilever beam. The results are in good agreement with theoretical solution than the classical Q4 isoparametric element. It shows that the precision and efficiency of computation can be improved greatly by using Wilson non-conforming element in beam/plate bending problem.

I.
INTRODUCTION

The Numerical Manifold Method (NMM) is a flexible method to solve the problem containing continuum and discontinuum. The meshes of this new method are finite covers: the mathematical covers define only the rough approximations. The real material boundary or the physical mesh defines the integration fields. Using the finite cover systems, continuous, jointed or blocky materials can be computed in a mathematically consistent manner. The difficulty in practical application is to choose the cover functions and weight functions. A simple and efficient way is the use of finite element covers. That is to say, the finite element meshes can be used to define finite covers. In these covers, the weight functions are the shape functions of FEM. Shi (1996) has given details on the triangular finite element Covers, Shyu and Salami (I995)have considered quadrilateral isoparametric element covers in NMM. As we all know, in FEM, the quadrilateral Q4 isoparametric element is more efficient than triangular element. For bending problem and 3- D problem, the precision and efficiency of the Q4 element is not sufficient. Wilson has suggested to use non-conforming isoparametric element in FEM (Wang & Shao. 1995). In NMM, the research work of this element has not been done but it may be important in real application. In this paper, the use of Wilson non-conforming elements In NMM is discussed and the details of the matrices of equilibrium equations are also given for program coding. An example of cantilever beam is used to verify the precision of the Wilson isoparametric element in NMM.

3.
THE THEORY OF NMM AND THE COVER WEIGHT FUNCTIONS

The Manifold Method (MM) connects many individual folded domains together to cover the entire material volume. The global displacement functions are the weight averages of local independent cover functions on the common part of several covers. So, determining the weight functions is very important in NMM.

5.
CONCLUSIONS

The choice of suitable cover functions is very important for successful use of NMM. The FEM isoparametric element is often used in NMM because of its convenience. This paper discussed the application of Wilson non-conforming element in NMM and the matrices of the equilibrium equations are derived. A problem of cantilever beam is studied in this paper. Compared with classical Q4 isoparametric element.

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