ISSN:
0029-5981
Keywords:
numerical method
;
high-order function
;
Manifold method
;
discontinuous deformation analysis
;
rock
;
blocks
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original first-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems. © 1998 John Wiley & Sons, Ltd.
Additional Material:
11 Ill.
Type of Medium:
Electronic Resource
Permalink
