Premium
Automatic adaptive refinement for plate bending problems using Reissner–Mindlin plate bending elements
Author(s) -
Lee C. K.,
Hobbs R. E.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980115)41:1<1::aid-nme264>3.0.co;2-o
Subject(s) - bending of plates , bending , discretization , estimator , plate theory , finite element method , boundary (topology) , mathematics , convergence (economics) , boundary value problem , shear (geology) , geometry , mathematical analysis , structural engineering , materials science , engineering , composite material , statistics , economics , economic growth
The influence of the presence of singular points and boundary layers associated with the edge effects in a Reissner–Mindlin (RM) plate in the design of an optimal mesh for a finite element solution is studied, and methods for controlling the discretization error of the solution are suggested. An effective adaptive refinement strategy for the solution of plate bending problems based on the RM plate bending model is developed. This two‐stage adaptive strategy is designed to control both the total and the shear error norms of a plate in which both singular points and boundary layers are present. A series of three different order assumed strain RM plate bending elements has been used in the adaptive refinement procedure. The locations of optimal sampling points and the effect of element shape distortions on the theoretical convergence rate of these elements are given and discussed. Numerical experiments show that the suggested refinement procedure is effective and that optimally refined meshes can be generated. It is also found that all the plate bending elements used can attain their full convergence rates regardless of the presence of singular points and boundary layers inside the problem domain. Boundary layer effects are well captured in all the examples tested and the use of a second stage of refinement to control the shear error is justified. In addition, tests on the Zienkiewicz–Zhu error estimator show that their performances are satisfactory. Finally, tests of the relative effectiveness of the plate bending elements used have also been made and it is found that while the higher order cubic element is the most accurate element tested, the quadratic element tested is the most efficient one in terms of CPU time used. © 1998 John Wiley & Sons, Ltd.