Reissner-Mindlin板无网格法数值锁死问题及对策

he purpose of this paper is to firstly discuss the root of shear locking phenomena existing in Reissner-Mindlin plate, secondly compare the benefits and shortcomings of several common used solutions, thirdly summarize some new schemes for alleviating shear locking ,with the matching approximation fields scheme, and finally introduce a comparative analysis of element-free Garlekin (EFG) method and radial point interpolation method(RPIM) for shear locking problems. In this study, the root of shear locking phenomena existing in Reissner-Mindlin plate was firstly discussed, and the advantages and disadvantages of several common used solution procedures were compared, additionally, several new schemes for alleviating shear locking were summarized. With the matching approximation fields scheme, a comparative analysis of element-free Garlekin (EFG) method and radial point interpolation method (RPIM) were introduced for shear locking problems. The Dirichlet boundary conditions were imposed through penalty function method to gain modified potential energy functional. Numerical tests show that meshless method with the matching approximation fields scheme has its own superiority. However, the change of the domain of influence and other corresponding parameters makes significant effect on shear locking, therefore, it is still necessary to carry out research on their theory and application, which can be suitable for more complex analysis of plate and shell. The value range of the influence area was discussed for EFG based on the matching approximation fields scheme, this has also been used in this paper for a size design sensitivity analysis of a plate. numerical examples show the applicability and convergence of proposed method with the analytical solution.