Study On Composite Laminated Plates By Incompatible Extended Layerwise Method

Composite laminated plates and shells is a kind of structure which is widely used in the engineering,thus lots of analysis theory and damage analysis theory about the composite laminated plates and shells appear.The extended layerwise method(XLWM)combines the advantages of layerwise method(LWM)and the extended finite element method(XFEM),which provides a precise method for the damage research on composite laminated structures.But in practical application,it is found that the convergence rate of the analysis on bending model by using extended layerwise method is slow,especially about analyzing large bending deformation problem.In order to reach a certain precision requirement,meshing very fine grid is needed,which costs a lot of computation time.In addition,for the composite laminated plate structure,due to the occurrence of delamination and crack,bending modes happen regularly.This paper takes advantage of Wilson incompatible technology in analyzing bending deformation to improve the convergence rate of the extended layerwise method.Introduced Wilson incompatible technology into the extended finite element,the layerwise method,and the extended layerwise method;established IXFEM,ILWM,and IXLWM.The correctness of the method proposed was verified through a lot of numerical examples,and the convergence performance was analyzed by being compared with the original method.Furthermore,according to the characteristics of Wilson incompatible displacement,the influence of different introduction strategies of incompatible displacement(directions and scopes)on convergence speed was researched,as well as the convergence performance of methods proposed under different levels of bending deformation(including rectangular plates with different crack length,and different side length/thickness ratio of plate and spherical shell).The results indicated that as to the bending problem,adopting the appropriate incompatible displacement strategy,the convergence speed after added incompatible displacement item is faster than that of the original method.For the model which only has bending deformation in some regions,the convergence effect added in local is better than that in global.When the bending deformation is larger,the convergence speed in both added in local and added in global is close,but the former is more efficient.When the model whichonly has small bending deformation in local is being analyzed,the addition of incompatible degree of freedom will lead to larger calculation results and oscillation.Therefore,the principle of addition of the incompatible displacement item for the three methods mentioned is that it should be only added in the region and direction where bending deformation occurred.