meshless local Petrov-Galerkin method for static shakedown analysis of elasto-plastic structures

Shakedown analysis is an important branch of plasticityand can provide a theoretical basis for engineering designs and safetyassessments. Based on the static theorem of shakedown analysis, a novelnumerical method is developed to perform lower bound shakedown analysis bymeans of meshless local Petrov-Galerkin method (MLPG) with the Voronoi cellsand the reduced-basis technique. The natural neighbour interpolation isemployed instead of the moving least squares approximation to constructtrial functions. The natural neighbour interpolants are strictly linearbetween adjacent nodes on the boundary of the convex hull, which facilitatesimposition of essential boundary conditions with ease as it is in theconventional finite element method. By introducing the conception of loadvertex in the basic load domain, the numerical difficulties caused by thevariable of time parameter in lower bound shakedown analysis are overcome.Based on the reduced-basis technique, the lower bound shakedown analysisproblem is reduced to a series of non-linear programming sub-problems withrelatively few optimization variables. In each sub-problem of non-linearprogramming, the self-equilibrium stress field is simulated by linearcombination of several self-equilibrium stress basis vectors with parametersto be determined. These self-equilibrium stress basis vectors are generatedby performing an equilibrium iteration procedure during elasto-plasticincremental analysis. Several numerical examples are presented to verify theavailability of the developed method.