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| Shakedown analysis by using the element free Galerkin method with orthogonal basis and nonlinear programming |
| Received:March 20, 2007 |
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| DOI：10.7511/jslx20091013 |
| KeyWord:element free Galerkin method orthogonal basis shakedown analysis nonlinear programming Complex method |
| Author | Institution |
| 陈莘莘 |
清华大学 工程力学系,北京 |
| 刘应华 |
清华大学 工程力学系,北京 |
| 岑章志 |
清华大学 工程力学系,北京 |
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| Abstract: |
| The computational formulation of lower bound shakedown analysis of structures under the action of variable loads is established by using the element free Galerkin (EFG) method with orthogonal basis. The considered structure is made up of elasto-perfectly plastic material. The fictitious elastic stress field associated with the corners of the given load domain can be computed by using the EFG method with orthogonal basis. The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are determined by equilibrium iteration procedure during elasto-plastic incremental analysis. Through modifying the self-equilibrium stress subspace continuously, the lower bound shakedown analysis problem is finally reduced to a series of sub-problems of nonlinear programming with relatively few optimization variables. The Complex method is used to solve these nonlinear programming sub-problems. The numerical results of the solution procedure adopted herein appear to be satisfactory and rather insensitive to the choice of the initial Complex configurations and load increments used to create self-equilibrium stress basis vectors. |