Finite Element Elastoplastic and Limit Analysis: Some Consistency Criteria and Their Implications
The formulation of element elastic-plastic laws is considered in the framework of the displacement approach. The finite element model is regarded as an actually discrete system, composed of a finite number of parts whose individual behaviour is described in terms of generalized stresses and strains. A general procedure for formulating the element laws is proposed, and it is shown that some commonly used formulations of finite element elastic-plastic analysis can be recovered on the basis of particular assumptions. It is pointed out that these formulations may violate some “consistency” requirements, which are discussed in the paper; these violations may explain some of the inaccuracies experienced in computations. A fairly general method for restoring consistency is proposed. The implications of some of the approximations involved are also discussed, with particular reference to the limit analysis problem. Simple examples illustrate the effects of lack of consistency.
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