Hybrid stress finite element analysis of bending of a plate with a through flaw

H. C. Rhee, S. N. Atluri

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

A hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through‐the‐thickness crack is presented. Reissner's sixth‐order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated. The effects of the explicit enforcement of traction‐free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction‐free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensity factor.

Original languageEnglish
Pages (from-to)259-271
Number of pages13
JournalInternational Journal for Numerical Methods in Engineering
Volume18
Issue number2
DOIs
StatePublished - Feb 1982

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