Abstract
ABSTRACT This paper presents an analysis of the stress concentralion in a shape-memory alloy sheet containing a circular hole andsubject to aibitrary in-plane loading at great distances from the hole. The generalized Tanaka model is used to describe theconstitutive behavior ofthe material and an approximate approach due to Stowell is used for the stress analysis.Keywords: circular holes, inplane loading, plane stress state, shape-memoiy alloy, stress analysis, stress concentration,stress distribution 1. INTRODUCTION Problems of stress distribution in thin sheets with geometric discontinuifies such as holes have been of continuing interestfrom the famous Kirsch solution' of 1898, through the plasticity solutions ofthe 1950s and 1960s, cf.2'3, and the piezoelectricsolutions ofthe past five years, to the recent work6 on SMA (shape-memory alloy) sheets subjected to balanced biaxialstresses.The present work extends the work of Birman6 to the case of aibitrary planestress loading. The material model used isthe Tanaka model7 as extended to multiple dimensions by Boyd and Lagoudas8. For an extensive review of the literature onthe mechanics of shapememory alloy structures, see Birman9.
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