ANALYTICAL SOLUTION OF THE COUPLED BUCKLING PROBLEM FOR A PLATE FROM A SHAPE MEMORY ALLOY SUBJECTED TO INVERSE MARTENSITE TRANSFORMATION

摘要

Analytical solutions of the linearized problem of buckling induced in a shape memory alloy rectangular plate by inverse martensite transformation were obtained within the framework of various hypotheses. The stability regions were constructed on the basis of two different versions of the constitutive relation for characteristic temperatures of the phase transformation. More consistent results are obtained if these temperatures are linear functions of the stress deviator, rather than the stress intensity. There are relatively few publications that have been devoted to the buckling analysis of shape memory alloy thin-walled structures [1-6]. In [2], the experimental results, which indicate that the martensite phase transformations themselves can cause buckling, are presented. In [3-6], various hypotheses, within the framework of which this phenomenon can be adequately described by solving the linearized buckling problem, have been analyzed. It is established that the continuing phase transformation concept provides qualitatively correct description of this phenomenon. In accordance with this concept, the material undergoes an additional phase transformation when transferring to a neighboring equilibrium shape. It is shown that the least critical loads are obtained within the framework of the continuing loading concept. In accordance with this concept, the additional phase transformation occurs in the entire cross-section of the body. In [3,4], the buckling problem for the Shenly column with the supporting rods made of a shape memory alloy and subjected to the direct martensite transformation was solved in various statements. The buckling of a shape memory alloy rod induced by direct or inverse martensite transformation was studied in [5]. The buckling of a rectangular plate caused by direct martensite transformation under the action of biaxial compression was investigated in [6]. In the present paper, we obtain analytical solutions of various buckling problems for a rectangular plate that undergoes the inverse martensite transformation under the action of biaxial compression after the direct martensite transformation under the action of biaxial loading. The loads acting during the direct and subsequent inverse martensite transformations are different in the general case. The problems are solved for two versions of the constitutive relations for inverse transformation characteristic temperatures in order to choose the more adequate form of these relations.