Analysis Of Asymmetric Bending Problem Of Shape Memory Alloy Beam

With the rapid development of new intelligent materials,shape memory alloys stand out among many new intelligent materials because of their shape memory effect and super elasticity.The research reveals that these two characteristics are related to the phase transition between austenite and martensite,considering the study of phase transition to non-symmetric bending problem the of the shape memory alloy beam is very important.This paper mainly study the asymmetric bending problem of shape memory alloy beams,the statically indeterminate problem of shape memory alloy beams under thermal and mechanical loads and the asymmetric bending problem of functionally gradient shape memory alloy beams under statically indeterminate.Firstly,based on the bending theory of beam and the constitutive relation of shape memory alloy material,the asymmetric bending problem of shape memory alloy beam under concentrated load is studied.Considering the asymmetry of the phase transition on both sides of the tension and compression in the process of bending deformation,this paper introduces the asymmetry coefficient of tension and compression and analyzes the distribution of stress,curvature,neutral axis displacement and the changes of phase boundary on the section of the I-section shape memory alloy beam at each phase transition stage.The results show that the larger the displacement and curvature of the neutral axis are,the easier the phase transition will occur,and the phase transition that the rectangular section is easy to occur than I-section section when the shape of the two sections are different.Secondly,considering the relationship between critical stress and temperature of shape memory alloy,the nonlinear mechanical behaviors of statically indeterminate beam of shape memory alloy under the condition of impure bending are analyzed.In order to visually describe the asymmetry of phase transition about the beam on both sides of the tension and compression,the asymmetry coefficients of tension and compression are introduced to analyze the stress distribution on the cross section of the rectangular section and the I-section section at each phase transition stage,and get the information of the cross section curvature,the neutral axis displacement as well as the changes of the phase boundary along the axial direction by solving the balance equations.Finally,based on the continuum mechanics and composite material mechanics,the stress distribution on cross section of the function gradient shape memory alloy statically indeterminate beams is analyzed,considering the asymmetry of uniformly distributed load,the asymmetry coefficient of tension and compression and the volume fraction of shape memory alloy under the change of circumstances,and get the information of the functional gradient shape memory alloy statically indeterminate beam on the phase change of curvature,the neutral axis displacement and deformation characteristics of the distribution of the border through establishing the balance equations of the cross section on the force and moment.The conclusions obtained in this paper have a positive role in promoting the asymmetric bending problem of shape memory alloy beam and can provide guidance and references for the engineering application of asymmetric bending problem of shape memory alloy beam.