The Mechnics Analysis Of Composite Material Beam With Non-Symmetry Paved Sma-Layer Subjected To Thermal Load

Employing theoretical analysis and incorporating with numerical computation, bending,thermal post-buckling and vibration of composite beams with shape memory alloy(SMA) layer paved in non-symmtry are analyzed.Especially,the problem how to realize active control to the deformation of bending,buckling and vibration in the pre/post buckling configuration of the beam under active strain energy(ASET) is discussed in detail.The main research are as following.Firstly,the physical properties,phase-change process and the constitutive model are introduced.Based on Brinson's one-dimensional thermomechanical constitutive model,a linear constitutive model of recovery stresses for fully restrained SMA layer is proposed.Secondly,based on Brinson's constitutive relations and the geometrically nonlinear theory for axially extensible beams,governing equations for nonlinear thermal bending, buckling and vibration of beams subjected to temperature load are derived.Thirdly,by using the shooting method to solve the corresponding nonlinear governing equations,the deformation responses for SMA composite beams with three different boundry conditions(pinned-pinned,fixed-fixed and pinned-fixed) under uniform temperature rising are obtained and the equilibrium paths and configurations for a specific example are presented.The results show that the deformation exsits at the beginning of elevation temperature for pinned-pinned and pinned-fixed supported beams.In the process of elevation temperature,the deformation trend exacerbates with the SMA's phase change.To the beam with fixed-fixed ends,the equilibrium paths and configurations have same trend compared with the beams uniformly embedded with SMA wires.Finally,by using the shooting method to solve the corresponding governing equations of vibration,the linear vibration responses for SMA composite beams with three different supported(fixed-fixed,pinned-pinned) under uniform temperature rise are obtained.The characteristic curves of the first to fourths natrual frequencies versus temperature rising are given.The results show that for the fixed-fixed supported beams, enlarging the thickness of the SMA layer can rise the frequencies when the temperature lower than the critical thermal buckling temperature,and decline them when the temperature higher than the critical thermal buckling temprature.To the beams with pinned-pinned ends,because there is not buckling deformation in the beams,almost all the frequencies can decline with the increase of the SMA layer's thickness.