形状记忆合金纤维复合材料梁非线性变形、热屈曲和振动

Nonlinear deformation,thermal buckling and vibration of SMA fiber composite beams

研究具有形状记忆合金(SMA)纤维的复合材料梁非线性静变形、热屈曲和振动。采用Euler-Bernoulli梁理论、Timoshenko梁理论和Reddy高阶理论进行结构建模;根据Von-Kármán应变场理论描述梁的几何非线性;采用Brinson热力学本构方程计算SMA纤维的受限回复特性;基于Hamilton原理导出梁的非线性偏微分控制方程;采用Galerkin法导出两端简支对称铺层SMA纤维复合材料梁的非线性静变形、热屈曲和振动近似解。通过数值计算揭示SMA纤维含量、激励温度和初始应变对非线性静变形、热屈曲和振动的影响规律。研究表明,当长厚比较大时,剪切变形的影响很小,上述理论均可适用;但长厚比较小时,Euler-Bernoulli和Timoshenko梁理论的结果与Reddy高阶理论的结果相差较大,剪切变形的影响是显著的。

This paper presents an investigation into the nonlinear deformation,thermal buckling and vibration of the composite beams embedded with shape memory alloy(SMA)fibers.The beams were modeled by using Euler-Bernoulli,Timoshenko and Reddy higher-order beam theories.The Von Kármán type nonlinear strain-displacement equations were employed to describe the geometric nonlinearity of the beam.One-dimensional thermo-mechanical constitutive equation proposed by Brinson was utilized to calculate the recovery stress of the constrained SMA fibers.The nonlinear partial differential equations of the beams were derived based on the Hamilton’s principle.The approximate solutions to the nonlinear deformation,thermo-buckling and vibration were obtained by using the Galerkin approach.Numerical calculation was carried out to show the effect of the volume fraction,actuation temperature,and the initial strain of SMA fibers on the nonlinear deformation,thermal buckling and vibration of the SMA fiber composite beams.Results of this study show that for a larger ratio of length to thickness,the shear-deformation effect is very insignificant and the three theories mentioned above are all applicable.However,for a low ratio oflength to thickness,the results of Euler-Bernoulli,Timoshenko and Reddy higher-order theories differ greatly,and the shear deformation is shown to have an important effect on the deformation,thermal buckling and vibration behaviors.