一维准晶功能梯度层合圆柱壳热电弹性精确解

EXACT THERMO-ELECTRO-ELASTIC SOLUTION OF FUNCTIONALLY GRADED MULTILAYERED ONE-DIMENSIONAL QUASICRYSTAL CYLINDRICAL SHELLS

两种或多种不同性质材料组成的层状结构可以满足工业发展的需求.然而,材料属性在接触面的突变问题,容易导致层间界面处产生应力集中、裂纹以及分层等问题.功能梯度材料利用连续变化的组分梯度来代替突变界面,可以消除界面处的物理性能突变,提高结构的粘结强度.本文以一维准晶功能梯度层合圆柱壳为研究对象,利用类Stroh公式和传递矩阵方法,建立了材料参数沿径向呈现幂函数变化的层合圆柱壳模型,获得了简支边界条件对应的一维准晶功能梯度层合圆柱壳的热电弹性精确解.数值算例中讨论了层合圆柱壳内外表面承受温度载荷时,功能梯度指数因子对温度场、电场、声子场和相位子场的影响,尤其是对层合圆柱壳内外表面的影响.结果表明,指数因子改变了材料参数的空间分布情况,进而对温度场、电场、声子场和相位子场都有影响;增加功能梯度指数因子,可减小温度载荷引起的内表面变形,进而提升结构强度.本文得到的结果可以为功能梯度准晶层合圆柱壳的设计和制造提供可靠的理论依据.

Layered structures made of two and more materials with different properties can meet the needs of industrial development. However, the abrupt change of material properties at the interface of the laminated structures can easily cause some interface problems, such as stress concentration, interface cracks, and interface delamination phenomena.Functionally graded materials refer to utilize a continuously changing component gradient instead of the original sudden change interface, which can eliminate or weaken the abrupt change of the physical properties and then increase the bonding strength of the layered structures. In this paper, the research object is the functionally graded multilayered onedimensional quasicrystal cylindrical shells. By virtue of the pseudo-Stroh formalism and the propagator matrix method,we establish the layered one-dimensional quasicrystal cylindrical shells model with the material parameters following the power-law type distribution along its radius direction, and obtain the exact thermo-electro-elastic solution of the functionally graded layered one-dimensional quasicrystal cylindrical shells with simply supported boundary condition.Numerical examples are carried out to investigate the influences of the exponential factor on temperature, electric, phason and phonon fields of the functionally graded layered one-dimensional quasicrystal cylindrical shells subjected to both inner and outer surfaces temperature variations, especially the effects on physical quantities at the inner and outer surfaces of the layered one-dimensional quasicrystal cylindrical shells. The obtained results indicate that: the exponential factor can change the distribution characteristic of material parameters, which can cause a significant influence on the physical quantities in the temperature, electric, phason, and phonon fields;by increasing the exponential factor, the deformation at the internal surface induced by temperature stimuli is reduced and the strength of the layered one-dimensional quasicrystal cylindrical shells is improved. The results obtained in this paper can provide a reliable theoretical basis for the design and manufacture of functionally graded layered one-dimensional quasicrystal cylindrical shells.