湿—热—力载荷作用下的功能梯度板的分析

发布时间：2018-06-07 14:09

本文选题：功能梯度板 + 横法向应变　；参考：《沈阳航空航天大学》2017年硕士论文

【摘要】：Reddy型高阶剪切变形理论被广泛应用于工程实践中,然而由于此理论忽略了横法向应变,难以准确分析功能梯度板的湿热行为。本文提出了考虑横法向湿热应变的Reddy型功能梯度板理论,用于分析功能梯度板的湿热力行为。虽然此模型考虑了横法向湿热应变,但并未增加额外的位移变量。基于本文所提模型,通过最小势能原理推导出湿热力载荷共同作用下功能梯度板的平衡方程及边界条件,根据Navier理论给出了在四边简支边界条件下功能梯度板的解析解。将基于本文方法计算的应力及位移分别与文献中的理论结果进行对比,数值结果表明正弦剪切变形理论(SPT)、指数剪切变形理论(ESPT)、高阶剪切变形理论(HSDT-98)、五阶剪切变形理论(FiSDT)由于忽略了横法向湿热应变,计算的应力和位移精度较低,而基于本文所提模型计算的数值结果与精确解吻合良好,通过分析功能梯度板的湿热行为,评估了该模型的准确性和有效性。同时研究了温度、水分浓度、横法向应变、体积分率和跨厚比对于功能梯度板的位移与应力的影响。
[Abstract]:Reddy high order shear deformation theory is widely used in engineering practice. However, it is difficult to accurately analyze the hygrothermal behavior of functionally gradient plates because of its neglect of transverse normal strain. In this paper, the theory of Reddy type functional gradient plate considering the transverse normal hygrothermal strain is proposed to analyze the hygrothermal force behavior of the functionally graded plate. Although the transverse normal hygrothermal strain is considered in this model, no additional displacement variables are added. Based on the model proposed in this paper, the equilibrium equation and boundary conditions of functionally gradient plate under the action of hydro-thermal load are derived by the principle of minimum potential energy. According to Navier's theory, the analytical solution of functionally gradient plate under the condition of simply supported boundary on four sides is given. The stresses and displacements calculated based on the present method are compared with the theoretical results in the literature. The numerical results show that the sinusoidal shear deformation theory is SPT, the exponential shear deformation theory is ESPT, the high order shear deformation theory is HSDT-98, the fifth order shear deformation theory is FiSDT) and the calculation accuracy of stress and displacement is low because of neglecting the transverse normal hygrothermal strain. The accuracy and validity of the model are evaluated by analyzing the hygrothermal behavior of the functionally gradient plate. The effects of temperature, water concentration, transverse normal strain, volume fraction and span thickness ratio on the displacement and stress of the functionally gradient plate were studied.
【学位授予单位】：沈阳航空航天大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34

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