A novel symplectic approach is employed in the analysis of homogenous and functionally graded beams subjected to arbitrary tractions on the lateral surfaces. Two models of functionally graded beams are heterogeneous in the sense that the material properties are exponential functions of the length and thickness, respectively. Within the symplectic framework, the method of separation of variables alone with the eigenfunction expansion technique is adopted to obtain the exact analysis of displacement and stress fields. The complete solutions include homogenous solutions with coefficients to be determined by two end boundary conditions and particular solutions satisfying the lateral boundary conditions. Two examples are presented for functionally graded beams to demonstrate the effects of material inhomogeneity. The efficiency and accuracy of the symplectic analysis are shown through numerical results.

Moisture condensation often occurs in the cave wall in service, which results in the deterioration of the internal environment of the cavern and the decline of its functionality and durability. In this paper, the corrosion mechanism of concrete structure caused by the dew-condensation inside the cavern wall is analyzed, the daily temperature and humidity environment change inside and outside the cavern is measured, the influence of wind speed and ventilation condition on the dew-condensation inside the cavern is discussed, and the change rule of the external atmosphere temperature, the air temperature and humidity inside the cavern wall temperature is discussed. The results show that it is an inevitable physical phenomenon that the internal temperature of the cavern is lower than the dew point temperature, and the measures to deal with cold condensation such as sealing the cave with dry gas when no one is around, filling the cavern with air of appropriate temperature and humidity when there are people, and setting up dehumidification system are effective ways to improve the durability of the concrete structure of the cavern.