Buckling and Dynamic Behavior of Non-Uniformly Heated Cylindrical Panels

Abstract

Today, curved panels especially cylindrical and conical are considered as a backbone of numerous engineering structures. Knowledge of buckling and dynamic behavior of structures over a range of temperature is essential for their better design. Most of the studies carried out on heated panels are based on uniform temperature distribution assumption. However, in real life application, the cylindrical panels employed in structures are exposed to non-uniform temperature variation due to the location of the heating source and thermal boundary conditions. In the present study, the thermal buckling strength of the non-uniformly heated metallic panel predicted numerically is validated experimentally using in-house developed experimental set-up. Further studies are extended to investigate the effect of non-uniform temperature variation on buckling strength and free vibration characteristics of metallic, laminated composite, and functionally graded carbon nanotube (FGCNT) reinforced polymer composite, cylindrical panels using the finite element method. Finally, the optimization of a non-uniformly heated laminated cylindrical panel against thermal buckling strength and fundamental natural frequency is also carried out. Typical variation of temperature-deflection plot for different temperature fields is obtained experimentally and further, inflection point method is used to predict the critical buckling temperature from temperature-deflection plot. Experimental studies are further extended to analyze the influence of geometrical parameters and structural boundary constraints on critical buckling temperature. Experimentation results reveal that the location of the heat source and resulting non-uniform ivtemperature field influences the thermal buckling strength significantly. Among three cases examined in experimentation for the position of heat source, minimal buckling strength is observed when the heater is located at the center of the panel while maximum buckling strength is observed when the heater is located at the forefront curved edge. It is also found that aspect ratio and structural boundary constraints play a major role in deciding the buckling strength of the panel. From the numerical studies carried out on non-uniformly heated panels, a relation known as magnification factor is established to evaluate the buckling strength of non-uniformly heated cylindrical panels knowing the buckling strength of uniformly heated panels. Among five cases investigated for the position of heat source, the highest magnification factor is observed for a panel with the heat source located at the forefront curved edge. It is observed that the free vibration mode shapes of the panel change significantly with increase in elevated temperature. The changes are observed in terms switching of modes with a significant change in modal indices. With the rise in temperature, nodal and anti-nodal positions of a particular free vibration mode shape are shifting towards the location where the intensity of the heat source is high and structural stiffness is low. It is found that for a stiffer panel, the buckling strength of the laminated and FG-CNT composite panels with temperature-dependent elastic properties is significantly lesser than that of the panels with temperature independent elastic properties. Panel with maximum area exposed to a peak temperature of particular non-uniform temperature fields shows lowest buckling strength. Functional grading of CNTs with more amount of CNTs located close to top and bottom of the panel (FG-X) results in higher buckling strength and free vibration frequencies compared to those panel with maximum CNTs distribution near the mid-plane. Free vibration frequencies of non-uniformly heated FG-CNT panel with temperature dependent properties is observed to decrease drastically with elevated temperature compared to the panel with temperature independent properties. Variation vin frequencies observed in a pre-stressed panel with temperature dependent and independent properties is more significant in stiffer panels. Irrespective of temperature dependent and independent properties, shifting of nodal and anti-nodal lines and change of modal indices are also observed at elevated temperature. Well-known and generally acknowledged optimization technique, particle swarm optimization is employed for the optimization of thermal buckling strength of laminated composite panels exposed to five different temperature fields. Two different optimization approach like single objective optimization approach and multiobjective optimization approach are employed. In single objective optimization, the panel is exposed known temperature field whereas, in multi-objective optimization, the panel is exposed to unknown temperature fields when in-service. It is found from the analysis that the variation in the optimum buckling strength of non-uniformly heated panels is more significant at lower curvature ratio. Whereas, variation in the optimum fiber orientation under different temperature fields is significant at higher curvature ratio. Multi-objective optimization approach has proved to be superior to that of single objective optimization approach when panels are exposed to the unpredictable thermal environment. Further, studies are carried out on optimization of both thermal buckling strength and fundamental free vibration frequency of heated panels using particle swarm optimization in conjunction with the artificial neural network. Multiobjective design index (MODI) has been derived for the panel considering buckling strength and fundamental frequency as objectives for optimization. It is found that MODI of the cylindrical panels under thermal load is complex and significantly influenced by the temperature fields, lamination scheme, in-plane boundary constraints, elevated temperature and geometric parameters. It is also observed that the MODI of the panel can be maximized by optimizing laminate orientations. Further, it is observed that panel with lamination scheme of (θ°/–θ°/θ°/–θ°)S gives higher value of MODI compared to other lamination schemes considered.