Free Vibration Analysis of Functionally Graded Beams

Free vibration analysis of functionally graded beams is carried out for various classical boundary conditions. Two separate finite element formulations, one based on Euler-Bernoulli beam theory and other based on Timoshenko beam theory are developed. Principle of virtual work is used to obtain the finite element system of equations. Numerical results are provided to demonstrate the effect of transverse shear on the natural frequencies and mode shapes for different length-to-thickness ratios and volume fraction exponents of functionally graded material (FGM) beams for the boundary conditions considered. It was observed that transverse shear significantly affects the fundamental frequency and mode shape for lower length to thickness ratios of FGM beams. Further, the effect was observed to be more prominent at higher modes for all the volume fraction exponents of FGM beam.Defence Science Journal, 2012, 62(3), pp.139-146, DOI:http://dx.doi.org/10.14429/dsj.62.132

Thermal Buckling and Free Vibration Analysis of Heated Functionally Graded Material Beams

The effect of temperature dependency of material properties on thermal buckling and free vibration of functionally graded material (FGM) beams is studied. The FGM beam is assumed to be at a uniform through thickness temperature, above the ambient temperature. Finite element system of equations based on the first order shear deformation theory is developed. FGM beam with axially immovable ends having the classical boundary conditions is analysed. An exhaustive set of numerical results, in terms of buckling temperatures and frequencies, is presented, considering the temperature independent and temperature dependent material properties. The buckling temperature and fundamental frequency obtained using the temperature independent material properties is higher than that obtained by using the temperature dependent material properties, for all the material distributions, geometrical parameters in terms of length to thickness ratios and the boundary conditions considered. It is also observed that the frequencies of the FGM beam will reduce with the increase in temperature. This observation is applicable for the higher modes of vibration also. The necessity of considering the temperature dependency of material properties in determining thermal buckling and vibration characteristics of FGM beams is clearly demonstrated.Defence Science Journal, 2013, 63(3), pp.315-322, DOI:http://dx.doi.org/10.14429/dsj.63.237

Delamination Buckling of Composite Conical Shells Under External Pressure

Airframe construction in conical form is the most desired shape of flight hardware due to their low drag profileand are located at the fore-end region of flight vehicles encountering high drag loads. Owing to their tailoringcapability, materials with orthotropic mechanical properties are preferred choice. Delamination defects formed inthem while manufacturing or when subjected to loads would unfavorably influence the mechanical performanceof the orthotropic airframe. In the current work, FE simulation of delamination which is embedded in orthotropiccone shaped shells under external pressure load is performed as per the method cited in published literature. A layer wise element based on shell theory has been used and the effect of delamination size and its through the thickness position on the mechanical performance of the cone shaped shell is investigated. Circumferential and rectangular shapes of defects have been simulated. The investigation is performed for metal and composite materials with 3 types of stacking sequences generally used in practical designs. Verification of the procedure is carried out by equating with the procedure cited in published studies on shells of thin orthotropic cylinders. The eigen value of the first mode is taken as the critical buckling factor under external pressure. The buckling factor of the delaminated cone is normalized with the buckling factor of the ideal cone. The normalized buckling factor is showed graphically with the normalised defect size. Global, as well as local buckling and also symmetric as well as asymmetric buckling shapes, are observed in the results of the simulation. Shift from global mode to local mode of buckling is also observed in certain cases. Drastic reduction in buckling capability with the local mode is observed when the defect location is close to the surface and more prominent for an outer surface case