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The present work aims at the determination of thermal buckling loads of various functionally graded material beams with both ends clamped. Thermal loading is applied by applying linear temperature distribution and nonlinear temperature distribution at steady state heat conduction condition, across the beam thickness. Temperature dependences of the material properties, considered in the formulation, make the present problem physically nonlinear. Also, the effect of limit thermal load at which the effective elastic modulus and/or thermal expansion coefficient become theoretically zero is considered. The mathematical formulation is based on Euler-Bernoulli beam theory. An energy based variational principle is employed to derive the governing equations as an eigenvalue problem. The solution of the governing equation is obtained using an iterative method. The validation of the present work is carried out with the available results in the literature and with the results generated by finite element software ANSYS. Four different functionally materials are considered, namely, stainless steel/silicon nitride, stainless steel/alumina, stainless steel/zirconia, and titanium alloy/zirconia. Comparative results are presented to show the effects of variations of volume fraction index, length-thickness ratio, and material constituents on nondimensional thermal buckling loads.

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Nonlinear free vibration analysis of clamped isotropic skew plates has been presented. The large amplitude of vibration is imparted statically by subjecting the plate under uniform transverse pressure. The mathematical formulation is based on the variational principle in which the displacement fields are assumed as a combination of orthogonal polynomial or transcendental functions, each satisfying the corresponding boundary conditions of the plate. The large amplitude dynamic problem is addressed by solving the corresponding static problem first and subsequently with the resultant static displacement field, the dynamic problem is formulated. The vibration frequencies are obtained from the solution of a standard eigenvalue problem. Entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique. Results of the reduced problem revealed excellent agreement with other studies and a typical comparison of the actual problem is also carried out successfully. Results are furnished in dimensionless amplitude-frequency plane, in the form of backbone curves, and pictorial representations of some vibration mode shapes are made.