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Abstract
On the basis of modified couple stress theory, the postbuckling behavior of the Euler-Bernoulli microscale FG beams is investigated by means of an exact solution method. The modified couple stress theory as a nonclassical continuum theory is capable of interpreting the size dependencies which become more significant at micro/nanoscales. The Von-Karman type nonlinear strain-displacement relationships are employed. The thermal effects are also incorporated into formulation. The governing equation of motion and the corresponding boundary conditions are derived using Hamilton’s principle. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A closed-form solution is obtained for the postbuckling deformation which is beyond the critical buckling load. To study the vibrations taking place in the vicinity of a buckled equilibrium position, the linear vibration problem is exactly solved around the first three buckled configurations. The natural frequencies of the lowest vibration modes around each of the first three buckled configurations are obtained. The influences of power-law exponent, boundary condition, length scale parameter, and thermal environment changes on the static deflection and free vibration frequencies are studied. A comparison is also made between the present results and those obtained via the classical beam theories.
Highlights
Since the first introduction by Japanese scientists in 1984, functionally graded materials (FGMs) have been under worldwide development during the past years
An exact solution is obtained for the thermal postbuckling behavior of the microscale functionally graded EulerBernoulli beams on the basis of modified couple stress theory
The critical temperature parameter values associated with the clamped-clamped support are the most amongst the three aforementioned end conditions which clarify the high stability of a beam with this type of boundary condition
Summary
Since the first introduction by Japanese scientists in 1984, functionally graded materials (FGMs) have been under worldwide development during the past years. Fallah and Aghdam [22] studied the large amplitude free vibration and postbuckling of FG beams rested on nonlinear elastic foundation and subjected to axial load by means of an analytical method based on the variational approach Their analysis is based upon the EBT assumptions together with the Von-Karman strain-displacement relations. There is a need for further study on their mechanical behavior To this aim, based on the modified couple stress theory (MCST) [37], Ke et al [38] investigated the nonlinear free vibration of the sizedependent FG Timoshenko microbeams. The discretized equations of motion are solved via the pseudoarclength continuation technique to obtain the frequency-response and force-response curves They studied the nonlinear size-dependent behavior of an electrically actuated MEMS resonator based on the MCST and the same numerical approach as in their previous works [47].
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