Size-dependent analysis of porous multi-directional FG shell structures based on the modified couple stress theory using the unsymmetric finite element method.

The work proposes an efficient quadratic hexahedral solid element for size-dependent static and dynamic analyses of porous multi-directional functionally graded materials within the modified couple stress elasticity. The new element is constructed by following the process of the penalty unsymmetric finite element method in which the C1 continuity is enforced in weak sense. Furthermore, the independent rotation is introduced to approximate the continuum rotation and enhance the C0 continuous isoparametric interpolation for determining the test functions. In contrast, the trial functions are formulated based on the metric stress functions and the weighted residual method. Several benchmark tests involved with shell structures of different geometric forms and material distributions are evaluated, and the numerical results demonstrate that the new element can capture the size effect of porous multi-directional FG shells accurately. The findings also reveal that, as the material length scale parameter (MLSP) grows, the bending behavior is locked up gradually so that the out-plane vibration modes become more and more difficult to excite than in-plane vibration modes. Thus, not only the natural frequency but also the order of modes can be controlled by MLSP. [ABSTRACT FROM AUTHOR]