FREE VIBRATION ANALYSIS OF CURVILINEARLY STIFFENED KIRCHHOFF-MINDLIN PLATES

Compared with traditional stiffened plates, curvilinearly stiffened plates can deliver the mechanical properties of materials more adequately. In mechanical analysis of stiffened thick plates, Reissner-Mindlin theory is usually adopted. However, difficulties are encountered in connection with shear locking when the plate thickness approaches zero. In order to avoid the above problem, the discrete Kirchhoff-Mindlin theory was investigated by employing the assumption of shear strain field. An efficient finite element approach for free vibration analysis of curvlinearly stiffened KirchhoffMindlin plates is presented in this paper. The discrete Kirchhoff-Mindlin triangular (DKMT) element and the Timoshenko curved beam element are employed for modeling the plate and the stiffeners, respectively. The finite element equation is established through the displacement interpolation function of plate and the displacement compatibility conditions at the plate-stiffener interfaces. In order to verify the efficiency and accuracy of the present method, linearly stiffened thin plate and curvilinearly stiffened thin and thick plates are used as numerical examples. The reasonable finite element mesh density is selected by convergence and accuracy analysis. The first 20 natural frequencies of the linearly stiffened plate are in good agreement with the literature. In the examples of the curvilinearly stiffened plate, the number of plate elements satisfying the convergence condition is 2469, while the number in Nastran model is 6243. The maximum error of the natural frequency between the present method and Nastran is 3.4%. Results show that present approach can guarantee the accuracy of calculation with less number of elements. The present method can be applied to the free vibration analysis of both stiffened thin and thick plates.