A new triangular element based on higher order shear deformation theory for flexural vibration of composite plates

Abstract

<jats:p> A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis. </jats:p>