Application of a Modified Differential Quadrature Finite Element Method to Flexural Vibrations of Composite Laminates with Arbitrary Elastic Boundaries

This paper formulates a modified differential quadrature finite element method (DQFEM) by a combination of the standard DQFEM and the virtual boundary spring technique, which makes it easy to implement arbitrary elastic restraints by assigning reasonable values to the boundary spring stiffnesses. This new formulated method can offer a unified solution for flexural vibrations of composite laminates subjected to general elastic boundary combinations including all the classical cases. The influences of the number of Gauss-Lobatto nodes and the boundary spring stiffnesses on the convergence characteristics of natural frequencies are investigated, and some conclusions are drawn in terms of the minimum number of unilateral nodes required to generate convergent solutions and the optimal values of the boundary spring stiffnesses to simulate classical boundaries. Numerical examples are performed for composite laminates under various classical boundary conditions. Excellent accuracy, numerical stability, and reliability of the present method are demonstrated by comparisons with available exact and numerical solutions in open literatures. Additionally, for elastically constrained composite laminates, which are beyond the scope of most existing approaches, numerous new results obtained by the present method may serve as reference values for other research.

Automated summary

This paper presents a modified differential quadrature finite element method (DQFEM) that combines the standard DQFEM with the virtual boundary spring technique to easily implement arbitrary elastic restraints. The method provides a unified solution for flexural vibrations of composite laminates under general elastic boundary combinations. Numerical examples demonstrate the accuracy, stability, and reliability of the method, and the new results obtained for elastically constrained laminates can serve as reference values for future research.