Free vibration of laminated beams and stiffened plates using a high-order element

Abstract

Free vibration analysis of laminated composite beams, plates and stiffened plates using the finite element method has been presented. To give due importance to the shear deformation in composite materials, a high-order element which considers the quadratic variation of shear strain along the thickness of the element has been developed. The element has been developed using the quadratic isoparametric shape functions. Therefore, it can accommodate curved boundaries. Moreover, the stiffener element can have an arbitrary planform and it need not pass through any nodal point. The stiffener element has been developed in such a fashion to make the mesh division free from the location of the stiffener. This is extremely advantageous for optimisation of the path of the stiffener in a stiffened plated structure, while it is not necessary to modify the mesh division whenever the stiffener path is modified. Two different shape functions — the eight-node Serendipity and the nine-node Lagrangian — have been employed and a comparison between their performances has been presented. Two schemes for the generation of mass matrix, namely the lumped mass scheme and the consistent mass scheme, have been developed. The elements have been implemented in the ASKA element library and they can be used along with any standard ASKA element.

Finite element modeling of stiffened piezolaminated plates and shells with piezoelectric layers for active vibration control

“…These stiffeners are usually placed along the major load carrying directions. However, the analysis of stiffened laminated plates and shell structure becomes more complicated than that of the non-stiffened structures, due to the shellstiffener interactions [1][2][3][4][5][6][7].…”

“…Mukherjee [6] studied the free vibration of laminated composite stiffened plates using quadratic finite elements derived based on higher order shear deformation with stiffeners capable of being oriented in any shape and plane. Mukherjee et al [7] studied active vibration control of piezolaminated stiffened plates.…”