Layerwise Finite Element Formulation Research Articles

Layerwise Laminate Analysis of Functionally Graded Piezoelectric Bimorph Beams

A layerwise finite element formulation developed for piezoelectric materials is used to investigate the displacement and stress response of a functionally graded piezoelectric bimorph actuator. The formulation is based on the principles of linear thermopiezoelectricity and accounts for the coupled mechanical, electrical, and thermal responses of piezoelectric materials. The layerwise laminate theory is implemented into a linear beam element in order to provide a more accurate representation of the transverse and shear effects that are induced by the increased inhomogeneities introduced through-the-thickness by the functionally graded materials. The accuracy of the formulation is verified with previously published experimental results for a piezoelectric bimorph actuator. Additional studies are conducted to analyze the impact of electric and thermal loads on the deflections and stresses in a bimorph actuator. Results of the study help to demonstrate the capability of the layerwise theory to provide a more complete representation of the through-the-thickness effects that are no longer negligible even in thin piezoelectric beams. In addition, the effects of varying piezoelectric properties through-the-thickness of the beam are shown to provide additional benefits in minimizing the induced deformations and stresses.

Bending Analysis of Stiffened Laminated Plates

Stiffeners are commonly attached to composite laminates to achieve higher stiffness/weight and strength/weight ratios. A layer-wise finite element formulation is developed for the bending analysis of stiffened laminated plates. The laminated plate is discretized into layers in the thickness direction and then the degenerated shell elements are employed to model each layer. The stiffener is modeled using a general 3-D beam element. Interlayer continuity relations are established for all the layers in the thickness direction. The primary advantage of the proposed finite element model lies in its application to both thin and thick laminated plates. Extensive numerical examples are presented for non-stiffened isotropic plates, non-stiffened laminates, stiffened isotropic and laminated plates. Parametric studies are conducted with different aspect ratios, plate width to thickness ratios, ply orientations, and number of layers. The results agree well with the ones reported in the literature.

Buckling behavior of stiffened laminated plates

A layerwise (zigzag) finite element formulation is developed for the buckling analysis of stiffened laminated plates. The laminated plate is discretized into layers along the thickness direction. Each layer of the laminated plate is modeled by the degenerated shell elements, and the stiffener is modeled by the general 3-D beam elements. Layers are stacked together according to the interlayer continuity. In-plane displacements are considered in the derivation of geometric stiffness matrix. The advantage of the proposed model is its applicability to both thin and thick laminated plates. The significance of this study lies in the disclosure of the interaction between the lateral buckling of the stiffener and the buckling of the laminate. The inverse iteration method is adopted to extract the lowest eigenvalue corresponding to buckling. Parametric and comparative studies are conducted for different plate aspect ratios, plate thickness to length ratios, degrees of layer orthotropy, ply orientations, and stiffener depth to plate thickness ratios.