A plate bending element based on a generalized laminate plate theory

Abstract

SUMMARYA plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions of the generalized plate theory and the 3D-elasticity theory. The element accounts for transverse shear deformation and layerwise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented. BACKGROUNDLaminated composite plates are often modelled using the classical laminate plate theory (CLPT) or the first-order shear deformation plate theory (FSDT). In both cases the laminate is treated as a single-layer plate with equivalent stiffnesses, and the displacements are assumed to vary through the thickness according to a single expression (see Reddy' ), not allowing for possible discontinuities in strains at an interface of dissimilar material layers.Recently, Reddy' presented a general laminate plate theory that allows layer-wise representation of inplane displacements, and an improved response of inplane and transverse shear deformations is predicted. Similar but different theories have appeared in the l i t e r a t~r e .~-~ In the generalized laminate plate theory (GLPT) the equations of three-dimensional elasticity are reduced to differential equations in terms of unknown functions in two dimensions by assuming layer-wise approximation of the displacements through the thickness. Consequently, the strains are different in different layers. Exact analytical solutions of the theory were developed by the authors',* to evaluate the accuracy of the theory compared to the 3D-elasticity theory. The results indicated that the generalized laminate plate theory allows accurate determination of interlaminar stresses.The present study deals with the finite-element formulation of the theory and its application to laminated composite plates. In the interest of brevity only the main equations of the theory are reviewed and the major steps of the formulation are presented. The accuracy of the numerical

Bending of Laminated Composite Plates in Layerwise Theory

“…Additionally, the approximation of the displacement through the thickness of the plate is conducted with one-dimensional interpolation functions of coordinate perpendicular to the plane of the layer. Mathematical model is based on the Generalized Laminated Plate Theory (GLPT) developed by Reddy and Reddy et al [10][11][12][13][14].…”

“…Closed analytical solution of bending equations in LW theory is done by using the double trigonometric series of the simple supported rectangular plate with the angle of the layers orientation 0 and 90 , see Refs. [10,18,[22][23][24][25][26].…”

“…These are the reasons why the applied Finite Element Method (FEM) as one of the most used numerical methods was used, see Refs. [1,[10][11][12][13][14]21]. The idea of the FEM is a representation of the domain as the sets of appropriate simple geometrical shapes called the finite elements.…”

Application of layered finite elements in the numerical analysis of laminated composite and sandwich structures with delaminations

“…Reddy-eva opšta laminatna teorija plo a (GLPT) [28], koju su kasnije unapredili Barbero i Reddy [29], postala je osnova za razvoj familije slojevitih kona nih elemenata koji imaju mogu nost da opišu nezavisno kretanje svakog sloja posebno. etkovi i Vuksanovi su razvili analiti ko i numeri ko slojevito rešenje opšte laminatne teorije plo a za analizu laminatnih kompozitnih i sendvi -plo a bez ošte enja [30] i verifikovali su model primenom postoje ih eksperimentalnih i numeri kih rezultata [31][32][33][34].…”

Direct Assessment of Interlaminar Stresses in Composite Multilayered Plates Using a Layer-Wise Mixed Finite Element Model

“…(6)) could be imposed in a procedure similar to standard assembly techniques through the thickness involved in a finite element implementation, such as Refs. [7,8]. However, the use of Lagrange multipliers is preferred herein in order to directly assess the interlaminar transverse stresses.…”