FE analysis of laminated composite plates using a higher order shear deformation theory with assumed strains

Abstract

A study on the finite element (FE) analysis of laminated composite plates is described in this paper. In order to investigate structural behavior of laminated composite plates, a four-node laminated plate element is newly developed by using a higher order shear deformation theory (HSDT). In particular, assumed natural strains are introduced in the present FE formulation to alleviate the locking phenomenon. Several numerical examples are carried out and its results are then compared with the existing reference solutions. It is found to be that the proposed FE is very effective to remove the locking phenomenon and produces reliable numerical solutions for most laminated composite plate structures.

On the Free Vibration Analysis of Laminated Composite and Sandwich Plates: A Layerwise Finite Element Formulation

“…In the literature, several two-dimensional theories and approaches have been used to study the behavior of composite sandwich structures. Starting by the simple classical laminated plate theory (CLPT), based on the Kirchhoff's assumptions, which does not includes the effect of the transverse shear deformation, the first-order shear deformation theory (FSDT), where the effect of the transverse shear deformation is considered (Reissner 1975, Whitney and Pagano 1970, Mindlin 1951, Yang et al 1966, but this theory gives a state of constant shear stresses through the plate thickness, and the higher-order shear deformation theories (HSDT) where a better representation of transverse shear effect can be obtained (Lo et al 1977, Manjunatha and Kant 1993, Reddy 1984, Lee and Kim 2013. Regarding the approaches used to model the behavior of composite structures, we distinguish the equivalent single layers (ESL) approach where all the laminate layers are referred to the same degrees-of-freedom (DOFs).…”

A MITC3+ element improved by edge-based smoothed strains for analyses of laminated composite plates using the higher-order shear deformation theory

“…The plate is discretized by various meshes N × N ×2 with N gradually increasing from 12, 16, 20, 24 to 28. The relative errors wc − wref c / wref c , in which wc and wref c are the normalized deflection at the plate center given by the smoothed finite elements and the 3D-Elasticity solution [4,30], respectively, versus the element sizes in log-log scale are presented in Fig. 16.…”

“…In contrast, the numerical methods can predict the behavior of arbitrary laminated composite plates in practice within acceptable tolerances. Nowadays, laminated composite plates have been largely analyzed by such numerical methods as the finite element methods (FEM) [23][24][25][26][27][28][29][30][31], meshless methods [27,32,33] and isogeometric methods [13,[34][35][36][37]. The recently developed meshless and isogeometric methods can represent high-order displacement approximations and then satisfy the C 1 -continuous requirement of the HSDT.…”

Bending and free vibration behaviors of composite plates using the C0-HSDT based four-node element with in-plane rotations

“…The geometry data of problem are given as follows: the aspect ratio a/b = 1 and length-to-thickness ratios a/h = 4, 10, 100 for the sinusoidal load case. The nondimensional displacements and stresses at the centroid of four layer 0 The results of the present method are compared with several other methods such as finite element method (FEM) based on HSDT by Reddy [8], the elasticity solution 3D proposed by Pagano [9], the C 0 -type higher order shear deformation theory by Loc et al [10], finite element method based on HSDT and node-based smoothed discrete shear gap by Chien et al [11], the a higher order shear deformation theory with assumed strains [12] as shown in Table 1. It is observed that the present results match very well with the exact solution [9].…”