An unsymmetric FRC laminate C° finite element model with 12 degrees of freedom per node

Abstract

A C° finite element formulation for flexure‐membrane coupling behaviour of an unsymmetrically laminated plate based on a higher‐order displacement model and three‐dimensional state of stress and strain is presented. This theory incorporates the more realistic non‐linear variation of displacements through the plate thickness, thus eliminating the use of a shear correction coefficient. The discrete element chosen is a nine‐noded quadrilateral with 12 degrees of freedom per node. The computer program developed incorporates the realistic prediction of interlaminar stresses from equilibrium equations. The present solution for deflection and stresses is compared with those obtained using three‐dimensional elasticity theory, another higher‐order shear deformation theory and Mindlin theory. In addition, numerical results for unsymmetric sandwich plates are presented for future reference.

Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory

“…In addition, the transverse normal strain may vary nonlinearly through the plate thickness. The displacement field which satisfies the above criteria may be assumed in the form [23] …”

“…This theory considers three-dimensional Hooke's law, incorporates the effect of transverse normal strain in addition to transverse shear deformations. Pandya and Kant [18][19][20][21][22], Kant and Manjunatha [23,24] and Manjunatha and Kant [25] have extended this theory and presented C 0 finite element formulations and solutions for the stress analysis of symmetric and unsymmetric laminated composite and sandwich plates. Rohwer [26] made a comparative study of various higher order theories for the bending analysis of multilayer composite plates.…”

Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory

“…In addition, the transverse normal strain may vary nonlinearly through the plate thickness. The displacement ®eld which satis®es the above criteria may be assumed in the form [30] …”

“…This theory considers three-dimensional Hooke's law, incorporates the eect of transverse normal strain in addition to transverse shear deformations. Symmetric and unsymmetric composite and sandwich plates Pandya and Kant [25±29], Kant and Manjunatha [30,31] and Manjunatha and Kant [32] have extended this theory and presented C°®nite element formulations and solutions for the stress analysis of symmetric and unsymmetric laminated composite and sandwich plates. Later Mallikarjuna [33], Mallikarjuna and Kant [34] and Kant and Mallikarjuna [35,36] presented a simple C°®nite element formulation and solutions using a set of higher order displacement models for the free vibration analysis of general laminated composite and sandwich plate problems.…”

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

“…A review on the various methods used in the estimation of transverse and inter-laminar stresses for laminated composite plates and shell including both analytical and numerical methods was provided by Kant and Swaminathan [9]. Kant and Manjunatha [10] provided the FE based on HSDT having twelve degrees of freedom per node. They presented three-dimensional stress and strain states to investigate the flexure-membrane coupling behavior of unsymmetrical laminated plate.…”