Reply to the comments by Thuc P. Vo on the article: “A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core”, by Anupam Chakrabarti, H.D. Chalak, Mohd. Ashraf Iqbal, Abdul Hamid Sheikh [Composite Structures 93 (2011) 271–279]

In the present work, a new higher-order zigzag theory is proposed for the analysis of laminated sandwich beams under static and free vibration conditions. Fourth-order in-plane and transverse displacement fields are chosen along with linear unit Heaviside step function. The present theory satisfies interlaminar transverse stress continuity conditions along with zero value at the top and bottom surface for transverse shear stresses. The proposed approach is also free from any kind of C-1 or penalty requirements. A three-noded one-dimensional finite element having eight degrees of freedom per node is used during analysis. The efficiency of the proposed model is carried out by comparing the present results with those available based on elasticity solutions and zigzag theories in the literature. New results are also reported in the present work, which will serve as a benchmark for future studies. The influence of boundary condition on the nature of stress distribution across the length of beam and frequencies of the beam with different end conditions is also carried out. A comparative study has also been carried out between symmetric and unsymmetric laminated sandwich beam.

Download Full-text

A New C0 2D Fe Model Based on Improved Higher Order Zigzag Theory for the Analysis of Soft Core Sandwich Plate

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2013-0024 ◽

2013 ◽

Vol 18 (2) ◽

pp. 395-423 ◽

Cited By ~ 3

Author(s):

R.P. Khandelwal ◽

A. Chakrabarti ◽

P. Bhargava

Keyword(s):

Shear Stress ◽

Displacement Field ◽

Transverse Shear ◽

Sandwich Plate ◽

Higher Order ◽

Least Square ◽

Soft Core ◽

Fe Model ◽

Transverse Shear Stress ◽

The Core

An efficient C0 continuous finite element (FE) model is developed based on a combined theory (refine higher order shear deformation theory (RHSDT) and least square error (LSE) method) for the static analysis of a soft core sandwich plate. In this (RHSDT) theory, the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zig-zag linearly varying displacement field with a different slope in each layer. The transverse displacement assumes to have a quadratic variation within the core and it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements. In order to calculate the accurate through thickness transverse stresses variation, the Least Square Error (LSE) method has been used at the post processing stage. The proposed combined model (RHSDT and LSE) is implemented to analyze the laminated composites and sandwich plates. Many new results are also presented which should be useful for future research.

Download Full-text