Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect.

Michele Bacciocchi,Angelo Marcello Tarantino

doi:10.3390/ma14071771

Abstract

The aim of the paper is the development of a third-order theory for laminated composite plates that is able to accurately investigate their bending behavior in terms of displacements and stresses. The starting point is given by the corresponding Reddy’s Third-order Shear Deformation Theory (TSDT). This model is then generalized to consider simultaneously the Classical Laminated Plate Theory (CLPT), as well as the First-order Shear Deformation Theory (FSDT). The constitutive laws are modified according to the principles of the nonlocal strain gradient approach. The fundamental equations are solved analytically by means of the Navier methodology taking into account cross-ply and angle-ply lamination schemes. The numerical applications are presented to highlight the nonlocal effects on static behavior.

Highlights

Higher-order plates theories for laminates have been introduced in the last decades to avoid some issues related to the use of lower-order and simpler approaches, such as the Classical Laminated Plate Theory (CLPT) and First-order Shear Deformation Theory (FSDT) [1,2]
Due to the general features of the theoretical approach, the solutions are presented for different nonlocal theories, which are CLPT, FSDT and Third-order Shear Deformation Theory (TSDT), setting properly the values of c1 and F
The theories have been modified to include the strain gradient effect, in order to take into account nonlocal contributions in the evaluation of stresses

Summary

Introduction

Higher-order plates theories for laminates have been introduced in the last decades to avoid some issues related to the use of lower-order and simpler approaches, such as the Classical Laminated Plate Theory (CLPT) and First-order Shear Deformation Theory (FSDT) [1,2]. Higher-order approaches have been justified by the use of more and more advanced materials [14,15,16,17] and the need of innovative configurations for the optimal design of structures [18,19]. Their introduction could be essential when these innovative constituents are included in the stacking sequences of multilayered or sandwich structures [20,21,22,23,24,25]. Accurate and effective higher-order structural models based on a unified formulation have been presented

Objectives

Methods

Results

Conclusion