On the deformation of laminated composite and sandwich curved beams

Pravin V Avhad,Atteshamuddin S Sayyad

doi:10.1515/cls-2022-0001

Pravin V Avhad, Atteshamuddin S Sayyad

Open Access

https://doi.org/10.1515/cls-2022-0001

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Abstract

Abstract Plenty of research articles are available on the static deformation analysis of laminated straight beams using refined shear deformation theories. However, research on the deformation of laminated curved beams with simply supported boundary conditions is limited and needs more attention nowadays. With this objective, the present study deals with the static analysis of laminated composite and sandwich beams curved in elevation using a new quasi-3D polynomial type beam theory. The theory considers the effects of both transverse shear and normal strains, i.e. thickness stretching effects. In the present theory, axial displacement has expanded up to the fifth-order polynomial in terms of thickness coordinates to effectively account for the effects of curvature and deformations. The present theory satisfies the zero traction boundary condition on the top and bottom surfaces of the beam. Governing differential equations and associated boundary conditions are established by using the Principal of virtual work. Navier’s solution technique is used to obtain displacements and stresses for simply supported beams curved in elevation and subjected to uniformly distributed load. The present results can be benefited to the upcoming researchers.

Highlights

Laminated composite curved beams/arches are widely used in aerospace, automobile, ships, civil and mechanical industries due to their superior properties such as highReddy [6] has developed a well-known third order shear deformation theory for the analysis of laminated composite beams which is further extended by Khdeir and Reddy [7, 8] for the analysis of cross-ply laminated beams/arches
Axial displacement has expanded up to the fifth-order polynomial in terms of thickness coordinates to effectively account for the effects of curvature and deformations
Li et al [11] have studied the free vibration analysis of laminated composite beams of different boundary conditions using various higher-order beam theories and spectral finite element method which is used by Nanda and Kapuria [12] for the wave propagation analysis of laminated composite curved beams

Summary

Introduction

Laminated composite curved beams/arches are widely used in aerospace, automobile, ships, civil and mechanical industries due to their superior properties such as high. Zenkour [17] has developed a new shear and normal deformation theory for the static analysis of crossply laminated composite and sandwich beams. Kurtaran [27] applied a differential quadrature method for the static and transient analysis of functionally graded curved beams using first order shear deformation theory. Matsunaga [28] has investigated the displacements and stresses of the laminated and sandwich curved beams under mechanical/thermal loading by using higher order theory. Marur and Kant [33] have analyzed the static behaviour of laminated arches using transverse shear and normal deformation theory Sayyad and his co-authors’ [34,35,36,37,38] have presented various polynomial, and non-polynomial type beam theories for the static, vibration, and buckling analysis of isotropic, functionally graded, laminated, and sandwich beams. Carrera et al [46, 47] have developed a new finite element for the analysis of metallic and composite plates and shells

Scientific soundness of the topic

Mathematical formulation of the present theory for curved beam

The Navier solution

Illustrative problems

Conclusions

Present