Elastic Buckling of Composite Laminated Plates: A Numerical Investigation

Abstract

This paper presents a numerical method using ANSYS to estimate the buckling loads of composite plates. Our approach employs an element based on FSDT that considers out-of-plane shear deformation. We used an Eight node SHELL281 element that is well-suited for analyzing plate and shell structures. The ANSYS results for buckling loads of isotropic and orthotropic layered laminates are in good agreement with other theories from the literature. In this study, we investigated uniaxial and biaxial buckling of the plates and also considered the degree of orthotropy to study its impact on the plates\' buckling.

Introduction

I. INTRODUCTION

Researchers have extensively studied the load-carrying capacity of fiber-reinforced composites in the form of relatively thick plates, considering various loading and boundary conditions to prevent buckling. The following is a list of researchers who have investigated the elastic buckling of laminated composite plates.

Jones [1] investigated the behavior of composite laminated plates, including both macro and micromechanical behavior, and analyzed the plates. Reddy [2] presented different shear deformation theories for composite laminated plates and their finite element formulation, while also analyzing them. Kaw [3] introduced composite materials and analyzed their macro and micromechanical behavior, including failure, analysis, and design of laminates. Gibson [4] studied fiber-reinforced composite laminate, analyzing hygrothermal effects, interlaminate stresses, laminate strength analysis, deflection and buckling of laminates, and selection of laminate design. Ferreira et al. [5] used radial basis function to analyze the static deformations of composite beams and plates. Reddy and Phan [6] studied higher-order shear deformation theory and its application to stability and vibration of composite laminated plates. Kant and Swaminathan [7] presented an analytical solution for composite plates, including the effect of transverse shear deformation, transverse normal strain/stress, and a nonlinear variation of in-plane displacements with respect to the thickness coordinates. Noor et al. [8] used numerical simulations to study the buckling and post-buckling responses and failure initiation of flat, unstiffened composite panels. Reddy and Barbero [9] developed a plate bending element based on the generalized laminate plate theory and presented a method for computing interlaminar stresses. Hsuan and Horng [10] used a sequential linear programming method to maximize the buckling resistance of symmetrically laminated plates with a given material system and subjected to uniaxial compression. Matsunaga [11] analyzed the natural frequencies and buckling stresses of cross-ply laminated composite plates, considering the effects of shear deformation, thickness change, and rotatory inertia. Bert and Devarakonda [12] presented a solution for the buckling of a rectangular plate subjected to a half-sine load distribution on two opposite sides. Akavci et al. [13] studied laminated plates on an elastic foundation, analyzing the bending deflections of symmetric cross-ply laminates. Panda and Ramchandra [14] studied the buckling and post-buckling behavior of simply supported composite plates, including the effect of shear deformation on the buckling load. Khdeir [15] developed an exact solution to the buckling of antisymmetric angle-ply laminated plates, and Shukla et al. [16] estimated critical or buckling loads of laminated composite rectangular plates under in-plane loading. The study by Nemeth and Nemith and Weaver [17] presented non-dimensional parameters and equations that govern the buckling behavior of rectangular symmetrically laminated plates. These equations can be applied to plates made of various structural materials in a general and comprehensive way to represent their buckling resistance. York [18] focused on the benchmark configuration of fully extensionally isotropic laminated plates with matching elastic properties in both extension and bending, as well as some special cases. Ren and Tong [19] reviewed previous research on the elastic buckling of rectangular plates with different boundary conditions and simulated the realistic load and restraining conditions of web plates in I-girders. They analyzed the buckling load of a large number of models under patch load using ANSYS and proposed formulas to predict the elastic buckling coefficients of the webs in I-girders. Their formulas accurately considered the rotational restraints provided by the flanges on the web plates.

Chacon et al. [20] proposed a mechanism solution to reproduce the ultimate load capacity of steel girders under patch loading, particularly for steel plate girders with closely spaced transverse stiffening. The authors presented the ultimate load capacity of the girder under patch loading in this paper and a companion paper. Qiao and Shan [21] calculated the local buckling load for fiber-reinforced plastic composite structural shapes. They analyzed the local buckling of rectangular orthotropic composite plates with various boundary conditions and obtained explicit solutions for plate local buckling coefficients in terms of rotational restraint stiffness using a variational formulation of the Ritz method. Ragheb [22] presented an analytical stability model for the local buckling of pultruded fiber-reinforced polymer (FRP) structural shapes under eccentric compression. The model considered each shape as a group of orthotropic plates linked together, and the differential equations that describe the buckling behavior of each plate were solved using Levy's solution. The model was used to investigate the effect of the main parameters governing the local buckling behavior of such shapes. Graciano [23] proposed a methodology to determine buckling coefficients for longitudinally stiffened plate girders under partial edge loading or concentrated loads. They found the optimum parameters that govern the transition from a global buckling mode to a more local buckling mode after an extensive parametric analysis. The results showed that the location and relative flexural/torsional rigidity of the stiffener were relevant parameters that governed the final buckling shape, and the authors presented an expression for the buckling coefficient used to determine the critical buckling load for longitudinally stiffened girder webs. Chacon et al. [24] analyzed hybrid girders under patch loading in detail, focusing on longitudinally stiffened steel girders with transverse stiffening plates.

II. FINITE ELEMENT ANALYSIS USING ANSYS
The research utilized an Eight node SHELL281 element, which is well-suited for analysing plate and shell structures due to its six degrees of freedom at each node as shown in Figure 1. Additionally, this element can be employed for modelling laminated composite shells and sandwich constructions that have layered applications. The software program ANSYS, which employs the Mindlin-Reissner theory, specifically the First Order Shear Deformation Theory, was used to model SHELL281. The ANSYS student version was utilized in the investigation.

Conclusion

The aim of this paper is to introduce a numerical method for estimating buckling loads of composite plates using ANSYS. The FSDT element is used in this method considers out-of-plane shear deformation. The following are the conclusions drawn from this study. For uniaxial compression ((N ) ?_xx ), plate with aspect ratio (a/b) = 1 that is (square plate) having less buckling resistance than for aspect ratio 0.4. With an aspect ratio of 1.4, the resistance to buckling is almost equivalent to that of a square plate. This is because the plate\'s dimensions are planar, and the load applied is in the X-direction. Therefore, when using a square plate or a plate with an aspect ratio of 1.4, the plate does not provide as much resistance in the length direction and buckles at a lower load. By observing different buckling loads for isotropic plates with aspect ratios of 5, 10, and 100, it can be concluded that the thickness of the plate provides stiffness or resistance against buckling. In this study, we conducted a buckling analysis of a composite plate with simply supported boundary conditions under uniaxial compression. The composite plate was examined at various aspect ratios using FSDT. Our findings suggest that the aspect ratio has an impact on the buckling of the plate, which is influenced by the stiffness provided by the plate\'s thickness. We investigated the influence of the degree of orthotropy on the buckling of a composite plate made up of orthotropic material with different properties in the longitudinal and transverse directions. The results of this study indicate that although the material properties in the X and Y directions are different, the plate exhibits very high stiffness against buckling. Additionally, the E1/E2 ratio of the material is such that E1 is always greater than E2, providing greater resistance when an applied load is in the X-direction (i.e., the longitudinal direction).

References

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Copyright

Copyright © 2023 Sandeep Shiyekar, Apurva Patil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.