Buckling Analysis of Laminated Composite Plate Using FE Method

Abstract

This study investigates the use of finite element analysis to composite plate structures. The major purpose of this research is to use FEA techniques to evaluate the buckling behavior of composite plates. FEA simulation and CAD modeling are both possible with the help of ANSYS APDL. It has been determined that carbon composite is a material and that the individual plates may take on either a hexahedral or a quadrilateral geometry. The buckling load of the plate is determined by applying the structural loads on it. The FEA is performed for all permutations, which include changing the h/b ratio from 0.08 to 0.16 and then from 0.16 to 0.24. The buckling load is determined by the eigenvalues and is different for each h/b ratio. According to FEA predictions, increasing the h/b ratio increases the buckling load. The findings of this study suggest that finite element analysis (FEA) may be utilized to enhance the design of composite structures subjected to a wide range of loading scenarios.

Introduction

I. INTRODUCTION

Composite plates, made from bonded materials like fibers or laminates, are multi-layered structures that are robust and lightweight. The performance of a composite plate may be optimized for a given application by selecting the materials used in the plate depending on their desired attributes, like strength, stiffness, & durability[1].

Composite plates have several applications; only some of them include the shipping, vehicle, aircraft, and sports equipment industries. Aerospace manufacturers often employ composite plates for fuselage and wing construction among other structural uses. Their strength and low weight make them ideal for usage in car body panels, hoods, and other structural components. Boat hulls, decks, and other marine parts that are often exposed to salt water often make use of composite plates due to their durability and corrosion resistance. 

The Benefits of Composites Included [2]:

1. Compared to its individual fiber/particle and matrix, the strength to weight ratio of composite material is very high.
2. In comparison to its individual parts, composite materials have a high degree of stiffness.
3. Due to the excellent damping qualities of composite materials, vibration amplitude has become lessened as compared to conventional materials.
4. Increased wear resistance lengthens the life of the composite construction.
5. By adding graphite fibers, for instance, composite materials' electrical conductivity can be improved.
6. The design of composite materials can be flexible.
7. The poor thermal conductivity of many composite materials makes them advantageous for applications.
8. Compared to other materials, composites are frequently more enduring and demand fewer maintenance tasks over time.  

II. LITERATURE REVIEW

Teter et al. [2016] analyzed the vibrational characteristics of composite materials made up of various lignocelluloses, while Savin et al. (2016) performed tests to determine the rotor's modal analysis. They discovered how material structures affected natural modes[3].

Eslami et al. [2017] ‘s big rectangular composite plates' mode forms, natural frequencies, and buckling behaviour were predicted using FEA and compared to results from a Rayleigh-Ritz approato of modelling vibrations. Clamping and simple support were used as boundary conditions for the plate. It was determined that as the aspect ratio drops below 0.25, inherent frequencies of plate convergence[4].

Shrigandhi et al. [2011] used FEA to perform a modal study on composite sandwich panels. Utilizing finite element & harmonic balance techniques, the researcher analyzed the vibrations of a composite laminated plate. In comparison to the h-version of identical finite element techniques, the hierarchical finite element method needs a much less number of degrees of freedom[5].

Wang et al. [2020] Effects of free vibration of laminated and sandwich composite laminated plates were investigated, with a focus on the role of higher-order facet shell components. As a result of their investigation, they concluded that, for composite laminates, there is little to choose between First Order Shear Deformation Theory and Higher Order Shear Deformation Theory. On the other hand, sandwich panels have a significant frequency differential that rises with laminate thickness [6].

Huihui et al. [2019] carried out research to determine the vibrational characteristics of woven fiber laminated composite plates when subjected to hygrothermal conditions. The governing equation employed in this study was FSDT. Experiments were performed with both freely supported and clamped-supported boundaries. Both experimental and analytical studies demonstrated that 4 sides clamped (CCCC) boundary conditions had greater vibration frequencies than simply supported owing to clamping impacts & improved elastic rigidities limitations [7].

Zhaoji et al. [2022] performed free and forced vibration experiments utilizing experimental setup to analyze the vibrational properties of a carbon fiber-reinforced polymer composite containing numerous carbon nanotubes. It was determined that after incorporating carbon nanotubes into a composite, a decreased natural frequency was detected. On the other hand, the damping properties of composite improved following the inclusion of carbon nanotubes [8].

Jiang et. al. [2018] Utilized FEM (finite element method) software ANSYS, they determined the natural frequencies & mode shapes of laminated cantilever boxed beams exposed to both uniform or asymmetric stiffness at their peripheries, as seen in Fig. 2.2 [9].

Sun et al. [2022] employed finite element analysis to find out how a composite laminated plate vibrates. The greater the concentration of fibers in the plate's middle part, the greater the buckling stress and natural frequencies. If more fibers are focused on the plate's exterior, critical buckling stress will rise [10].

Chang et al. [2020] Using the finite difference approach, we calculated the vibration characteristics of both symmetric and angle-ply laminated composite plates. It was determined that the orientation of fibers in an angle-ply laminated plate had a significant influence on the natural frequencies of the plate. Nevertheless, the largest natural frequency response was found when fibers were oriented at 45 degrees [11].

III. OBJECTIVE

The purpose of this study is to use Finite Element Method to Conduct structural analysis and assess the Buckling behaviour of composite plates. The CAD modelling and FEA simulation are conducted using ANSYS APDL. From the FEA analysis, the eigenvalue buckling load is determined for different combinations of h/b ratio. The h/b ratio taken for the analysis is .08, .16, and .24.

IV. METHODOLOGY

 This section discusses the comprehensive processes involved

A. Modelling of Plate

The methodology involves modeling of the plate with an area tool. The model of the plate is developed using key points, and lines and added to form area. In total, 10 layers are created with 5mm thickness each. The developed model of the composite plate is shown in Figure 4.

D. Loads and Boundary Conditions

The structural loads are applied on a plate to determine the buckling load. The initial load of 1N is applied on the top right and bottom right key point of the composite plate. The left line of the composite plate is applied with fixed support. The simulation is executed once loads and boundaries are applied to the structure. In the process, the matrix is created and assembled to form a global stiffness matrix.

E. Solution

Upon specifying the loads and boundary conditions, the simulation is executed by selecting the "solve" icon. During the process of solving, the matrix of stiffness for the element is formulated and the outcomes are interpolated for the complete length of the element's edge using nodal outcomes.

V. RESULTS AND DISCUSSION

The present study involves the utilization of carbon composite material for conducting structural analysis to determine the xy shear stress, 1st principal stress, and xy shear elastic strain. The analysis is carried out for varying h/b ratios of .08, .16, and .24.

A. h/b Ratio of .08

A structural investigation was conducted on a rectangular plate constructed from carbon composite material, featuring a h/b ratio of 0.08. The plot of shear stress in the xy direction is derived through FEA of a rectangular plate. The maximum xy shear stress is observed to occur at the corners of the plate, where a magnitude of 4.33 MPa is obtained.

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Conclusion

Finite Element Analysis (FEA) is a popular choice for analyzing composite plates because it provides precise and specific data on how composite structures act when subjected to varying loads. It is challenging to study complicated geometries and material characteristics using conventional analytical techniques, but FEA makes it possible to do so. When the h/b ratio was raised, the findings indicated that the plate deformation also increased. Similar to the bending moment, the buckling load rose as the h/b ratio became bigger, with the greatest buckling load being found at a h/b ratio of.24. Where buckling behavior is critical, such as in the aerospace and automotive sectors, this study\'s results may be valuable in the design and production of composite plates for these and other applications. Even though this study examined the buckling Behavior of a single composite material, it is crucial to highlight that future research might investigate the buckling behavior of many composite materials and plate geometries.

References

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Copyright

Copyright © 2023 Kapil Raje, Jyoti Vimal, Vedansh Chaturvedi. 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.