S.A.M. Ghannadpour and H.R. Ovesy
The purpose of this paper is to develop and apply an exact finite strip (F‐a FSM) for the buckling and initial post‐buckling analyses of box section struts.
Abstract
Purpose
The purpose of this paper is to develop and apply an exact finite strip (F‐a FSM) for the buckling and initial post‐buckling analyses of box section struts.
Design/methodology/approach
The Von‐Karman's equilibrium equation is solved exactly to obtain the buckling loads and deflection modes for the struts. The investigation is then extended to an initial post‐buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. Through the solution of the Von‐Karman's compatibility equation, the in‐plane displacement functions are developed in terms of the unknown coefficient. These in‐plane and out‐of‐plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient.
Findings
The F‐a FSM is applied to analyze the buckling and initial post‐buckling behavior of some representative box sections for which the results were also obtained through the application of a semi‐energy finite strip method (S‐e FSM). For a given degree of accuracy in the results, however, the F‐a FSM analysis requires less computational effort.
Research limitations/implications
In the present F‐a FSM, only one of the calculated deflection modes is used for the initial post‐buckling study.
Practical implications
A very useful and computationally economical methodology is developed for the initial design of struts which encounter post‐buckling.
Originality/value
The originality of the paper is the fact that by incorporating a rigorous buckling solution into the Von‐Karman's compatibility equation, and solving it, a fairly efficient method for post‐buckling stiffness calculation is achieved.
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Hamid Reza Ovesy, Ali Gharibi and Reza Khaki
This study aims to develop a new correlation method for prediction of in-flight wings deflections by integration of the experimental ground tests with computational fluid dynamics…
Abstract
Purpose
This study aims to develop a new correlation method for prediction of in-flight wings deflections by integration of the experimental ground tests with computational fluid dynamics (CFD) analysis.
Design/methodology/approach
The ground test results are implemented in the curve fitting process to determine deflections at 66 specific points (SPs) on the front and rear wing torque box. By using the obtained deflections and the corresponding applied loads, an experimental deflection equation (EDE) for each point is established through the Castigliano’s theorem. The CFD aerodynamic loads of typical aircraft, which have been obtained earlier by the authors, are once again used in the current research. The total applied loads to each part are achieved via summation of inertia and aerodynamic loads. The obtained loads are transformed to the equivalent concentrated loads at the SPs. By substituting the concentrated load values in the EDEs, the SPs deflections are achieved for mentioned flight conditions. The resulted deflections and the corresponding input flight parameters, i.e. M and α, are incorporated into a linear regression method for development of the appropriate in-flight deflection equations (IFDEs). The validity of IFDEs is approved by comparing IFDEs’ deflections with the corresponding ones calculated through EDEs for different flight conditions.
Findings
As an alternative approach to the fairly expensive flight tests, the IFDEs can be used to predict the in-flight wing deflections with comparable degree of accuracy.
Originality/value
Prediction of actual wing deflections distributions without flight tests execution at any given flight condition.
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Kamal Kishore Joshi and Vishesh Ranjan Kar
The purpose of this study is the comprehensive numerical assessment of multidirectional (1D/2D/3D) functionally graded composite panel structures with different material gradation…
Abstract
Purpose
The purpose of this study is the comprehensive numerical assessment of multidirectional (1D/2D/3D) functionally graded composite panel structures with different material gradation patterns and degrees of material heterogeneity. Here, deformation characteristics are obtained under different loading and support conditions.
Design/methodology/approach
The finite element solutions of multidirectional functionally graded composite panels subjected to uniform and sinusoidal transverse loads are presented under different support conditions. Here, different functionally graded composites, such as unidirectional (1D) and multidirectional (2D/3D), are considered by distributing constituent materials in one, two and three directions, respectively, using single and multivariable power-law functions. A constitutive model with fully spatial-dependent elastic stiffness is developed, whereas the kinematics of the present structure is defined using equivalent single-layer higher-order theory. The weak form, based on the principle of virtual work, is established and solved consequently using isoparametric finite element approximations via quadrilateral Lagrangian elements.
Findings
The appropriate mesh-refinement process is carried out to achieve the mesh convergence; whereas, the correctness of proposed heterogeneous model is confirmed through a verification test. The comprehensive numerical assessment of multidirectional functionally graded panels under various loading and support conditions depicts the importance of degree of material heterogeneity with different gradation patterns and volume-fraction exponents.
Originality/value
A comprehensive analysis on the deformation behaviour of 1D-functionally graded materials (FGMs) (X-FGM, Y-FGM and Z-FGM), 2D-FGMs (XY-FGM, YZ-FGM and XZ-FGM) and 3D-FGM composite panels FGM structures is presented. Multifaceted heterogeneous FGMs are modelled by varying constituent materials in one, two and three directions, using power-law functions. The constitutive model of multi-directional FGM is developed using fully spatial-dependent elastic matrix and higher-order kinematics. Isoparametric 2D finite element formulation is adopted using quadrilateral Lagrangian elements to model 1D/2D/3D-FGM structures and to obtain their deflection responses under different loading and support conditions.
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Tayyeb Pourreza, Ali Alijani, Vahid A. Maleki and Admin Kazemi
The study explores frequency curves and natural frequencies as functions of crack length, crack angle, magnetic field strength and small size effects under the three boundary…
Abstract
Purpose
The study explores frequency curves and natural frequencies as functions of crack length, crack angle, magnetic field strength and small size effects under the three boundary conditions.
Design/methodology/approach
This study investigates the nonlinear dynamics of a single-layered graphene nanoplate with an arbitrarily oriented crack under the influence of a magnetic field. The research focuses on three boundary conditions: simply supported, clamped and clamped-simply supported. The crack effect is modeled by incorporating membrane forces and additional flexural moments created by the crack into the equation of motion.
Findings
Results reveal that increasing the crack length, small size effects and magnetic field intensity reduces the flexural stiffness of the nanoplate, increases the compressive load and lowers its natural frequency. Additionally, excessive magnetic field intensity may lead to static buckling. The critical dimensionless magnetic fields are found to be 33.6, 95.1 and 72.3 for All edges of the nanoplate are simply supported (SSSS), fully clamped edges (CCCC) and two opposite edges are clamped and the other are simply supported (CSCS) nanoplates, respectively. Furthermore, for SSSS and CCCC boundary conditions, an increase in the crack angle results in a softening behavior of the hard spring. In contrast, the SCSC boundary condition exhibits the opposite behavior. These findings emphasize the importance of considering the effects of angled cracks and electromagnetic loads in the analysis and design of graphene-based nanostructures.
Originality/value
Novel equations are derived to account for the applied loads induced by the magnetic field. The nonlinear equation of motion is discretized using the Galerkin technique, and its analytical response is obtained via the multiple time-scales perturbation technique.
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Ming-Xian Lin, Chia-Hsiang Tseng and Chao Kuang Chen
This paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on…
Abstract
Purpose
This paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.
Design/methodology/approach
The governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.
Findings
The results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.
Originality/value
The results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.
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Jayaram Mohanty, Shishir Kr. Sahu and Pravat Kr. Parhi
With the widespread use of the composites over other metallic materials in different fields of engineering, studies on damages of composite structures have assumed great…
Abstract
Purpose
With the widespread use of the composites over other metallic materials in different fields of engineering, studies on damages of composite structures have assumed great importance. Among various kinds of damages, delamination is of very serious concern to composite applications. It may arise as a consequence of impact loading, stress concentration near a geometrical or material discontinuity or manufacturing defects. The presence of one or more delaminations in the composite laminate may lead to a premature collapse of the structure due to buckling at a lower level of compressive loading. So the effect of delamination on stability of composite structures needs attention and thus constitutes a problem of current interest. The purpose of this paper is to deal with both numerical and experimental investigations on buckling behaviour of single and multiple, delaminated, industry driven, woven roving glass/epoxy composite plates on clamped free clamped free (CFCF) rectangular plates.
Design/methodology/approach
For numerical analysis, a finite element model was developed with an eight noded two dimensional quadratic isoparametric element having five degrees of freedom per node. The elastic stiffness matrices were derived using linear first order shear deformation theory with a shear correction factor. Green's nonlinear strain equations are used to derive the geometric stiffness matrix. The computation of buckling load based on present formulation is compared with the experimental results for the effect of different parameters on critical load of the delaminated composite panels. In the experimental study, the influences of various parameters such as delamination area, fiber orientations, number of layers, aspect ratios on the buckling behaviour of single and multiple delaminated woven roving glass/epoxy composite plates were investigated. Buckling loads were measured by INSTRON 1195 machine for the delaminated composite plates.
Findings
Comparison of numerical results with experimental results showed a good agreement. Both the results revealed that the area of delaminations, fiber orientations, number of layers and aspect ratio have paramount influence on the buckling behaviour of delaminated plate.
Originality/value
The present study is part of Jayaram Mohanty's doctoral thesis, an original research work.
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Elluri Venkata Prasad and Shishir Kumar Sahu
The purpose of this study is to study the buckling behavior of new aircraft material, i.e. glass fiber metal laminated (GFML) plates.
Abstract
Purpose
The purpose of this study is to study the buckling behavior of new aircraft material, i.e. glass fiber metal laminated (GFML) plates.
Design/methodology/approach
The first-order Reissner–Mindlin theory is used in the present finite element formulation to determine the buckling loads of GFML plates. A program is developed in MATLAB for analyzing the effect of different parameters on buckling loads GFML plates. A set of experiments was performed to determine critical buckling loads of GFML plates using universal testing machine INSTRON 8862 and compared with predictions using the numerical model.
Findings
The effects of various parameters such as aspect ratio, side to thickness ratio, ply orientation and boundary conditions on buckling loads of GFMLs are examined. With the increase of aspect ratio, the reduction in buckling load is observed, while the increase inside to thickness ratio decreases the buckling load of GFML plates. There is a slight variation in buckling load with the increase of ply orientation. The buckling load is significantly influenced by boundary conditions because of restraint at the edges.
Practical implications
These types of materials are used in lightweight structures such as aircraft, aerospace and military vehicles. The results reported in the present study can be used as design guidelines while designing fiber metal laminated (FML) plated structures.
Originality/value
For the first time, the authors have studied the buckling behavior of bidirectional woven FML plates using both numerical and experimental techniques.
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Phaneendra Kumar Kopparthi, Srikar Gemaraju, Bhaskara Rao Pathakokila and Suresh Gamini
Delamination is a common and crucial damage mode which occurs during manufacturing of layered composites or their service life. Its existence leads to degradation in mechanical…
Abstract
Purpose
Delamination is a common and crucial damage mode which occurs during manufacturing of layered composites or their service life. Its existence leads to degradation in mechanical properties or even structural failure of composites. Hence, the purpose of this article is to study the effect of induced delamination on flexural performance of CFRP composites.
Design/methodology/approach
In this article, the flexural behaviors of intact and delaminated carbon/epoxy laminates were investigated under pure bending. A circular PTFE film was introduced during fabrication to create artificial delamination. Moreover, finite element models were developed for intact and delaminated composites using ANSYS. The created models were discretized using 3D structural eight node solid elements.
Findings
The delamination influenced considerably flexural properties of composite. The composite exhibited a linear elastic nature prior to the damage of top ply on the compression side. The flexural strength and stiffness of the composite reduced to 44.5% and 18.2% respectively due to the existence of artificial delamination. The results of four point bending experiments and finite element analysis agreed for both intact and delaminated composites within acceptable error. Finally for same composites, first ply failure analysis was carried out using Tsai-Hill, Tsai-Wu and Hashin failure criteria.
Originality/value
In pure bending, beam section of the middle portion is free from shear. It is not so in case of three-point bending. Hence, the effect of embedded artificial defect on bending performance of CFRP composite due to pure bending has been investigated.
Details
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Mokhtar Bouazza and Noureddine Benseddiq
The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal…
Abstract
Purpose
The purpose of this paper is to investigate an analytical modeling for the thermoelastic buckling behavior of functionally graded (FG) rectangular plates (FGM) under thermal loadings. The material properties of FGM are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Derivations of equations are based on novel refined theory using a new hyperbolic shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. In addition, numerical results for a variety of FG plates with simply supported edge are presented and compared with those available in the literature. Moreover, the effects of geometrical parameters of dimension the length to width aspect ratio (a/b), the plate width to thickness ratio (b/h), and material properties index (k) on the FGM buckling temperature difference are determined and discussed.
Design/methodology/approach
In the current paper, the application of the refined theory proposed by Shimpi is based on the assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. It is extended to the analysis of buckling behavior of ceramic-metal FG plates subjected to the three types of thermal loadings, namely; uniform temperature rise, linear temperature change across the thickness, and nonlinear temperature change across the thickness. The material properties of the FG plates are assumed to vary continuously through the thickness of the plate, according to the simple power-law distribution. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results, wherever possible. Additionally, the effects of geometrical parameters and material properties on the buckling temperature difference of FGM plates are determined and discussed.
Findings
Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power-law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.
Originality/value
To the best of the authors’ knowledge, there are no research works for thermal buckling analysis of FG rectangular plates based on new four-variable refined plate theory (RPT). The novelty of this paper is extended the use of the above-mentioned RPT with the addition of a new function proposed by Shimpi for thermal buckling analysis of plates made of FG materials. Unlike any other theory, the number of unknown functions involved is only four, as against five in the case of other shear deformation theories. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. The plates subjected to the two types of thermal loadings, namely; uniform temperature rise and nonlinear temperature change across the thickness. Numerical results for a variety of FG plates with simply supported edges are given and compared with the available results.