• Advances in nano research
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• v.8 no.1
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• pp.83-94
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• 2020

An analytical formulation and solution process for the buckling analysis of porous magneto-electro-elastic functionally graded (MEE-FG) beam via different thermal loadings and various boundary conditions is suggested in this paper. Magneto electro mechanical coupling properties of FGM beam are taken to vary via the thickness direction of beam. The rule of power-law is changed to consider inclusion of porosity according to even and uneven distribution. Pores possibly occur inside FGMs due the result of technical problems that lead to creation of micro-voids in these materials. Change in pores along the thickness direction stimulates the mechanical and physical properties. Four-variable tangential-exponential refined theory is employed to derive the governing equations and boundary conditions of porous FGM beam under magneto-electrical field via Hamilton's principle. An analytical model procedure is adopted to achieve the non-dimensional buckling load of porous FG beam exposed to magneto-electrical field with various boundary conditions. In order to evaluate the influence of thermal loadings, material graduation exponent, coefficient of porosity, porosity distribution, magnetic potential, electric voltage and boundary conditions on the critical buckling temperature of the beam made of magneto electro elastic FG materials with porosities a parametric study is presented. It is concluded that these parameters play remarkable roles on the buckling behavior of porous MEE-FG beam. The results for simpler states are proved for exactness with known data in the literature. The proposed numerical results can serve as benchmarks for future analyses of MEE-FG beam with porosity phases.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.701-711
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• 2020

This papers studies nonlinear stability and post-buckling behaviors of geometrically imperfect metal foam doubly-curved shells with eccentrically stiffeners resting on elastic foundation. Metal foam is considered as porous material with uniform and non-uniform models. The doubly-curved porous shell is subjected to in-plane compressive loads as well as a transverse pressure leading to post-critical stability in nonlinear regime. The nonlinear governing equations are analytically solved with the help of Airy stress function to obtain the post-buckling load-deflection curves of the geometrically imperfect metal foam doubly-curved shell. Obtained results indicate the significance of porosity distribution, geometrical imperfection, foundation factors, stiffeners and geometrical parameters on post-buckling characteristics of porous doubly-curved shells.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.75-82
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• 2007

This paper addresses a method for shape optimization of a continuous elastic body considering stability, i.e., buckling behavior. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Unlike the conventional finite difference method (FDM), this method is efficient in that only a couple of analyses are required regardless of the number of design parameters. Commercial software such as ANSYS can be employed since the method requires only the result of the analysis in computation of the sensitivity. Though the buckling problem is more efficiently solved by structural elements such as a beam and shell, elastic solids have been chosen for the buckling analysis because solid elements can generally be used for any kind of structure whether it is thick or thin. Sensitivity is then computed by using the mathematical package MATLAB with the initial stress and buckling analysis of ANSYS. Several problems we chosen in order to illustrate the efficiency of the presented method. They are applied to the shape optimization problems to minimize weight under allowed critical loads and to maximize critical loads under same volume.

• Steel and Composite Structures
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• v.41 no.6
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• pp.805-820
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• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Steel and Composite Structures
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• v.17 no.1
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• pp.1-19
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• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• Steel and Composite Structures
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• v.30 no.5
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• pp.483-492
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• 2019

In the current study, the influence of the initial lateral (sweep) shape and the cross-sectional twist imperfection on the lateral torsional buckling (LTB) response of doubly-symmetric steel I-beams was investigated. The material imperfection (residual stress) was not considered. For this objective, standard European IPN 300 beam with different unbraced span was numerically analyzed for three imperfection cases: (i) no sweep and no twist (perfect); (ii) three different shapes of global sweep (half-sine, full-sine and full-parabola between the end supports); and (iii) the combination of three different sweeps with initial sinusoidal twist along the beam. The first comparison was done between the results of numerical analyses (FEM) and both a theoretical solution and the code lateral torsional buckling formulations (EC3 and AISC-LRFD). These results with no imperfection effects were then separately compared with three different shapes of global sweep and the presence of initial twist in these sweep shapes. Besides, the effects of the shapes of initial global sweep and the inclusion of sinusoidal twist on the critical buckling load of the beams were investigated to unveil which parameter was considerably effective on LTB response. The most compatible outcomes for the perfect beams was obtained from the AISC-LRFD formulation; however, the EC-3 formulation estimated the $P_{cr}$ load conservatively. The high difference from the EC-3 formulation was predicted to directly originate from the initial imperfection reduction factor and high safety factor in its formulation. Due to no consideration of geometric imperfection in the AISC-LFRD code solution and the theoretical formulation, the need to develop a practical imperfection reduction factor for AISC-LRFD and theoretical formulation was underlined. Initial imperfections were obtained to be more influential on the buckling load, as the unbraced length of a beam approached to the elastic limit unbraced length ($L_r$). Mode-compatible initial imperfection shapes should be taken into account in the design and analysis stages of the I-beam to properly estimate the geometric imperfection influence on the $P_{cr}$ load. Sweep and sweep-twist imperfections led to 10% and 15% decrease in the $P_{cr}$ load, respectively, thus; well-estimated sweep and twist imperfections should considered in the LTB of doubly-symmetric steel I-beams.

• Steel and Composite Structures
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• v.4 no.4
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• Advances in nano research
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• v.7 no.5
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• pp.293-310
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• 2019

In this paper, thermal-buckling behavior of the functionally graded (FG) nanocomposite plates reinforced with graphene oxide powder (GOP) is studied under three types of thermal loading once the plate is supposed to be rested on a two-parameter elastic foundation. The effective material properties of the nanocomposite plate are considered to be graded continuously through the thickness according to the Halpin-Tsai micromechanical scheme. Four types of GOPs' distribution namely uniform (U), X, V and O, are considered in a comparative way in order to find out the most efficient model of GOPs' distribution for the purpose of improving the stability limit of the structure. The governing equations of the plate have been derived based on a refined higher-order shear deformation plate theory incorporated with Hamilton's principle and solved analytically via Navier's solution for a simply supported GOP reinforced (GOPR) nanocomposite plate. Some new results are obtained by applying different thermal loadings to the plate according to the GOPs' negative coefficient of thermal expansion and considering both Winkler-type and Pasternak-type foundation models. Besides, detailed parametric studies have been carried out to reveal the influences of the different types of thermal loading, weight fraction of GOP, aspect and length-to-thickness ratios, distribution type, elastic foundation constants and so on, on the critical buckling load of nanocomposite plates. Moreover, the effects of thermal loadings with various types of temperature rise are investigated comparatively according to the graphical results. It is explicitly shown that the buckling behavior of an FG nanocomposite plate is significantly influenced by these effects.

• Steel and Composite Structures
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• v.32 no.2
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• pp.173-187
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• 2019

This study is concerned with the stability of laminated composite plates modelled using Eringen's nonlocal differential model (ENDM) and a novel refined-hyperbolic-shear-deformable plate theory. The plate is assumed to be lying on the Pasternak elastic foundation and is under the influence of an in-plane magnetic field. The governing equations and boundary conditions are obtained through Hamilton's principle. An analytical approach considering Navier series is used to fine the critical bucking load. After verifying with existing results for the reduced cases, the present model is then used to study buckling of the laminated composite plate. Numerical results demonstrate clearly for the first time the roles of size effects, magnetic field, foundation parameters, moduli ratio, geometry, lay-up numbers and sequences, fiber orientations, and boundary conditions. These results could be useful for designing better composites and can further serve as benchmarks for future studies on the laminated composite plates.

• Journal of the Korean Society of Marine Environment & Safety
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• v.20 no.6
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• pp.738-745
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• 2014

In this paper, It is performing to the elastic and elasto-plastic large deformation series analysis using a numerical method for the initial deflection effect of the aluminum alloy rectangular plate in the elasto-plastic loading area patch loading size. It is assumed a boundary condition to be a simply supported condition and consider the initial deflection amplitude, aspect ratio. It examined the critical elastic buckling load and post-buckling behaviour of aluminium alloy A6082-T6 rectangular plate. It used a commercial program for the elastic and elasto-plastic deformation series analysis. If the initial deflection amplitude is smaller, the in-plane rigidity with increasing to load is reduced from the start and occurs significantly more increasing the amplitude. More higher the aspect ratio, the initial yield strength is gradually decreased, and the plate thickness thicker and occurs larger than the thin walled plate a reduction ratio of the initial yield strength of the patch loading size as 0.5.