• Geomechanics and Engineering
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• 제17권2호
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• pp.175-180
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• 2019

This research is concerned with post-buckling investigation of nano-scaled beams constructed from porous functionally graded (FG) materials taking into account geometrical imperfection shape. Hence, two types of nanobeams which are perfect and imperfect have been studied. Porous FG materials are classified based on even or uneven porosity distributions. A higher order nonlinear refined beam theory is used in the present research. Both perfect and imperfect nanobeams are formulated based on this refined theory. A detailed study is provided to understand the effects of geometric imperfection, pore distribution, material distribution and small scale effects on buckling of FG nanobeams.

• Steel and Composite Structures
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• 제42권1호
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• pp.75-90
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• 2022

The pointwise equilibrium polynomial (PEP) element considering local second-order effect has been widely used in direct analysis of many practical engineering structures. However, it was derived according to Euler-Bernoulli beam theory and therefore it cannot consider shear deformation, which may lead to inaccurate prediction for deep beams. In this paper, a novel beam-column element based on Timoshenko beam theory is proposed to overcome the drawback of PEP element. A fifth-order polynomial is adopted for the lateral deflection of the proposed element, while a quadric shear strain field based on equilibrium equation is assumed for transverse shear deformation. Further, an additional quadric function is adopted in this new element to account for member initial geometrical imperfection. In conjunction with a reliable and effective three-dimensional (3D) co-rotational technique, the proposed element can consider both member initial imperfection and transverse shear deformation for second-order direct analysis of frame structures. Some benchmark problems are provided to demonstrate the accuracy and high performance of the proposed element. The significant adverse influence on structural behaviors due to shear deformation and initial imperfection is also discussed.

• Structural Engineering and Mechanics
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• 제87권1호
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• pp.85-94
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• 2023

In the present work, thermal buckling and post-buckling behaviors of imperfect graphene platelet reinforced metal foams (GPRMFs) doubly curved shells are examined. Material properties of GPRMFs doubly curved shells are presumed to be the function of the thickness. Reddy' shell theory incorporating geometric nonlinearity is utilized to derive the governing equations. Various types of the graphene platelets (GPLs) distribution patterns and doubly curved shell types are taken into account. The nonlinear equations are discretized for the case of simply supported boundary conditions. The thermal post-buckling response are presented to analyze the effects of GPLs distribution patterns, initial geometric imperfection, GPLs weight fraction, porosity coefficient, porosity distribution forms, doubly curved shell types. The results show that these factors have significant effects on the thermal post-buckling problems.

• Steel and Composite Structures
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• 제4권6호
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• pp.471-487
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• 2004

Modular steel scaffolds are commonly used as supporting scaffolds in building construction, and traditionally, the load carrying capacities of these scaffolds are obtained from limited full-scale tests with little rational design. Structural failure of these scaffolds occurs from time to time due to inadequate design, poor installation and over-loads on sites. In general, multi-storey modular steel scaffolds are very slender structures which exhibit significant non-linear behaviour. Hence, secondary moments due to both $P-{\delta}$ and $P-{\Delta}$ effects should be properly accounted for in the non-linear analyses. Moreover, while the structural behaviour of these scaffolds is known to be very sensitive to the types and the magnitudes of restraints provided from attached members and supports, yet it is always difficult to quantify these restraints in either test or practical conditions. The problem is further complicated due to the presence of initial geometrical imperfections in the scaffolds, including both member out-of-straightness and storey out-of-plumbness, and hence, initial geometrical imperfections should be carefully incorporated. This paper presents an extensive numerical study on three different approaches in analyzing and designing multi-storey modular steel scaffolds, namely, a) Eigenmode Imperfection Approach, b) Notional Load Approach, and c) Critical Load Approach. It should be noted that the three approaches adopt different ways to allow for the non-linear behaviour of the scaffolds in the presence of initial geometrical imperfections. Moreover, their suitability and accuracy in predicting the structural behaviour of modular steel scaffolds are discussed and compared thoroughly. The study aims to develop a simplified and yet reliable design approach for safe prediction on the load carrying capacities of multi-storey modular steel scaffolds, so that engineers can ensure safe and effective use of these scaffolds in building construction.

• Steel and Composite Structures
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• 제35권4호
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• pp.567-578
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• 2020

Based on third-order shear deformation shell theory, the present paper investigates post-buckling properties of eccentrically stiffened metal foam curved shells/panels having initial geometric imperfectness. Metal foam is considered as porous material with uniform and non-uniform models. The single-curve porous shell is subjected to in-plane compressive loads leading to post-critical stability in nonlinear regime. Via an analytical trend and employing Airy stress function, the nonlinear governing equations have been solved for calculating the post-buckling loads of stiffened geometrically imperfect metal foam curved shell. New findings display the emphasis of porosity distributions, geometrical imperfectness, foundation factors, stiffeners and geometrical parameters on post-buckling properties of porous curved shells/panels.

• Computers and Concrete
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• 제25권4호
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• pp.283-291
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• 2020

The present paper researches post-buckling behaviors of geometrically imperfect concrete beam resting on elastic foundation reinforced with graphene oxide powders (GOPs) based on finite element method (FEM). Distribution of GOPs are considered as uniform and linearly graded through the thickness. Geometric imperfection is considered as first buckling mode shape of the beam, the GOP reinforced beam is rested in initial position. The material properties of GOP reinforced composite have been calculated via employment of Halpin-Tsai micromechanical scheme. The provided refined beam element verifies the shear deformation impacts needless of any shear correction coefficient. The post-buckling load-deflections relations have been calculated via solving the governing equations having cubic non-linearity implementing FEM. Obtained findings indicate the importance of GOP distributions, GOP weight fraction, matrix material, geometric imperfection, shear deformation and foundation parameters on nonlinear buckling behavior of GOP reinforced beam.

• Steel and Composite Structures
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• 제30권6호
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.

• Steel and Composite Structures
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• 제33권2호
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• pp.261-275
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• 2019

The main objective of this paper is to study the axial buckling and post-buckling of geometrically imperfect single-layer graphene sheets (GSs) under in-plane loading in the theoretical framework of the nonlocal strain gradient theory. To begin with, a graphene sheet is modeled by a two-dimensional plate subjected to simply supported ends, and supposed to have a small initial curvature. Then according to the Hamilton's principle, the nonlinear governing equations are derived with the aid of the classical plate theory and the von-karman nonlinearity theory. Subsequently, for providing a more accurate physical assessment with respect to the influence of respective parameters on the mechanical performances, the approximate analytical solutions are acquired via using a two-step perturbation method. Finally, the authors perform a detailed parametric study based on the solutions, including geometric imperfection, nonlocal parameters, strain gradient parameters and wave mode numbers, and then reaching a significant conclusion that both the size-dependent effect and a geometrical imperfection can't be ignored in analyzing GSs.

• Steel and Composite Structures
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• 제45권5호
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• pp.621-640
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• 2022

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e. along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.

• Advances in materials Research
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• 제8권3호
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• pp.237-257
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• 2019

The present article researches large-amplitude thermal free vibration characteristics of nonlocal two-phase piezo-magnetic nano-size beams having geometric imperfections by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All previous studies on vibrations of piezoelectric-magnetic nano-size beams ignore the influences of geometric imperfections which are crucial since a nanobeam is not always ideal or perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtain nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic imperfection amplitude and substrate constants.