•Fluid-conveying functionally graded pipe models associated with porosities and geometric imperfections are developed.•Two general cases of the functionally graded pipe with movable and immovable ...ends are discussed.•Closed-form solutions for nonlinear static response and linear free vibration problem are proposed.•Two geometrically imperfect cases exhibit different bifurcation-type post-bucklings.•Sensitivity of buckling and post-buckling behavior to system parameters are examined.
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In this study, the static and dynamic responses of functionally graded material (FGM) pipes with porosities and geometric imperfections are investigated. The material properties of the porous FGM pipe are assumed to vary continuously and smoothly along the radial direction based on the modified power-law distribution. The nonlinear equations of motion are derived on the basis of the Euler-Bernoulli beam hypothesis incorporating the effects of von Kármán nonlinearity and initial imperfection. Two general cases of pipes with movable and immovable ends are considered. Closed-form solutions for nonlinear critical buckling velocity and nonlinear stability behavior of system under different boundary conditions are proposed. Subsequently, the free vibration problem around the buckled configuration is solved as a eigenvalue problem, and the natural frequencies are calculated using a new exact solution procedure that considers the gyroscopic effect. The effects of important parameters including the initial imperfection, the power-law index, the porosity volume fraction, and geometric properties on buckling and post-buckling behavior of system are explored in numerical results.
Compression of a slender rod, tightly confined in a bore, is an archetypal problem that has relevance in a wide variety of situations ranging from worm like macromolecular chains and microtubules to ...drill strings in wellbores. If persistence length quantifies the stiffness of the rod, these problems span over cases where persistence length is of the order of the contour length to where it is many orders larger. In spite of this wide spread, all of these problems adopt the Kirchhoff rod theory, whereby, with appropriate normalisations, the force displacement response becomes independent of stiffness. This is true for unconstrained rods but not for rods constrained in bores. In fact, when the bore dimensions are much smaller compared to the length of the rod, i.e. the rod is ‘tightly’ constrained, post Euler buckling responses are characterised by abrupt large configurational adjustments or so-called ‘jump-instabilities’. The large and repeated configurational adjustments render the numerical simulation of the post-buckling force displacement responses difficult. We have used a geometrically exact 3-dimensional beam theory with rough constraining walls in order to successfully simulate the force displacement response of constrained rods up to large strains. In particular, we have simulated rods with stiffness values ranging over 6 orders of magnitude — starting from values comparable to microtubules in the cytoskeleton to those applicable to large scale engineering structures. Our results show that, unlike what is expected from the Kirchhoff rod theory, the geometry of the bore, and its size, play a significant role in rendering the compression response stiffness dependent. Moreover, nature and degree of confinement also dictate the stable 3-dimensional configuration to which the rod eventually evolves. In circular bores, the rod evolves to an almost perfect helical shape while in square ones, it does not.
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•Compression of tightly confined slender rods are studied using GEBT and rough contact at the confining walls.•Stable helical shapes of the rods result from isotropic nature of the confinement or large initial pre-twist.•Tight confinement increases load carrying capacity and leads to short wavelength post-buckled shapes.•A rod with stiffness comparable to its persistence length has jerky force displacement response.•A stiff rod in tight confinement stores a large part of its strain energy in axial compression.
•Thermal buckling analysis of FGM beams by various theories are presented.•A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths.•The ...post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any various displacement fields.
In the present work, attention is focused on the prediction of thermal buckling and post-buckling behaviors of functionally graded materials (FGM) beams based on Euler–Bernoulli, Timoshenko and various higher-order shear deformation beam theories. Two ends of the beam are assumed to be clamped and in-plane boundary conditions are immovable. The beam is subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. The governing equations are developed relative to neutral plane and mid-plane of the beam. A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. New results of thermal buckling and post-buckling analysis of the beams are presented and discussed in details, the numerical analysis shows that, for the case of uniform temperature rise loading, the post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any arbitrary value of the power law index and any various displacement fields.
This article focuses on the buckling response of columns formed by pre-twisting a flat, narrow and straight material strip of a rectangular cross section. The experimental analysis accomplished for ...birch plywood strips covers twisting up to 90 degrees. The corresponding computational analysis covers the twisting process (geometrically nonlinear analysis) and the subsequent compression (linear buckling analysis, including the residual stresses from the twisting process) and includes comparisons for 3D solid and 2D shell finite elements within orthotropic linear elasticity. A further finite element analysis provides findings up to twisting angles of 400 degrees and includes nonlinear post-buckling analyses for the compression subsequent to twisting, in addition to the linear buckling analyses. These sets of analyses reveal some new findings regarding this classical problem. Most importantly, there are four characteristic twisting angles which are associated to mode jumps in buckling, to a plateau in the curve relating the critical load and the twisting angle and, finally, to a loss of stability during the twisting process. The influence of the twisting-induced stresses on the buckling response is investigated as well.
•Compression response of twisted (by up to 90 degrees) plywood strips is studied experimentally.•3D solid and shell FE models confirmed significant increase in critical buckling load.•FE analyses (for twisting up to 400 degrees) revealed four characteristic angles associated to:•(1) Mode jumps in buckling, (2) A plateau in the curve relating critical load and twisting angle, (3) A loss of stability during the twisting process.
Material layering occurs in natural, biological, geological and synthetic load-bearing structures. The bucking and post-buckling behavior of such structures is a subject of great interest. While many ...studies were devoted to the case of a thin film attached to a thick substrate, little is available on the behavior of multilayers. We explore this subject using a model system consisting of 2-D, linearly elastic hard/soft multilayer under uniform edge displacement. The lateral edges of the multilayer are constrained by rigid, frictionless walls. The number of stiff layers n and layer-to-interlayer thickness and elastic moduli ratios, h and E, are systematically varied. The deformation and stresses in the multilayer are obtained with the aid a FEA. Buckling initiates in the interior layers and spreads to the outer ones. The layers adjacent to the constraining walls tend to flatten as the load is increased. For relatively large h or small E, this causes large membrane stresses that may lead to a buckling mode transition. As many as ≈ 50 stiff layers are needed in order for the multilayer to approach a laminate configuration (n ≫ 1). The multilayer as a whole displays nonlinear elastic stress–strain response. By a proper choice of the system variables n, h and E, a variety of strain hardening effects as well as large energy absorption can be achieved. The results of this study provide useful insights into the effects of b.c., material choice and load level on the response of multilayers in general.
•Thermal post-buckling analysis of functionally graded material shell structures is investigated.•A modified FSDT theory is used.•Transverse shear deformations are considered.•Numerical examples of ...FGM plates and cylindrical shells are presented in order to show the applicability and the efficiency of the present model.
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The thermal post-buckling responses of Functionally Graded Material shell structures are reported in this paper. Geometrically nonlinear analysis based on a modified First order Shear Deformation Theory are proposed. The modified theory takes into account the shear strains with a parabolic shape function and it verifies a zero shear stresses condition at the top and bottom surfaces. For the numerical computation, four nodes shell elements are implemented. The large displacement is described by Green–Lagrange nonlinear strains. Moreover, it is assumed that the shell structures are exposed to uniform, linear and nonlinear temperature distributions through the thickness direction. The thermal and the mechanical properties are described according to a power law distribution and either temperature-independent or temperature-dependent material properties are considered. Two numerical examples of functionally graded plates and cylindrical shells are presented to highlight the effectiveness and the accuracy of the present finite element procedure. The effect the geometrical parameters, the volume fraction index and boundary conditions on nonlinear responses are performed.
The optimal design of the postbuckling response of variable angle tow composite structures is an important consideration for future lightweight, high-performing structures. Based on this premise, a ...new optimisation tool is presented for shell-type structures. The starting point is an isogeometric framework which uses NURBS interpolation functions to provide a smooth description of the deformed shapes, thereby reducing the number of degrees of freedom with respect to standard finite elements. The stiffness variation is obtained by exploiting the same NURBS interpolation to describe lamination parameters, employed as intermediate optimisation variables. This choice allows the design space to be thoroughly explored with relatively few design variables in a smooth optimisation space. Therefore, the optimisation strategy is divided into two stages. Firstly, the optimal distribution of lamination parameters is determined using a gradient based algorithm. Afterwards, an actual distribution of fibre orientation is retrieved. The viability of the tool is tested firstly onto a cylindrical panel under compressive loading. Then, the postbuckling optimisation of a composite wingbox is given. For both structures, the optimised postbuckling response is compared with those of the corresponding quasi-isotropic baselines showing significant improvements.
Thin-walled composite structures operating in the post-buckling regime needs a thorough understanding of their stability behavior and failure mechanisms. For the accurate prediction of the collapse ...loads, one needs to account for the damage evolution precisely. In the current study, we have proposed a unified and generic numerical modeling approach that accounts for both the intra and inter-laminar damage modes in stiffened CFRP panels. A 3D finite element based progressive damage model (PDM) is proposed to simulate the collapse behavior of the single blade stiffened composite (SSC) CFRP panels with and without embedded de-bonding defects under uniaxial compression loading. A user-defined material subroutine based on 3D Hashin failure criteria is developed in Abaqus software to study the evolution of intra-laminar damages in SSC panel. Further, the skin-stiffener bonded interface, the inter-laminar interfaces in the skin, stiffener, including the noodle region, is modeled using the cohesive zone elements to simulate the de-bonding/delamination growth. The stability response and collapse load results obtained using the proposed PDM are compared with the experimental observations. Also, the damage evolution, failure mechanisms, the ultimate load, and the corresponding displacement data obtained from the developed PDM are validated with the experimental estimates. A comprehensive damage assessment involving the ultrasonic C-scans, infrared thermograms, and micrographic study is also carried out to supplement the PDM predictions. Thus, the proposed PDM is generic in terms of damage studies and can be used for investigating the collapse behavior of CFRP panels with multiple stiffeners.
The structural efficiency of composite stiffened panels can be substantially improved by utilizing curved stiffening components due to their exceptional mechanical performance and design flexibility. ...This paper aims to explore the impressive potential offered by the curved stiffening concept in the design of T-shaped stiffened composite panels featuring curved sub-stiffening components. An optimization design framework is proposed to optimize the laminates sequence of skin, ply orientation angles and distribution of the curved sub-stiffeners as well as the curvature of the sub-stiffeners of the proposed curved grid sub-stiffened composite panels to yield higher buckling performance without additional weight. Results demonstrate that introducing composite curved grid sub-stiffeners to the T-shaped stiffened composite panel leads to substantial improvements (+254.42%) in buckling performance, while maintaining equivalent weight designs. Furthermore, the introduction of composite curved grid sub-stiffeners reveals alterations to the post-buckling deformation paths of grid sub-stiffened composite panels, leading to varied collapse loads and degrees of deformation in the composite panels. This highlights the importance of utilizing the composite curved grid sub-stiffeners to improve stability and reduce the risk of failure in thin-walled structures, all while meeting lightweight design criteria.
•A novel grid sub-stiffening concept (composite curved grid sub-stiffeners) was introduced and optimized to improve the initial buckling performance of an existing T-stiffened composite panel design with no additional weight.•Substantial improvements in buckling performance were achieved when compared to the T-shaped stiffened and sub-stiffened composite panel with equivalent weight designs.•The curvature of the sub-stiffeners has a considerable influence on the buckling performance and alters the buckling mode shapes.•The introduction of composite curved grid sub-stiffeners alters the post-buckling deformation paths and further affects the initiation and propagation of various failure modes.
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