No abstract is provided for this article.
No abstract is provided for this article.
Structural systems made of high-strength and/or high-ductility metals are usually also rather slender, which means that their structural behaviour and ultimate strength are often governed by a combination of plasticity and instability effects. Currently, the rigorous numerical analysis of such systems can only be achieved by resorting to complex and computationally costly shell finite element simulations. This work aims at supplying to designers/researchers with an efficient and structurally clarifying alternative to assess the geometrically and/or materially non-linear behaviour (up to and beyond the ultimate load) of prismatic thin-walled members, such as those built from cold-formed steel. The proposed approach is based on Generalised Beam Theory (GBT) and is suitable for members exhibiting arbitrary deformation patterns (e.g., global, local, distortional, shear) and made of non-linear isotropic materials (e.g., carbon/stainless steel grades or aluminum alloys). The paper begins by providing an overview of the physically and geometrically non-linear GBT formulation recently developed and validated by the authors, which is followed by the presentation and thorough discussion of several illustrative numerical results concerning the structural responses of 5 members (beams and columns) made of distinct (linear, bi-linear or highly non-linear) materials. The GBT results consist of equilibrium paths, modal participation diagrams and amplitude functions, stress contours, displacement profiles and collapse mechanisms – some of which are compared with Abaqus shell finite element analysis (SFEA) values. An excellent correlation is found in all cases and, moreover, it is shown that GBT analyses including judiciously selected deformation mode sets involve only 25% (on average) of the number of d.o.f. required by similarly accurate SFEA. Moreover, it is clearly evidenced that the GBT modal nature makes it possible to acquire in-depth knowledge on the member behavioural mechanics in the elastic and elastic–plastic regimes.
Graphyne is an allotrope of carbon with excellent mechanical, electrical, and optical properties. The scientific community has been increasingly interested in its characterization and computational simulation, using molecular dynamics (MD) simulations and density functional theory (DFT). The present work presents, for the first time (to the authors’ knowledge), a finite element (FE) model to evaluate the elastic properties of graphyne. After presenting a brief literature review on the latest developments of graphyne and its mechanical characterization through computational methods, the FE model of graphyne sheet is presented in detail and the calculation of its elastic properties described. The linear elastic properties (Young’s modulus, Poisson’s ratio, bulk modulus, and shear modulus) obtained from the proposed FE models are in general agreement with those previously obtained by other authors using more complex computational models (MD and DFT). The influence of van der Waals (vdW) interatomic forces on the linear elastic properties of planar graphyne is negligible and can be disregarded if small strain hypothesis is adopted. The FE models also show that graphyne exhibits marginal orthotropic behavior, that is, “quasi-isotropic” behavior, a fact that agrees with the conclusions reported by other researchers.
This paper addresses the distortional kinematics and mechanics of thin-walled sections and provides clear definitions of cross-section properties that characterise the distortional deformation, as it is usually done for conventional modes (axial, bending and torsion). In particular, a procedure to build the distortional displacement field of a given thin-walled section is described. The first part of the paper describes the essentials of distortion in comparison with the conventional modes of classical beam theories. It is shown that primary warping is the key factor that controls the distortion of thin-walled sections. Then, an analytical procedure to determine the distortional warping displacement distribution of a given cross-section is described, on the basis of orthogonality conditions existing between the distortional and conventional modes. Next, an overview of the kinematical assumptions underlying the distortional deformation is presented and a simple procedure to build distortional displacement fields of thin-walled sections is provided. This procedure is then applied to obtain the distortional displacement field of C-sections and general expressions of distortional cross-section properties are given. Finally, a simple example is presented to illustrate how the distortional displacement field of a C-section is built, on the basis of simple kinematics principles. The distortional critical stress and half wavelength are determined and good agreement with exact numerical estimates is found.
In the present paper, a multilevel approach for the local nanobuckling analysis of carbon nanotube (CNT) based composite materials is proposed and described. The approach comprises four levels, all of them at nanoscale. The first level aims to propose the potential that describes the interatomic forces between carbon atoms. In the second level, molecular dynamics simulations are performed to extract the elastic properties of the CNT. The third level aims to determine the stiffness of the material that surrounds the CNT (matrix), using the annular membrane analysis. In the fourth level, finite strip analysis of the CNT elastically restrained by the matrix is performed to calculate the critical strain at which the CNT buckles locally. In order to achieve accurate results and take the CNT-matrix interaction into account, the <TEX>$3^{rd}$</TEX> and <TEX>$4^{th}$</TEX> steps may be repeated iteratively until convergence is achieved. The proposed multilevel approach is applied to several CNTs embedded in a cylindrical representative volume element and illustrated in detail. It shows that (i) the interaction between the CNT and the matrix should be taken into account and (ii) the buckling at nanoscale is sensitive to several types of local buckling modes.
Neste artigo apresenta-se uma formulacao da GBT para analises elasto-plasticas de 1a ordem e ilustra-se a sua aplicacao a uma viga simplesmente apoiada com seccao em I, constituida por um material elastico-perfeitamente plastico e submetida a cargas concentradas a meio vao. Os resultados da GBT sao validados por comparacao com os resultados obtidos atraves de um modelo de elementos de casca utilizando o programa ABAQUS. Constata-se uma excelente correlacao entre os resultados da GBT e do ABAQUS, em particular no que respeita a trajectorias de equilibrio e configuracoes deformadas. No que respeita a diagramas de tensoes, os resultados da GBT sao bastante satisfatorios no que respeita a tensoes axiais, de corte e de Von Mises, mas distintos dos resultados do ABAQUS no que diz respeito a tensoes normais transversais. No entanto, as distribuicoes 3D de tensoes normais transversais sao qualitativamente semelhantes em todo o dominio da barra.
This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform first-order elastic–plastic analyses of thin-walled members experiencing arbitrary deformations and made of non-linear materials exhibiting isotropic hardening. After presenting the GBT fundamental assumptions and kinematic relationships, the member non-linear equilibrium equations are derived and a non-linear one-dimensional (beam) finite element is formulated. The arc-length control technique is adopted in the numerical solution of the non-linear equations and J2-flow theory is used to model plasticity in conjunction with the Backward Euler return-mapping algorithm. In order to show the capabilities and potential of the implemented formulation, a set of numerical illustrative examples are presented and discussed. For validation purposes, most of the GBT results obtained (equilibrium paths, modal participation diagrams, displacement profiles, stress distributions and deformed configurations) are compared with values yielded by Abaqus shell finite element analyses.
The mechanical behavior of light steel framing (LSF) walls under horizontal (shear) loadings is reported and assessed in this paper. In total, an experimental program with twelve LSF walls (six under monotonic and six under cyclic loading) was conducted, and the main parameters investigated were (i) the thickness and (ii) the material used as the cladding (OSB, a plasterboard, and a steel sheet), (iii) the spacing between fasteners (150 or 75 mm), and (iv) the influence of using steel bracing elements. It is concluded that doubling the number of fasteners and increasing the thickness of OSB by 80% lead to increases in ultimate loads, respectively, of 33 and 13%. The ductility index of the walls with steel sheets was 50 to 75% lower than those of the remaining walls. The wall with the steel strap x-bracing system presented (i) the lowest initial rigidity (a diaphragm effect could not be triggered with these elements) and (ii) the highest damage extent at the end of testing (a damage parameter of 0.85, due to damage of the steel strap-to-steel structure connection). It is confirmed that the results obtained with testing of the walls under a monotonic load can be good predictors of their behavior under cyclic loading as, for instance, the ultimate loads of walls under both loading cases present an average difference of 4%.
This paper gives the formulation and illustrates the application of a generalized beam theory (GBT) developed to analyze the structural behavior of thin-walled members displaying arbitrary orthotropy. First- and second-order GBT equations are derived and physically interpreted, and the GBT equations are then used to investigate the local and global buckling behavior of FRP-lipped channel columns displaying general orthotropy.
After providing a brief overview of a recently developed and validated elastoplastic post-buckling General-ised Beam Theory (GBT) formulation, the paper presents and discusses illustrative numerical results concerning three tubular members exhibiting bi-linear and non-linear material behaviours. The GBT results consist of equilibrium paths, modal participation diagrams, stress contours, displacement profiles and collapse mechanisms, most of which are compared with values obtained from ABAQUS shell finite element analyses. The GBT modal nature makes it possible to (i) acquire in-depth knowledge about the member behavioural mechanics at any given equilibrium state (elas-tic or elastic-plastic), as well as (ii) evidence the GBT computational efficiency (d.o.f. reduction of over 75%), partly due to the exclusion from the analyses of all deformation modes playing no role in a given member response.
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This paper presents a Generalised Beam Theory (GBT) formulation to analyse the local and global buckling behaviour of FRP (fibre-reinforced polymer) composite thin-walled columns with arbitrary open cross-sections, which takes into account both shear deformation and cross-section deformation effects. After describing the steps and procedures involved in performing the GBT cross-section analysis of an arbitrarily branched composite (laminate plate) thin-walled member, the paper addresses the numerical implementation of the proposed GBT formulation, carried out by means of the finite element method (GBT-based beam element) – particular attention is devoted to the derivation of the element linear and geometric stiffness matrices, which incorporate all the material coupling effects. In order to illustrate the application and capabilities of the proposed formulation and implementation, several numerical results are presented and discussed, dealing with the local and global buckling behaviour of FRP composite I-section columns with different ply orientations and stacking sequences. Taking advantage of the GBT modal features, deep insight is acquired on the complex composite member buckling mechanics, namely those involving bending–torsion or global–local coupling effects. In particular, one investigates the influence of (i) the constitutive assumption regarding the transverse extension occurring in the cross-section composite walls and (ii) the distribution of pre-buckling normal stresses (due to axial compression) on the buckling behaviour of I-section columns. For validation purposes, the above results are compared with values recently reported in the literature and estimates obtained from shell finite element analyses.
