No abstract is provided for this article.
This paper presents the incorporation of shear deformation effects into a generalized beam theory (GBT) formulation developed to analyze the first-order (linear) and buckling behavior of composite thin-walled members made of laminated plates displaying arbitrary orthotropy, often designated as anisotropic laminates. Unlike other existing beam theories, the proposed GBT formulation incorporates in a unified fashion (1) elastic coupling effects, (2) warping effects, (3) cross-section in-plane deformation, and (4) shear deformation. The main concepts and procedures involved in the currently available GBT are adapted and/or modified to account for the specific aspects associated with shear deformation. In particular, the GBT equilibrium equations and boundary conditions are derived, and their terms are physically interpreted. A lipped channel section is considered to illustrate the performance of a GBT cross-section analysis, namely, the operations required to determine the (additional) set of shear deformation modes. Finally, to clarify the concepts involved in the proposed GBT formulation and illustrate its application and capabilities, two numerical examples are presented and discussed in detail: the first concerns the first-order and buckling behaviors of a lipped channel column exhibiting nonaligned orthotropy; and the second assesses the influence of shear deformation on the buckling behavior of lipped channel columns with cross-ply orthotropy.
This paper presents an experimental study about the transverse tensile fracture properties of several off-the-shelf pultruded glass fiber-reinforced polymer (GFRP) materials, with different fiber layups and geometries and significant variations of elastic and strength properties. Determining these fracture properties should enable more-accurate advanced numerical simulation of the failure behavior of pultruded GFRP materials and members used in civil engineering applications, namely in the analysis of structural connections or members subjected to concentrated loads (web-crippling phenomenon). For the different GFRP materials, based on compact tension (CT) and wide compact tension (WCT) tests, both the critical energy release rate (Gc) and the cohesive law were determined at the laminate level, applying the following four data reduction methods: standardized analytical expressions, J-integral, Compliance Calibration (CC), and Modified Compliance Calibration (MCC). The CT tests were unsuccessful in reaching a stable propagation stage and provided overestimations of Gc. Conversely, the WCT tests were able to achieve a stable propagation stage and thus provided more-consistent estimates of Gc and cohesive laws. Among the various data reduction methods, a good agreement was found between visually based methods. On the contrary, the MCC method was found to provide significantly lower estimates of Gc when compared with the remainder. Different reasons for this variation are identified and discussed. The sample of GFRP materials presented a significant variation of Gc, which was found to be highly dependent on the fiber architecture: (i) for the material with weaker transverse reinforcement layers, consisting only of continuous filament mats, Gc ranged between 6.6 and 10.7 N/mm; (ii) materials presenting cross-ply layers presented intermediate Gc values, ranging from 13.1 and 21.3 N/mm; and (iii) materials comprising quasi-isotropic layups presented the highest overall Gc estimates, ranging from 19.3 N/mm (similar to cross-ply materials) to above 150 N/mm.
In this paper, the mechanical behavior of CFRP curved stiffened fuselage panels under high velocity transverse impact loading is studied numerically. For that purpose, Abaqus/Explicit is used to perform the numerical study. Firstly, a brief introduction to the topic and a literature review is made. Then, the numerical models are described in detail. Afterwards, the numerical results are presented firstly for five panels with stringers having five different cross-section shapes (T, I, J, C and Ω) with the objective of identifying which cross-section yields the panel most resistant to impact. Secondly, for the panel chosen, a parametric study is conducted considering the influence of the following parameters: (i) location of the impact (aligned or in-between stringers), (ii) angle of impact and (iii) dimension and (iv) shape of the projectile. Finally, the main conclusions of the work are put forward.
No abstract is provided for this article.
This paper proposes, for the first time, a design methodology against the web-crippling failure of pultruded glass fiber–reinforced polymer (GFRP) I-section beams, based on the direct strength method (DSM). This study took into consideration previous experimental and numerical data reported by the authors to calibrate the DSM expression. Approximate formulas were derived to estimate the web-buckling and web-crushing loads for beams under end two flange (ETF) and interior two flange (ITF) loading cases. Finite-element (FE) analyses were also performed to generate complementary data, particularly for higher levels of slenderness, providing a more robust basis for the calibration of the proposed design formulations. Both experimental and numerical results were very well approximated by unified DSM expressions, that fitted both ETF and ITF configurations simultaneously, for a significant variety of materials and section dimensions. Finally, the proposed DSM formula also provides an in-depth and important novelty by identifying the slenderness ranges for which the web-crippling failure is triggered by web crushing, web buckling, or an interaction thereof.
This paper aims to present an original formulation of Generalised Beam Theory (GBT) intended to perform first order elastoplastic analysis of thin-walled members, made of isotropic non-linear material and subjected to arbitrary deformation. The J2-flow theory is used to model plasticity in conjunction with the Euler-Backward return-mapping algorithm. After presenting the formulation, its application is illustrated by means of the first order analysis of beams with (i) rectangular hollow section (RHS) and (ii) LiteSteel section, made of an elastic-perfectly plastic material and subjected to distributed and point loading, respectively. The GBT results, which include equilibrium paths, displacement profiles, stress diagrams, 3D stress/displacement con-tours and deformed shapes, are compared with the ones obtained by ABAQUS code using a shell finite ele-ment model. GBT and ABAQUS results display a very good agreement.
Abordam-se a formulacao e implementacao computacional de elementos finitos de barra baseados na teoria generalizada de vigas (GBT - Generalised Beam Theory), que permitem analisar o comportamento global plano e espacial de estruturas porticadas metalicas a trabalhar em regime elastico. Para isso, torna-se indispensavel estabelecer relacoes cinematicas que permitam assegurar a compatibilidade entre deslocamentos e rotacoes nas ligacoes que unem duas ou mais barras com orientacoes distintas (principalmente no que respeita aos deslocamentos de empenamento). Apos uma breve revisao dos conceitos fundamentais envolvidos numa analise estrutural baseada na GBT, apresentam-se em detalhes a formulacao e implementacao numerica de elementos finitos baseados na GBT que incluem apenas os quatro modos de deformacao de corpo rigido - em particular, descrevem-se os procedimentos envolvidos na determinacao das matrizes de rigidez, linear e geometrica, do elemento finito e do portico (as ultimas devem incorporar a influencia das ligacoes e condicoes de apoio do portico). Em seguida, abordam-se os modelos cinematicos para simular a transmissao do empenamento em ligacoes de porticos que unem duas ou mais barras com seccao em U ou I e exibem tres configuracoes diferentes: continuidade da alma e continuidade dos banzos com reforco em diagonal ou em caixa. Finalmente, com o objectivo de ilustrar a aplicacao e o potencial dos elementos finitos desenvolvidos, apresentam-se e discutem-se resultados numericos relativos ao comportamento linear de um portico simples (com apenas duas barras ortogonais) e a estabilidade de porticos de edificios industriais com travessas inclinadas - validam-se alguns desses resultados pela sua comparacao com valores fornecidos por analises de elementos finitos de barra ou casca (convencionais) efectuadas no programa ANSYS.
In this paper, the buckling behaviour of single-walled carbon nanotubes (CNTs) is revisited by resorting to Donnell and Sanders shell models, which are put in parallel and shown to lead to very distinct results for CNTs with small aspect ratio (length-to-diameter). This paper demonstrates inability of the widely used Donnell shell theory while it shows the validity and accuracy of the Sanders shell theory in reproducing buckling strains and mode shapes of axially compressed CNTs with small aspect ratios. The results obtained by the later shell theory are close to molecular dynamics simulation results.The Sanders shell theory could capture correctly the length-dependent buckling strains of CNTs which the Donnell shell theory fails to achieve. In view of this study, researchers should adopt the Sanders thin shell theory from hereon instead of the Donnell theory when analyzing CNTs with small aspect ratios.
This chapter discusses the use of numerical techniques to perform vibration analysis, the concepts of finite element analysis (FEA) and finite strip analysis (FSA). The literature review in the chapter has been organized according to the particular methodology employed: there are separate sub-sections dealing with investigations carried out by means of (1) the finite element method (mostly shell element discretizations), (2) the finite strip method and (iii) the generalized beam theory (GBT) – because the aim of the chapter is to present the fundamentals and illustrate the application of a GBT formulation to analyze the vibration behavior of thin-walled members, the last sub-section also includes a brief outline of its content. Silvestre and Camotim (2003) formulated, implemented, and validated an efficient beam finite element intended to perform GBT-based buckling analyses in the context of arbitrarily orthotropic thin-walled members. The most relevant steps involved in the formulation of this finite element, specialized for the vibration analysis of isotropic thin-walled members, are described briefly in the chapter.
No abstract is provided for this article.
An accurate prediction of the mechanical behavior of long carbyne chains depends on the suitable modeling of bond alternation in these chains. While first-principles methods are a good approach, less computationally demanding empirical potentials are preferable for large carbyne-containing systems. AIREBO and Reax empirical potentials have extensively and successfully been used for simulating the mechanical behavior of graphene and carbon nanotubes. However, it remains unclear if these potentials can be directly applied in the accurate mechanical modeling of carbon nanostructures with sp hybridization, without re-parameterization. Here, a new force-field for carbyne, designated as C13 potential, that takes bond alternation into account, is presented. This new empirical potential was parameterized from ab initio calculations. Molecular dynamics (MD) simulations using the developed force-field are then conducted to determine the mechanical properties of carbyne chains under tensile loading, namely to assess their dependence on chain length and temperature. The bending stiffness of carbyne and its persistence length are also calculated. The results obtained are validated through comparison with results available in the literature. Lastly, the C13 potential is employed to model, for the first time, the tensile and the compressive behaviors of the hybrid system composed of carbon nanotubes infilled with carbyne chains.
Following the Eurocode 3 philosophy, it is expected that the design of elliptical hollow section (EHS) tubes will be based on the slenderness concept, which requires the calculation of the EHS critical stress. The critical stress of an EHS tube under compression may be associated with local buckling, distortional buckling or flexural buckling. The complexity in deriving analytical expressions for distortional critical stress from classical shell theories, led us to apply Artificial Neural Networks (ANN). This paper presents closed-form expressions to calculate the distortional critical stress and half-wave length of EHS tubes under compression, using ANN. Almost 400 EHS geometries are used and based solely on three parameters: the outer EHS dimensions (A and B) and its thickness (t). Two architectures are shown to be successful. They are tested for several statistical parameters and proven to be very well behaved. Finally, some simple illustrative examples are shown and final remarks are drawn concerning the accuracy of the closed-formed formulas.
An investigation on the distortional post-buckling behaviour of cold-formed steel Z-section columns and beams is presented. All the results are obtained by means of geometrically non-linear analyses based on a recently developed GBT formulation, which incorporates (i) conventional (shear undeformable), (ii) shear (non-linear warping) and (iii) transverse extension deformation modes. The results presented, most of which are compared with shell-element FEM analyses (for validation purposes), include post-buckling equilibrium paths and the evolution, along those paths, of the member deformed configuration and relevant displacements or stresses. Taking advantage of the GBT unique modal features, these results are discussed in great detail and it is possible to unveil, explain and/or shed some new light on a number of interesting and scarcely known phenomena.
