This computational study conducts a comprehensive all-scale analysis to predict the mechanical behavior (elasticity and strength) of polyimide matrices (Kapton@) reinforced with carbon nanostructures, spanning nanoscale, microscale, mesoscale, and macroscale. Representative volume elements at each scale undergo tensile and shear loadings to extract mechanical properties. Homogenization techniques are applied to transition between scales, considering these properties. Two nanostructures (graphene and γ-graphyne) are explored as reinforcements, evaluating the influence of volume fraction and orientation on composite mechanical properties. Results are validated through comparison with theoretical, computational, and experimental studies. Composite materials exhibited significant improvements in stiffness (up to 44% at a volume fraction of 0.5%) and tensile strength (up to 25% at a volume fraction of 0.5%) compared to the pristine polymeric matrix.
This paper reports the results of an investigation on the use of Generalized Beam Theory (GBT) to assess the buckling and vibration behaviors of thin-walled members and frames built from cold-formed steel circular hollow section (CHS) profiles. Initially, the concepts and procedures involved in performing GBT buckling and vibration analyses are presented, paying particular attention to the derivation of the mass tensors that account for the influence of the inertia forces. Then, the formulation, numerical implementation and validation of a GBT-based beam finite element for isolated members are described. Next, the determination of the frame linear stiffness, geometric stiffness and mass matrices, which incorporate the influence of the frame joints, is addressed. Finally, in order to illustrate the application and capabilities of the proposed GBT finite element formulation, numerical results are presented and discussed — they concern the buckling and vibration behaviors of an "L-shaped" frame. For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code ANSYS.
Following recent investigations on the decomposition of elastic buckling modes into combinations of structurally meaningful deformation modes, this work presents a novel extension of the above procedure to elastic–plastic collapse mechanisms and highlights the relevant role that this concept may play in the mechanical knowledge/interpretation of thin-walled member failures. In order to achieve the sought decomposition, a code based on a Generalised Beam Theory (GBT) formulation developed to perform first-order elastic–plastic analyses of thin-walled members is employed. Five illustrative examples are presented and discussed, and the results displayed, namely load-deflection curves, deformed configurations and stress contours, are validated through the comparison with values provided by shell finite element analyses. The most relevant modal results addressed consist of (i) load-deflection curves determined on the basis of pre-selected deformation mode sets, (ii) modal participation diagrams and (iii) modal amplitude functions. These results make it easy to characterise and interpret the mechanics associated with the thin-walled member elastic–plastic failures (as well as with the various loading stages), which may be of great importance in the improvement/development of existing/new design methods (e.g, yield-line theory, direct strength method).
No abstract is provided for this article.
This paper presents a study on the influence of the deformation mode nature (global, local, distortional) on the load carrying capacity of beams beyond the yield load. Following recent investigations on the decomposition of elastic buckling modes into combinations of structurally meaningful deformation modes, this work applies the same concept to the 1st order failure modes (elastic-plastic collapse mechanisms). To achieve this goal, a GBT-based code that performs first-order elastic-plastic analyses of thin-walled members is employed. In order to study the influence of the mode nature on the post-yielding strength, five beams with different cross-sections, lengths, supports and loadings are analysed, and the results displayed by means of load-deflection curves, failure mode configurations and modal participation diagrams. On the basis of the limited study performed, it is concluded that larger contributions of local and distortional modes to the beam failure mode lead to a higher post-yielding strength reserve, which implies a higher beam load carrying capacity beyond the yield load. The opposite occurs for the contributions of global modes. Therefore, the member strength reserve obtained in geometrically non-linear analysis should not be credited only to the elastic post-buckling effects, but also to the plastic post-yielding effects.
The unceasing upgrading of techniques and processes to fabricate high purity carbon nanotubes (CNTs) and the improvement of the available techniques to produce high performance matrix materials, have fostered the way to enhance composite materials and their properties, either mechanical, thermal, electrical or magnetic. CNTs reinforcements have been introduced into polymers, ceramics, cement-based materials and metals. Po ly mers were the first material to be explo ited as matrix material being reinforced by CNTs. Up to now other materials have tentatively been investigated for that purpose, including metals. Today, many applications of CNT reinforced co mposites exist but CNT reinfo rced metals are still scarce and only found in very specific applications. Several reasons can be identified but the still gro wing demand for lighter and stronger metals paved the way to more fundamental research on the topic of CNT reinforced metal matrix co mposites (MMCs). Th is review describes the state-of-the art in this field and highlights the excellent and promising mechanical, thermal, electrical properties of CNT reinforced MM Cs.
The computational modelling of the flange crushing phenomenon in cold-formed steel profiles is described in this paper, with particular emphasis to the development of shell finite element (SFE) models and performance of quasi-static analyses with an explicit integration scheme. Web crippling failure is widely recognised as the most relevant collapse mode of cold-formed steel members subjected to transverse concentrated loads. However, it has been experimentally and numerically observed that a somewhat different collapse mode may occur, due to the heavy stress concentrations stemming from the adoption of narrow bearing plates. This phenomenon, termed flange crushing, should not be confused with web crippling. Usually, the web crippling phenomenon is numerically investigated by means of non-linear static SFE models with an implicit integration scheme. In this study, SFE models are developed in ABAQUS code to study the flange crushing failure of a plain channel beam subjected to Internal Two Flange (ITF) loading conditions. These models are described in detail, as well as additional modelling concerns regarding quasi-static analyses and the explicit integration method. Different parameters are discussed in this article and the numerical results obtained are commented throughout. Such parameters include the (i) SFE type and mesh, (ii) load rate, mass scaling, adoption of smoothed displacement amplitude curves and control of inertial effects, (iii) contact and friction definitions, (iv) effects of forming cold-work and manufacturing process and (v) geometrical imperfections. Finally, the load–displacement response obtained with the quasi-static model and an equivalent non-linear static analysis are compared with the experimental test curves. It is concluded that very good results are achieved with the quasi-static approach, not only in terms of the ultimate load prediction, but also regarding the post-collapse load–deflection curve and the failure mechanism.
A coupled (two-step) numerical procedure to characterize the mechanical behaviour of Rubberized Concrete (RuC) is proposed and validated in this paper. In particular, the splitting tensile strength test is described in detail. In the first step, MATLAB Image Processing is used to obtain the model geometry and the RuC heterogeneous configuration (distribution of rubber particles within the concrete matrix). In the second step, the Extended Finite Element Method (XFEM) included in ABAQUS software is used to simulate the inelastic behaviour of the concrete matrix and allow the nucleation and development of cracks, as well as the damage evolution and ultimate strength of the RuC specimen cross-section. Additionally, a set of experimental results on mechanical behaviour of RuC is presented. This shows that RuC has both lower strength and stiffness but higher ductility (less brittle behaviour) than normal concrete (NC). Finally, a good agreement between the two-step procedure results and the experimental results (in terms of indirect tensile strength, stiffness and failure mode) is observed.
A theoretical investigation on the strength and stiffness of carbon nanotubes (CNTs) under combined shortening and twisting strains is presented. CNTs with similar length-to-diameter aspect ratios, L/D, but different atomic structures (zig-zag, armchair and chiral) have been selected. Molecular dynamics (MD) simulations have been performed to study the critical buckling behaviour and the pre-critical and post-critical stiffness of CNTs under combined shortening–twisting conditions. The main results are presented in the form of interaction diagrams between the critical strain and the critical angle of twist per unit of length. An interaction equation is proposed and validated by comparison with the MD results. If shortening is more dominant than twisting, the strain energy at the onset of buckling drops considerably with the increase of the twisting–shortening rate. If twisting is more influential than shortening, the energy at the onset of buckling decreases very slowly with the twisting–shortening rate. We also found an interaction factor of 1.5 for CNTs under combined shortening–twisting, which is much lower than the value 2.0 commonly adopted for circular tubes at macro-scale. We conclude that CNTs are much more sensitive to buckling under shortening–twisting interaction than macro-scale tubes.
A GBT formulation for 1st order elastoplastic analysis is presented and its application illustrated for a elastic-perfectly plastic simply supported I-setion beam subjected to point loads at mid-span. GBT results were validated against ABAQUS by means of shell finite element models. There is an excellent agreement in that comparison, particularlly regarding equilibrium paths and deformed configurations. With respect to stress diagrams, GBT results are very satisfactory for axial, shear and von Mises stresses, but distinct with respect to transverse normal stresses. However, the transverse normal stress 3D contours are qualitatively similar between GBT and ABAQUS in the whole beam domain.
No abstract is provided for this article.
The Part 2 of this two-part paper reports numerical and analytical studies concerning the serviceability dynamic behaviour under dynamic human loads of a typical GFRP-steel hybrid girder system for pedestrian bridges. These studies, which focused on the recent St. Mateus footbridge (Portugal), had two main objectives: (i) to assess the ability of conventional numerical models and analytical formulae to simulate the vibration behaviour of GFRP-steel hybrid footbridges; and (ii) to complement the observations and measurements made in the experimental campaign (Part 1), thus providing in-depth understanding of the vibration performance of this type of footbridges. First, a finite element (FE) model was developed and calibrated with the static and modal experimental data. Then, the FE-model was used to evaluate the vibration response of the footbridge for the same pedestrian activities induced in situ. The design formulae available in the literature for predicting the maximum acceleration of structural systems are also reviewed and were applied to evaluate the resonant response of the footbridge for both single and crowded conditions of pedestrian traffic. The results obtained confirmed the adequate structural behaviour of the St. Mateus footbridge under real dynamic (human) pedestrian load cases and show that this innovative GFRP-steel hybrid structural solution is suitable for pedestrian bridges. The results of the different investigations reported in this paper also showed that both numerical and analytical approaches are able to predict the vibration response of GFRP-steel hybrid footbridges with reasonable accuracy.
No abstract is provided for this article.
This paper presents an overview of the mechanics of distortion in members which have restrained thin-walled steel sections. First, the basic features that characterize the distortion of thin-walled sections under compression and/or bending are explained and the generally adopted kinematical assumptions are presented and discussed. On the basis of these assumptions, a simple procedure to build the distortional displacement fields is proposed. Then, two illustrative examples of restrained sections are given and their distortional displacement fields are built. The I-section illustrates the case of a symmetric section having a distortional displacement field with a single d.o.f. The Z-section exemplifies the case of a non symmetric section having a distortional field with two d.o.f. Based on an energy formulation, the equilibrium equation for buckling analysis of simply supported thin-walled members is derived. For two illustrative examples, the distortional displacement field is used to obtain distortional analytical formulae. Finally, some results (buckling loads and moments) were determined and validated by means of comparison with fully numerical obtained from finite strip analysis.
A formulation of generalised beam theory (GBT) developed to analyse the elastic buckling behaviour of circular hollow section (CHS) members (cylinders and tubes) is presented in this paper. The main concepts involved in the available GBT are adapted to account for the specific aspects related to cross-section geometry. Taking into consideration the kinematic relations used in the theory of thin shells, the variation of the strain energy is evaluated and the terms are physically interpreted, i.e., they are associated with the geometric properties of the CHS. Besides the set of shell-type deformation modes, the formulation also includes axisymmetric and torsion deformation modes. In order to illustrate the application and capabilities of the formulated GBT, the local and global buckling behaviour of CHS members subjected to (i) compression (columns), (ii) bending (beams), (iii) compression and bending (beam-columns) and (iv) torsion (shafts), is analysed. Moreover, the GBT results are compared with estimates obtained by means of shell finite element analyses and are thoroughly discussed.
