This paper presents several issues that characterize the buckling behaviour of elliptical cylindrical shells and tubes under compression. First, a formulation of Generalised Beam Theory (GBT) developed to analyse the elastic buckling behaviour of non-circular hollow section (NCHS) members is presented. Since the radius varies along the cross-section mid-line, the main concepts involved in the determination of the deformation modes are adapted to account for the specific aspects related to elliptical cross-section geometry. After that, two independent sets of fully orthogonal deformation modes are determined: (i) local-shell modes satisfying the null membrane shear strain but exhibiting transverse extension and (ii) shell-type modes satisfying both assumptions of null membrane shear strain and null transverse extension. In order to illustrate the application, capabilities and versatility of the formulation, the local and global buckling behaviour of elliptical hollow section (EHS) members subjected to compression is analysed. In particular, in-depth studies concerning the influence of member length on the variation of the critical load and corresponding buckling mode shape are presented. Moreover, the GBT results are compared with estimates obtained by means of shell finite element analyses and are thoroughly discussed. The results show that short to intermediate length cylinders buckle mostly in local-shell modes, exhibiting only transverse extension, while intermediate length to long cylinders buckle mostly in shell-type modes (distortional and global modes), which are characterized by transverse bending and primary warping displacements. It is also shown that the present formulation is very efficient from the computational point of view since only three deformation modes (one local-shell, one distortional and one global) are required to evaluate the buckling behaviour of EHS cylinders for a wide range of lengths.
The synthesis of long and stable carbyne chains inside carbon nanotubes (CNTs) have recently drawn renewed attention to this linear one-dimensional carbon allotrope. Carbyne's mechanical properties are predicted to exceed that of CNTs and graphene, making it a very suitable structural component for many nanoscale applications. While carbyne's mechanical behavior under tensile loading is excellent, this carbon chain readily buckles under compressive loading. Taking this effect into account, here we study the compressive behavior of carbyne chains under the bracing effect of confinement in small diameter CNTs such as (5,5) and (6,6) and the formation of helix-shaped springs of carbyne under compressive loading in larger diameter CNTs such as (7,7) and (8,8), using molecular dynamics simulations (MD). The Young's modulus of confined carbyne chains under compression was estimated in average to be 4029 GPa when confined in (5,5) CNT and 3858 GPa when confined in (6,6) CNT, showing slight increases with chain length. We found that for looser confinements carbyne chains can buckle into a coiled helix-shaped spring with properties that depend on confinement radius and chain length. The behavior of these nanosprings follows Hooke's law and may be envisaged for applications in nanodevices.
The 6th International Conference on Advances in Steel Structures in conjunction with IJSSD Symposium on Progress in Structural Stability and Dynamics & IStructE Asia-Pacific Forum (ICASS'09 / IJSSD / IStructE Asia-Pacific Forum), Hong Kong, China, 16-18 December 2009. In Proceedings of the 6th International Conference on Advances in Steel Structures, 2009, p. 470-479
Apresentam-se, nesse trabalho, os resultados de uma investigação em curso sobre a utilização do Método da Resistência Directa (MRD) para estimar a resistência última de colunas e vigas de seção em C afetadas por fenômenos de interação entre modos de instabilidade locais-de-placa e distorcionais. Inicialmente, faz-se uma breve descrição das fórmulas do MRD, destinadas a verificar a segurança de colunas e vigas em relação ao colapso em modos distorcionais, e aborda-se, também, uma extensão recentemente proposta para tomar em consideração os fenômenos de interação referidos anteriormente. Em seguida, descrevem-se os resultados de um estudo paramétrico, efetuado com o programa Abaqus, em que se determinam os valores "exatos" da resistência última de 108 colunas e 90 vigas com diversas geometrias (dimensões da seção transversal e comprimento), todas elas escolhidas de forma a garantir a relevância dos efeitos da interação entre modos de instabilidade locais-de-placa e distorcionais. Finalmente, faz-se a comparação entre esse conjunto de valores da resistência última e as estimativas fornecidas pelas fórmulas do MRD atualmente existentes e, com base nas conclusões dessa comparação, identificam-se alguns aspectos que devem, obrigatoriamente, ser incluídos numa nova abordagem baseada no MRD, para que esta possa refletir, adequadamente, a influência dos fenômenos de interação local-de-placa/distorcional.
A new gradient-enhanced strain-tensor formulation for finite-strain problems is introduced, based on the Raviart-Thomas face-interpolation scheme and the Hellinger-Reissner variational principle. The screened-Poisson equation is employed to relate the kinematic Green-Lagrange strain with the mixed strain. The strain vector obtained from the face normals is now a (vector) degree-of-freedom at each face. In contrast with variational multiscale methods, there are no parameters to fit and stability in compression is verified. When compared with smoothed finite-elements, the formulation is straightforward and sparsity pattern of the classical system retained, albeit with high computational cost. In contrast with traditional gradient-enhanced formulations, a theoretically sound mixed formulation underlies the algorithm. High accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being solved. Traditional finite-strain benchmarks and a quasi-brittle damage numerical test are performed, with very competitive results.
This paper presents experimental, numerical and analytical studies on the flexural behavior of I-section hybrid fiber reinforced polymer (FRP) beams made of glass fibers (GF) and carbon fibers (CF) pultruded together and embedded in a polyester matrix. A reference profile (all-GFRP) and five series of hybrid C-GFRP profiles, with different types and architectures of CF reinforcement were tested under four-point bending to assess their structural response up to failure. The experimental results confirmed the effectiveness of hybridization in increasing the bending stiffness of pultruded beams. The experimental tests were simulated using finite element models with Hashin damage criterion to study the material progressive failure and delamination. Numerical results showed a good agreement with the experimental data both in terms of loading path and ultimate load. The design approaches of the Italian Guide and American Pre-Standard were assessed, the former being more accurate and conservative than the latter.
This paper presents a study on the mechanical behaviour of copper (Cu) nanocomposites reinforced with carbon nanotubes (CNTs) using Molecular Dynamics (MD). Tensile and compressive loadings are applied to two limit boundary conditions of CNT: (i) case A – loading applied to the Cu matrix (the embedded CNT is not loaded) and (ii) case B – loading applied to both Cu matrix and embedded CNT. The reference case (Cu matrix without CNT) is also considered. Curves of energy and stress vs. strain are presented and mechanical properties (Young's modulus, yield stresses and strains) are calculated. In the first case, the CNT has an overall detrimental effect to the CNT-Cu nanocomposite, reducing yield strains and stresses, while showing residual effect to the Young's modulus. In the second case, the Young's modulus and strengths (tensile and compressive) increase reasonably while the yield strains decrease fairly. This study shows that the CNT might increase the stiffness and strength of the nanocomposite, but also decrease its ductility. Additionally, this work also reports atomic stress distributions, dislocation patterns and crystalline structures of the loaded CNT-Cu nanocomposite, which explain not only the failure mechanisms but also the differences between compressive and tensile behaviours.
As extensions to our Lagrangian finite-strain plasticity framework based on the approximate exponential integrator, we introduce two new algorithms: (i) a fixed-radius trust region root finder for the nonlinear system involving the elastic right Cauchy Green tensor and plastic multiplier (ii) a partitioned approach for the hardening variables, which are determined in a staggered form using the strongly-coupled concept typically adopted for multiphysics problems. This allows the use of intricate hyperelastic laws combined with recent yield functions, which otherwise would involve a laborious treatment, and the use of corresponding work-hardening. Work-hardening would introduce significant nonlinearities in the constitutive system if used in a fully-coupled form. For the partitioned approach, a dynamic relaxation algorithm is adopted. This allows the efficient solution of the two nonlinear equations without significant drifting. Results show that robustness and efficiency are significantly improved. Herein, algorithms are described in detail. Significant testing is performed with imposed strains up to 100 for a carbon steel. This contributes to the robustness of equilibrium iterations. Drifting is also assessed as a function of number of steps in the dynamic relaxation algorithm. Numerical experimentation is performed in the 3D tension test for an anisotropic yield function.
Due to their prominent properties (mechanical, stiffness, strength, thermal stability), ceramic composite materials (CMC) have been widely applied in automotive, industrial and aerospace engineering, as well as in biomedical and electronic devices. Because monolithic ceramics exhibit brittle behaviour and low electrical conductivity, CMCs have been greatly improved in the last decade. CMCs are produced from ceramic fibres embedded in a ceramic matrix, for which several ceramic materials (oxide or non‐oxide) are used for the fibres and the matrix. Due to the large diversity of available fibres, the properties of CMCs can be adapted to achieve structural targets. They are especially valuable for structural components with demanding mechanical and thermal requirements. However, with the advent of nanoparticles in this century, the research interests in CMCs are now changing from classical reinforcement (e.g., microscale fibres) to new types of reinforcement at nanoscale. This review paper presents the current state of knowledge on processing and mechanical properties of a new generation of CMCs: Ceramics Nanocomposites (CNCs).
This work is part of an ongoing investigation aimed at comparing the mechanics underlying the application of generalized beam theory (GBT) and the constrained finite strip method (cFSM), two alternative modal approaches to analyze the elastic buckling behavior of open-sectional unbranched thin-walled members. Previous work included an overall comparison between the numerical results yielded by the two approaches for lipped channel columns and beams, which were shown to be essentially identical — the few minor discrepancies were fully explained. The next step consists of revisiting the kinematical assumptions and procedures adopted by GBT to identify and characterize the cross-sectional deformations modes, presenting, explaining, and interpreting them from a novel perspective, deemed more suitable for a true comparison with the displacement field constraints employed in cFSM — the main objective of this paper. The starting point is the derivation of the conventional finite strip method (FSM), intended to show that some of the corresponding matrices also appear in GBT. Indeed, it is demonstrated that the determination of the GBT deformation modes involves a set of particular FSM matrices, termed "cross-sectional matrices." After a brief comparison between the GBT and cFSM assumptions and procedures, an illustrative example is presented and discussed, in order to provide a better grasp of the concepts and procedures involved in the new approach to the GBT deformation mode determination. Finally, the paper closes with a few concluding remarks that also address the work to be carried out in the near future.
This paper reports on the use of a recently developed Generalised Beam Theory (GBT) formulation, and corresponding finite element implementation, to analyse the local and global buckling behaviour of thin-walled members with arbitrary loading and support conditions — this formulation takes into account longitudinal normal stress gradients and the ensuing pre-buckling shear stresses. After presenting an overview of the main concepts and procedures involved in the performance of a GBT-based (beam finite element) member buckling analysis, one addresses in detail the incorporation of non-standard support conditions, such as (i) full or partial localised displacement or rotation restraints, (ii) rigid or elastic intermediate supports or (iii) end supports corresponding to angle connections. In order to illustrate the application and capabilities of the proposed GBT-based approach, one presents and discusses numerical results concerning cold-formed steel (i) lipped channel beams and (ii) lipped I-section beams and columns with various “non-standard” support conditions — while the beams are acted by uniformly distributed or mid-span point loads, applied at the shear centre axis, the columns are subjected to uniform compression. In particular, it is possible to assess the influence of the different support conditions on the beam and column buckling behaviour (critical buckling loads and mode shapes). For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code Ansys.
No abstract is provided for this article.
This paper presents an experimental study about the fire resistance behaviour of pultruded glass fibre reinforced polymer (GFRP) beams. The main objectives of the study were to evaluate the influence on the fire resistance of GFRP beams of (i) the number of sides exposed to fire; (ii) the load level applied, and (iii) using different fire protection systems. To this end, a total of 12 GFRP tubular beams were exposed to the time-temperature curve of ISO 834, in either one or three sides, and simultaneously subjected to two different load levels corresponding to mid-span deflections of L/400 or L/250, L being the span. Different passive and active fire protection systems were assessed, including thick insulation boards, intumescent products and water-cooling. The results obtained show that three-side exposure causes a remarkable reduction of fire resistance, compared to one-side exposure, for both unprotected and protected profiles, highlighting the importance of adopting a building architecture with GFRP beams integrated in the floors. The efficacy of water-cooling for one-side exposure was confirmed; however, for three-side exposure it is shown that only passive protection is able to significantly extend the fire endurance of GFRP pultruded profiles. As expected, increasing the load level caused a (moderate) reduction of fire resistance.
Due to their outstanding mechanical, thermal, and durability properties, polymer matrix nanocomposites (PMCs) are currently a prominent area of research. The opportunity of applying PMCs in structural reinforcement and rehabilitation of damaged infrastructures, as well as working as a new structural material, justifies the increasing number of recent studies. In this review article, the effect of adding different reinforcements at nano-scale, such as carbon nanotubes, nanoclay, graphene, or nanosilica to polymer matrices, is discussed and the improvement in mechanical properties of PMCs is evaluated. Some concluding remarks and new perspectives on the use of PMCs in structures are given.
This paper reports the results of a numerical investigation concerning the elastic and elastic–plastic post-buckling behaviour of cold-formed steel lipped channel columns affected by local-plate/distortional buckling mode interaction. The results presented and discussed were obtained through analyses performed using the finite element code Abaqus and discretising the columns by means of fine 4-node shell element meshes. The columns analysed (i) are simply supported (end sections locally/globally pinned and free-to-warp), (ii) have cross-section dimensions that ensure equal local-plate and distortional critical buckling stresses, thus maximising the local-plate/distortional mode interaction effects, and (iii) contain critical-mode initial geometrical imperfections that exhibit different shapes but share the same combined amplitude. The numerical post-buckling results reported consist of (i) elastic and elastic–plastic non-linear equilibrium paths, (ii) curves and figures describing how the column deformed configuration (expressed as a linear combination of its local-plate and distortional components) evolves along the elastic post-buckling equilibrium paths and (iii) figures providing a clear visualisation of the (iii1) evolution of the elastic–plastic column deformed configurations, (iii2) the growth of the plastic strains and (iii3) failure mechanisms exhibited by a fairly large portion of the elastic–plastic columns that were analysed in this work.
