Nuno Silvestre

GBT buckling analysis of pultruded FRP lipped channel members

Abstract The main aspects concerning an orthotropic second order generalised beam theory (GBT), previously developed by the authors to enables the structural analysis of thin-walled members displaying special orthotropy, are briefly presented and discussed in the first part of the paper. Special attention is paid to the symbolic and numerical computational aspects related to the implementation of the GBT equations to perform member linear stability analyses. For this purpose, a finite element formulation is developed, validated and applied to solve the eigenvalue problem associated with the GBT system of differential equilibrium equations. Then, the second order orthotropic GBT is employed to investigate the buckling behaviour of pultruded fiber reinforced plastic lipped channel members, namely columns, beams and beam-columns. In particular, with the objective of illustrating the concepts and procedures involved in the performance of a GBT analysis, a detailed in-depth study of simply supported lipped channel columns is presented, in which the relevant (local and global) buckling modes are identified and the corresponding bifurcation stress values are determined. In addition, the results of an investigation concerning the influence of the applied stress distribution, cross-section geometry, material properties and end support conditions on the member buckling behaviour are presented, which required the completion of a number of parametric studies. In these investigations, careful consideration was given to the occurrence and characterisation of local-plate, distortional and mixed flexural–distortional buckling modes.

GBT-based Structural Analysis of Thin-walled members: Overview, Recent Progress and Future Developments

This paper provides an overview of the Generalised Beam Theory (GBT) fundamentals and reports on the novel formulations and applications recently developed at the TU Lisbon: the use of conventional GBT to derive analytical distortional buckling formulae and extensions to cover (i) the buckling behaviour of members with (i1) branched, closed and closed/branched cross-sections and (i2) made of orthotropic and elastic-plastic materials, and (ii) the vibration and post-buckling behaviours of elastic isotropic/orthotropic members. In order to illustrate the usefulness and potential of the new GBT formulations, a few numerical results are presented and briefly discussed. Finally, some (near) future developments are briefly mentioned.

Cold-Formed Steel Lipped Channel Columns Influenced by Local-Distortional Interaction: Strength and DSM Design

This paper deals with the ultimate strength and design of fixed-ended lipped channel columns experiencing local-distortional buckling mode interaction. First, the paper reports the results of an experimental investigation involving a set of 26 columns with several cross-section dimensions and yield stresses that were tested to determine their failure loads and also to provide experimental evidence of the occurrence of local-distortional mode interaction. These results consist of the column geometries, material properties, initial geometric imperfections, nonlinear equilibrium paths, and ultimate strength values. Then, after comparing the experimental column ultimate loads with the estimates provided by the current direct strength method (DSM) design curves against local and distortional failures, which clearly show that they lead to inaccurate and often very unsafe ultimate strength estimates, the paper presents and assesses the quality of DSM-based design procedures based on approaches providing nominal strengths against local-distortional and distortional-local interactive failures. Next, an in-depth comparison is made between all the experimental ultimate strength results available in the literature and their estimates provided by the preceding DSM design procedures. Finally, the paper closes with design considerations and recommendations, motivated by the conclusions drawn from this investigation.

Shear Deformable Generalized Beam Theory for the Analysis of Thin-Walled Composite Members

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.

Liquid crystal boojum-colloids

Colloidal particles dispersed in a liquid crystal (LC) lead to distortions of the director field. The distortions are responsible for long-range effective colloidal interactions whose asymptotic behaviour is well understood. The short-distance behaviour depends on the structure and dynamics of the topological defects nucleated near the colloidal particles and a full nonlinear theory is required to describe it. Spherical colloidal particles with strong planar degenerate anchoring nucleate a pair of antipodal surface topological defects, known as boojums. We use the Landau–de Gennes theory to resolve the mesoscopic structure of the boojum cores and to determine the pairwise colloidal interactions. We compare the results in three (3D) and two (2D) spatial dimensions for spherical and disc-like colloidal particles, respectively. The corresponding free energy functionals are minimized numerically using finite elements with adaptive meshes. Boojums are always point-like in 2D, but acquire a rather complex structure in 3D, which depends on the combination of the anchoring potential, the radius of the colloid, the temperature and the LC elastic anisotropy. We identify three types of defect cores in 3D that we call single, double and split-core boojums, and investigate the associated structural transitions. The split-core structure is favoured by low temperatures, strong anchoring and small twist to splay or bend ratios. For sufficiently strong anchoring potentials characterized by a well-defined uniaxial minimum, the split-core boojums are the only stable configuration. In the presence of two colloidal particles, we observe substantial re-arrangements of the inner defects in both 3D and 2D. These re-arrangements lead to qualitative changes in the force-distance profile when compared to the asymptotic quadrupole–quadrupole interaction. In line with the experimental results, the presence of the defects prevents coalescence of the colloidal particles in 2D, but not in 3D systems.

Colloidal interactions in two-dimensional nematics

Abstract:The interaction between two disks immersed in a 2D nematic is investigated i) analytically using the tensor order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular.

GBT FORMULATION TO ANALYZE THE BUCKLING BEHAVIOR OF THIN-WALLED MEMBERS SUBJECTED TO NON-UNIFORM BENDING

In this paper, one investigates the local-plate, distortional and global buckling behavior of thin-walled steel beams subjected to non-uniform bending moment diagrams, i.e. under the presence of longitudinal stress gradients. One begins by deriving a novel formulation based on Generalized Beam Theory (GBT), which (i) can handle beams with arbitrary open cross-sections and (ii) incorporates all the effects stemming from the presence of longitudinally varying stress distributions. This formulation is numerically implemented by means of the finite element method: one (i) develops a GBT-based beam finite element, which accounts for the stiffness reduction associated to applied longitudinal stresses with linear, quadratic and cubic variation, as well as to the ensuing shear stresses, and (ii) addresses the derivation of the equilibrium equation system that needs to be solved in the context of a GBT buckling analysis. Then, in order to illustrate the application and capabilities of the proposed GBT-based formulation and finite element implementation, one presents and discusses numerical results concerning (i) rectangular plates under longitudinally varying stresses and pure shear, (ii) I-section cantilevers subjected to uniform major axis bending, tip point loads and uniformly distributed loads, and (iii) simply supported lipped channel beams subjected to uniform major axis bending, mid-span point loads and uniformly distributed loads — by taking full advantage of the GBT modal nature, one is able to acquire an in-depth understanding on the influence of the longitudinal stress gradients and shear stresses on the beam local and global buckling behavior. For validation purposes, the GBT results are compared with values either (i) yielded by shell finite element analyses, performed in the code ANSYS, or (ii) reported in the literature. Finally, the computational efficiency of the proposed GBT-based beam finite element is briefly assessed.

Review on concrete nanotechnology

The study of the application of nanotechnology in the construction industry and building structures is one of the most prominent priorities of the research community. The outstanding chemical and physical properties of nanomaterials enable several applications ranging from structural reinforcement to environmental pollution remediation and production of self-cleaning materials. It is known that concrete is the leading material in structural applications, where stiffness, strength and cost play a key role in the high attributes of concrete. This paper reviews the literature on the application of nanotechnology in the construction industry, more particularly in concrete production. The paper first presents general information and definitions of nanotechnology. Then, it focuses on the most effective nanoadditives that readily improve concrete properties, such as (i) nanosilica and silica fume, (ii) nanotitanium dioxide, (iii) iron oxide, (iv) chromium oxide, (v) nanoclay, (vi) CaCO3, (vii) Al2O3, (viii) carbon nanotubes and (ix) graphene oxide. Besides summarising the main nanomaterials used in concrete production as well as the results achieved with each addition, some future potential consequences of nanotechnology development and orientations to explore in construction are discussed.

EXAMINATION OF CYLINDRICAL SHELL THEORIES FOR BUCKLING OF CARBON NANOTUBES

This paper examines the validity and accuracy of cylindrical shell theories in predicting the critical buckling strains of axially loaded single-walled carbon nanotubes (CNTs). The shell theories considered are the Donnell thin shell theory (DST), the Sanders thin shell theory (SST), and the first-order shear deformation (thick) shell theory (FSDST). Molecular dynamic (MD) simulation solutions for armchair and zig-zag CNTs with clamped ends were used as reference results to assess the shell models. The MD simulations were carried out at room temperature to eliminate the thermal effect on the buckling behavior. By adopting Youngs modulus of 5.5 TPa, Poissons ratio of 0.19, and tube thickness of 0.066 nm, it was found that DST is not able to capture the length dependency of the critical buckling strains and thus it should not be used for buckling analysis of CNTs. On the other hand, SST and FSDST are able to predict the critical buckling strains of armchair and zig-zag CNTs reasonably well for all aspect ratios, especially the results produced by the FSDST are found to be closer to the MD simulation results, because it allows for the effect of transverse shear deformation that becomes significant for CNTs with small aspect ratios. Thus, FSDST is recommended as a very suitable and convenient continuum mechanics model for buckling analysis of CNTs. The superior FSDST model is used to generate critical buckling strains of axially loaded single-walled CNT with different boundary conditions. These results should be useful for designers of nanodevices that make use of CNTs as axially loaded members. It is worth noting that for long and moderately long CNTs, the Timoshenko beam model may be used instead due to its simplicity.

ON THE INFLUENCE OF MATERIAL COUPLINGS ON THE LINEAR AND BUCKLING BEHAVIOR OF I-SECTION COMPOSITE COLUMNS

This paper presents the incorporation of shear deformation effects into a Generalized Beam Theory (GBT) developed to analyze the structural behavior of composite thin-walled columns made of laminated plates and displaying arbitrary orthotropy. Unlike other existing beam theories, the present GBT formulation incorporates in a unified fashion (i) elastic coupling effects, (ii) warping effects, (iii) cross-section in-plane deformation and (iv) shear deformation. The main concepts and procedures involved in the available GBT are adapted/modified to account for the specific aspects related to the member shear deformation. In particular, the GBT fundamental equilibrium equations are presented and their terms are physically interpreted. An I-section is used to illustrate the performance of GBT cross-section analysis and the mechanical properties are explained in detail. With the purpose of solving the GBT system of differential equilibrium equations, a finite element formulation is briefly presented. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, the linear (first-order) and stability behavior of three composite I-section members displaying non-aligned orthotropy are analyzed and the results obtained are thoroughly discussed and compared with estimates available in the literature.