A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Elastic lateral buckling of simply supported LiteSteel beams subject to transverse loading

The buckling strength of a new cold-formed hollow flange channel section known as LiteSteel beam (LSB) is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion for its intermediate spans. Recent research has developed a modified elastic lateral buckling moment equation to allow for lateral distortional buckling effects. However, it is limited to a uniform moment distribution condition that rarely exists in practice. Transverse loading introduces a non-uniform bending moment distribution, which is also often applied above or below the shear centre (load height). These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors to allow for these effects. But they were derived mostly based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The moment distribution and load height effects of transverse loading for LSBs, and the suitability of the current design modification factors to accommodate these effects for LSBs is not known. This paper presents the details of a research study based on finite element analyses on the elastic lateral buckling strength of simply supported LSBs subject to transverse loading. It discusses the suitability of the current steel design code modification factors, and provides suitable recommendations for simply supported LSBs subject to transverse loading.

Numerical simulation of axially loaded concrete columns under transverse impact and vulnerability assessment

With a view to assessing the vulnerability of columns to low elevation vehicular impacts, a non-linear explicit numerical model has been developed and validated using existing experimental results. The numerical model accounts for the effects of strain rate and confinement of the reinforced concrete, which are fundamental to the successful prediction of the impact response. The sensitivity of the material model parameters used for the validation is also scrutinised and numerical tests are performed to examine their suitability to simulate the shear failure conditions. Conflicting views on the strain gradient effects are discussed and the validation process is extended to investigate the ability of the equations developed under concentric loading conditions to simulate flexural failure events. Experimental data on impact force–time histories, mid span and residual deflections and support reactions have been verified against corresponding numerical results. A universal technique which can be applied to determine the vulnerability of the impacted columns against collisions with new generation vehicles under the most common impact modes is proposed. Additionally, the observed failure characteristics of the impacted columns are explained using extended outcomes. Based on the overall results, an analytical method is suggested to quantify the vulnerability of the columns.

Elastic lateral buckling of cantilever LiteSteel beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.

Suitable stiffening systems for LiteSteel beams with web openings subjected to shear

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a simultaneous cold-forming and dual electric resistance welding process. It is commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. A cost effective method of eliminating the detrimental effects of a large web opening is to attach suitable stiffeners around the web openings of LSBs. Experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs with circular web openings reinforced using plate, stud, transverse and sleeve stiffeners with varying sizes and thicknesses. Both welding and varying screw-fastening arrangements were used to attach these stiffeners to the web of LSBs. Finite element models of LSBs with stiffened web openings in shear were developed to simulate their shear behaviour and strength of LSBs. They were then validated by comparing the results with experimental test results and used in a detailed parametric study. These studies have shown that plate stiffeners were the most suitable, however, their use based on the current American standards was found to be inadequate. Suitable screw-fastened plate stiffener arrangements with optimum thicknesses have been proposed for LSBs with web openings to restore their original shear capacity. This paper presents the details of the numerical study and the results.

Shear-critical impact response of biaxially loaded reinforced concrete circular columns

A study on the vulnerability of biaxially loaded reinforced concrete (RC) circular columns in multi-story buildings under low- to medium-velocity impacts at shear-critical locations is presented. The study is based on a previously validated nonlinear explicit dynamic finite element (FE) modeling technique developed by the authors. The impact is simulated using force pulses generated from full-scale vehicle impact tests abundantly found in the literature with a view to quantifying the sensitivity of the design parameters of the RC columns under the typical impacts that are representative of the general vehicle population. The design parameters considered include the diameter and height of the column, the vertical steel ratio, the concrete grade, and the confinement effects. From the results of the simulations, empirical equations to quantify the critical impulses for the simplified design of the short, circular RC columns under the risk of shear-critical impacts are developed.

Shear capacity of lipped channel beams with web openings : design rules and improvements

Cold-formed steel Lipped Channel Beams (LCB) with web openings are commonly used as floor joists and bearers in building structures. Shear behaviour of these beams is more complicated and their shear capacities are considerably reduced by the presence of web openings. Hence detailed numerical and experimental studies of simply supported LCBs under a mid-span load with aspect ratios of 1.0 and 1.5 were undertaken to investigate the shear behaviour and strength of LCBs with web openings. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative. Improved design equations were therefore proposed for the shear strength of LCBs with web openings based on both experimental and numerical results. This research showed a significant reduction in shear capacities of LCBs when large web openings are included for the purpose of locating building services. A cost effective method of eliminating such detrimental effects of large circular web openings was also therefore investigated using experimental and numerical studies. For this purpose LCBS were reinforced using plate, stud, transverse and sleeve stiffeners with varying sizes and thicknesses that were welded and screw-fastened to the web of LCBs. These studies showed that plate stiffeners were the most suitable. Suitable screw-fastened plate stiffener arrangements with optimum thicknesses were then proposed for LCBs with web openings to restore their original shear capacities. This paper presents the details of finite element analyses and experiments of LCBs with web openings in shear, and the development of improved shear design rules. It then describes the experimental and numerical studies to determine the optimum plate stiffener arrangements and the results. The proposed shear design rules in this paper can be considered for inclusion in the future versions of cold-formed steel design codes.

Inter-lamellar shear resistance confers compressive stiffness in the intervertebral disc: An image-based modelling study on the bovine caudal disc

The intervertebral disc withstands large compressive loads (up to nine times bodyweight in humans) while providing flexibility to the spinal column. At a microstructural level, the outer sheath of the disc (the annulus fibrosus) comprises 12–20 annular layers of alternately crisscrossed collagen fibres embedded in a soft ground matrix. The centre of the disc (the nucleus pulposus) consists of a hydrated gel rich in proteoglycans. The disc is the largest avascular structure in the body and is of much interest biomechanically due to the high societal burden of disc degeneration and back pain. Although the disc has been well characterized at the whole joint scale, it is not clear how the disc tissue microstructure confers its overall mechanical properties. In particular, there have been conflicting reports regarding the level of attachment between adjacent lamellae in the annulus, and the importance of these interfaces to the overall integrity of the disc is unknown. We used a polarized light micrograph of the bovine tail disc in transverse cross-section to develop an image-based finite element model incorporating sliding and separation between layers of the annulus, and subjected the model to axial compressive loading. Validation experiments were also performed on four bovine caudal discs. Interlamellar shear resistance had a strong effect on disc compressive stiffness, with a 40% drop in stiffness when the interface shear resistance was changed from fully bonded to freely sliding. By contrast, interlamellar cohesion had no appreciable effect on overall disc mechanics. We conclude that shear resistance between lamellae confers disc mechanical resistance to compression, and degradation of the interlamellar interface structure may be a precursor to macroscopic disc degeneration.

Improved prediction of plane transverse jets in supersonic crossflows

THE flowfield due to transverse injection of a round sonic jet into a supersonic flowis a configuration of interest in the design of supersonic combustors or thrust vector control of supersonic jets. The flow is also of fundamental interest because it presents separation from a smooth surface, embedded subsonic regions, curved shear layers, strong shocks, an unusual development of the injected jet into a kidney-shaped streamwise vortex pair, and a wake behind the jet. Although the geometry is simple, the flow is complex and is a good candidate for assessing the behavior of turbulence models for high-speed flow, beginning with the corresponding two-dimensional flow shown in Fig. 1. At the slot, an underexpanded sonic jet expands rapidly into the supersonic crossflow. Expansion waves reflect at the jet boundary, coalesce, and give rise to a Mach surface (Mach disk for round jets).

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Penetration Characteristics of Air, Carbon Dioxide and Helium Transverse Sonic Jets in Mach 5 Cross Flow

An experimental investigation of sonic air, CO2 and Helium transverse jets in Mach 5 cross flow was carried out over a flat plate. The jet to freestream momentum flux ratio, J, was kept the same for all gases. The unsteady flow topology was examined using high speed schlieren visualisation and PIV. Schlieren visualisation provided information regarding oscillating jet shear layer structures and bow shock, Mach disc and barrel shocks. Two-component PIV measurements at the centreline, provided information regarding jet penetration trajectories. Barrel shocks and Mach disc forming the jet boundary were visualised/quantified also jet penetration boundaries were determined. Even though J is kept the same for all gases, the penetration patterns were found to be remarkably different both at the nearfield and the farfield. Air and CO2 jet resulted similar nearfield and farfield penetration pattern whereas Helium jet spread minimal in the nearfield.

In-plane effective shear modulus of generalized circular honeycomb structures and bundled tubes in a diamond array structure

Use of circular hexagonal honeycomb structures and tube assemblies in energy absorption systems has attracted a large number of literature on their characterization under crushing and impact loads. Notwithstanding these, effective shear moduli (G*) required for complete transverse elastic characterization and in analyses of hierarchical structures have received scant attention. In an attempt to fill this void, the present study undertakes to evaluate G* of a generalized circular honeycomb structures and tube assemblies in a diamond array structure (DAS) with no restriction on their thickness. These structures present a potential to realize a spectrum of moduli with minimal modifications, a point of relevance for manufactures and designers. To evaluate G* in this paper, models based on technical theories - thin ring theory and curved beam theory - and rigorous theory of elasticity are investigated and corroborated with FEA employing contact elements. Technical theories which give a good match for thin HCS offer compact expressions for moduli which can be harvested to study sensitivity of moduli on topology. On the other hand, elasticity model offers a very good match over a large range of thickness along with exact analysis of stresses by employing computationally efficient expressions. (C) 2015 Elsevier Ltd. All rights reserved.