Finite volume approach of natural convection in a triangular enclosure with localized heating from below

In this study, natural convection heat transfer and buoyancy driven flows have been investigated in a right angled triangular enclosure. The heater located on the bottom wall while the inclined wall is colder and the remaining walls are maintained as adiabatic. Governing equations of natural convection are solved through the finite volume approach, in which buoyancy is modeled via the Boussinesq approximation. Effects of different parameters such as Rayleigh number, aspect ratio, prantdl number and heater location are considered. Results show that heat transfer increases when the heater is moved toward the right corner of the enclosure. It is also revealed that increasing the Rayleigh number, increases the strength of free convection regime and consequently increases the value of heat transfer rate. Moreover, larger aspect ratio enclosure has larger Nusselt number value. In order to have better insight, streamline and isotherms are shown.

Finite element shoulder models

Shoulder joint is a complex integration of soft and hard tissues. It plays an important role in performing daily activities and can be considered as a perfect compromise between mobility and stability. However, shoulder is vulnerable to complications such as dislocations and osteoarthritis. Finite element (FE) models have been developed to understand shoulder injury mechanisms, implications of disease on shoulder complex and in assessing the quality of shoulder implants. Further, although few, Finite element shoulder models have also been utilized to answer important clinical questions such as the difference between a normal and osteoarthritic shoulder joint. However, due to the absence of experimental validation, it is questionable whether the constitutive models applied in these FE models are adequate to represent mechanical behaviors of shoulder elements (Cartilages, Ligaments, Muscles etc), therefore the confidence of using current models in answering clinically relevant question. The main objective of this review is to critically evaluate the existing FE shoulder models that have been used to investigate clinical problems. Due concern is given to check the adequacy of representative constitutive models of shoulder elements in drawing clinically relevant conclusion. Suggestions have been given to improve the existing shoulder models by inclusion of adequate constitutive models for shoulder elements to confidently answer clinically relevant questions.

A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

Cohesive zone modelling of mineralized collagen fibril arrays in bending

Hard biological materials such as bone possess superior material properties of high stiffness and toughness. Two unique characteristics of bone microstructure are a large aspect ratio of mineralized collagen fibrils (MCF), and an extremely thin and large area of extrafibrillar protein matrix located between the MCF. The objective of this study is to investigate the effects of: (1) MCF aspect ratio, and (2) energy dissipation in extrafibrillar protein matrix on the mechanical behaviour of MCF arrays. In this study, notched specimens of MCF arrays in extrafibrillar protein matrix are subjected to bending. Cohesive zone model was implemented to simulate the failure of extrafibrillar protein matrix. The study reveals that the MCF array with a higher MCF aspect ratio and the MCF array with a higher protein energy dissipation in the interface direction are able to sustain a higher bending force and dissipate higher energy.

Review of current fire design rules for cold-formed steel wall systems

Light gauge steel frame wall systems are commonly used in industrial and commercial buildings, and there is a need for simple fire design rules to predict their load capacities and fire resistance ratings. During fire events, the light gauge steel frame wall studs are subjected to non-uniform temperature distributions that cause thermal bowing, neutral axis shift and magnification effects and thus resulting in a combined axial compression and bending action on the studs. In this research, a series of full-scale fire tests was conducted first to evaluate the performance of light gauge steel frame wall systems with eight different wall configurations under standard fire conditions. Finite element models of light gauge steel frame walls were then developed, analysed under transient and steady-state conditions and validated using full-scale fire tests. Using the results from fire tests and finite element analyses, a detailed investigation was undertaken into the prediction of axial compression strength and failure times of light gauge steel frame wall studs in standard fires using the available fire design rules based on Australian, American and European standards. The results from both fire tests and finite element analyses were used to investigate the ability of these fire design rules to include the complex effects of non-uniform temperature distributions and their accuracy in predicting the axial compression strength of wall studs and the failure times. Suitable modifications were then proposed to the fire design rules. This article presents the details of this investigation on the fire design rules of light gauge steel frame walls and the results.

Computational analysis of laminated glass panels under blast loads: A comparison of two dimensional and three dimensional modelling approaches

This paper illustrates the use of finite element (FE) technique to investigate the behaviour of laminated glass (LG) panels under blast loads. Two and three dimensional (2D and 3D) modelling approaches available in LS-DYNA FE code to model LG panels are presented. Results from the FE analysis for mid-span deflection and principal stresses compared well with those from large deflection plate theory. The FE models are further validated using the results from a free field blast test on a LG panel. It is evident that both 2D and 3D LG models predict the experimental results with reasonable accuracy. The 3D LG models give slightly more accurate results but require considerably more computational time compared to the 2D LG models.

Local stress-strain distribution and load transfer across cartilage matrix at micro-scale using combined microscopy-based finite element method

Articular cartilage is the load-bearing tissue that consists of proteoglycan macromolecules entrapped between collagen fibrils in a three-dimensional architecture. To date, the drudgery of searching for mathematical models to represent the biomechanics of such a system continues without providing a fitting description of its functional response to load at micro-scale level. We believe that the major complication arose when cartilage was first envisaged as a multiphasic model with distinguishable components and that quantifying those and searching for the laws that govern their interaction is inadequate. To the thesis of this paper, cartilage as a bulk is as much continuum as is the response of its components to the external stimuli. For this reason, we framed the fundamental question as to what would be the mechano-structural functionality of such a system in the total absence of one of its key constituents-proteoglycans. To answer this, hydrated normal and proteoglycan depleted samples were tested under confined compression while finite element models were reproduced, for the first time, based on the structural microarchitecture of the cross-sectional profile of the matrices. These micro-porous in silico models served as virtual transducers to produce an internal noninvasive probing mechanism beyond experimental capabilities to render the matrices micromechanics and several others properties like permeability, orientation etc. The results demonstrated that load transfer was closely related to the microarchitecture of the hyperelastic models that represent solid skeleton stress and fluid response based on the state of the collagen network with and without the swollen proteoglycans. In other words, the stress gradient during deformation was a function of the structural pattern of the network and acted in concert with the position-dependent compositional state of the matrix. This reveals that the interaction between indistinguishable components in real cartilage is superimposed by its microarchitectural state which directly influences macromechanical behavior.

Two-scale computational modelling of unsaturated flow in soils exhibiting small scale heterogeneities

Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

Numerical modelling and design of lipped channel beams subject to shear

Cold-formed steel members are increasingly used as primary structural elements in buildings due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. Many research studies have been carried out to evaluate the behaviour and design of LCBs subject to pure bending actions. However, limited research has been undertaken on the shear behaviour and strength of LCBs. Hence a numerical study was undertaken to investigate the shear behaviour and strength of LCBs. Finite element models of simply supported LCBs with aspect ratios of 1.0 and 1.5 were considered under a mid-span load. They were then validated by comparing their results with test results and used in a detailed parametric study based on the validated finite element models. Numerical studies were conducted to investigate the shear buckling and post-buckling behaviour of LCBs. Experimental and numerical results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LCBs. Improved design equations were therefore proposed for the shear strength of LCBs. This paper presents the details of this numerical study of LCBs and the results.

Experimental and finite element analysis to identify the source of vibration of a coach

This paper presents an investigation on the cause of severe vibration problem of a coach with four-cylinder engine running at an idle state using vibration and impact hammer modal experiments to obtain the main vibration frequency components and the natural characteristics of the coach. The vibration results indicate that the main vibration component comes from the vibration transmitted from the engine to the chassis frame, which is closely related with the engine idle speed. Based on structural simulation analysis of the coach’s chassis frame and comparison with modal testing, the coach severe vibration problem was due to coupling resonance between the engine idle frequency and the fourth natural frequency of the chassis frame. The solution to eliminate the vibration problem is provided by changing the local structure stiffness of the chassis frame. The contribution of this paper lies in providing a solution to solve similar problems.

Numerical modelling and analysis of the blast performance of laminated glass panels and the influence of material parameters

This paper presents a comprehensive numerical procedure to treat the blast response of laminated glass (LG) panels and studies the influence of important material parameters. Post-crack behaviour of the LG panel and the contribution of the interlayer towards blast resistance are treated. Modelling techniques are validated by comparing with existing experimental results. Findings indicate that the tensile strength of glass considerably influences the blast response of LG panels while the interlayer material properties have a major impact on the response under higher blast loads. Initially, glass panes absorb most of the blast energy, but after the glass breaks, interlayer deforms further and absorbs most of the blast energy. LG panels should be designed to fail by tearing of the interlayer rather than failure at the supports to achieve a desired level of protection. From this aspect, material properties of glass, interlayer and sealant joints play important roles, but unfortunately they are not accounted for in the current design standards. The new information generated in this paper will enhance the capabilities of engineers to better design LG panels under blast loads and use better materials to improve the blast response of LG panels.

Measuring, modelling and understanding the mechanical behavior of bagasse

In the Australian sugar industry, sugar cane is smashed into a straw like material by hammers before being squeezed between large rollers to extract the sugar juice. The straw like material is initially called prepared cane and then bagasse as it passes through successive roller milling units. The sugar cane materials are highly compressible, have high moisture content, are fibrous, and they resemble some peat soils in both appearance and mechanical behaviour. A promising avenue to improve the performance of milling units for increased throughput and juice extraction, and to reduce costs is by modelling of the crushing process. To achieve this, it is believed necessary that milling models should be able to reproduce measured bagasse behaviour. This investigation sought to measure the mechanical (compression, shear, and volume) behaviour of prepared cane and bagasse, to identify limitations in currently used material models, and to progress towards a material model that can predict bagasse behaviour adequately. Tests were carried out using a modified direct shear test equipment and procedure at most of the large range of pressures occurring in the crushing process. The investigation included an assessment of the performance of the direct shear test for measuring bagasse behaviour. The assessment was carried out using finite element modelling. It was shown that prepared cane and bagasse exhibited critical state behavior similar to that of soils and the magnitudes of material parameters were determined. The measurements were used to identify desirable features for a bagasse material model. It was shown that currently used material models had major limitations for reproducing bagasse behaviour. A model from the soil mechanics literature was modified and shown to achieve improved reproduction while using magnitudes of material parameters that better reflected the measured values. Finally, a typical three roller mill pressure feeder configuration was modelled. The predictions and limitations were assessed by comparison to measured data from a sugar factory.

Towards a multi-element simulation of heavily over-consolidated bagasse using a material subroutine

A better understanding of the behaviour of prepared cane and bagasse, and the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current process. There are opportunities to decrease bagasse moisture from a milling unit. The behaviour of bagasse in chutes is poorly understood. Previous investigations have shown that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr-Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Progress has been made in the last 11 years towards implementing a mechanical model for bagasse in finite element software. The objective is to be able to correctly simulate various simple mechanical loading conditions measured in the laboratory. Combining these behaviours together is thought to have a high probability of reproducing the complicated stress conditions in a milling unit. This paper reports on progress made towards modelling the fifth and final (and most challenging) of the simple loading conditions: the shearing of heavily over-consolidated bagasse, using a specific model for bagasse in a multi-element simulation.

Modelling of the mechanical behaviour of heavily over-consolidated bagasse

A better understanding of the behaviour of prepared cane and bagasse, and the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current process, for example to reduce final bagasse moisture. Previous investigations have proven that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr-Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Current Finite Element Models (FEM) available in commercial software have adequate permeability models. However, no commercially available software seems to contain an adequate mechanical model for bagasse. The same software contains a few material models for soil and other materials, while the coding of hundreds of developed models for soil and other materials remains confidential at universities and government research centres. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software code. This paper builds on that progress and carries out a further step towards obtaining an adequate material model. The fifth and final loading condition outlined previously, shearing of heavily over-consolidated bagasse, is outlined.