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.

Porohyperelastic analysis to explore mechanical properties of chondrocytes using numerical modeling and experiments : a finite element study

There are many continuum mechanical models have been developed such as liquid drop models, solid models, and so on for single living cell biomechanics studies. However, these models do not give a fully approach to exhibit a clear understanding of the behaviour of single living cells such as swelling behaviour, drag effect, etc. Hence, the porohyperelastic (PHE) model which can capture those aspects would be a good candidature to study cells behaviour (e.g. chondrocytes in this study). In this research, an FEM model of single chondrocyte cell will be developed by using this PHE model to simulate Atomic Force Microscopy (AFM) experimental results with the variation of strain rate. This material model will be compared with viscoelastic model to demonstrate the advantages of PHE model. The results have shown that the maximum value of force applied of PHE model is lower at lower strain rates. This is because the mobile fluid does not have enough time to exude in case of very high strain rate and also due to the lower permeability of the membrane than that of the protoplasm of chondrocyte. This behavior is barely observed in viscoelastic model. Thus, PHE model is the better model for cell biomechanics studies.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.

Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

Finite element modelling of load bearing cold-formed steel wall systems under fire conditions

Light Gauge Steel Framing (LSF) walls are made of cold-formed, thin-walled steel lipped channel studs with plasterboard linings on both sides. However, these thin-walled steel sections heat up quickly and lose their strength under fire conditions despite the protection provided by plasterboards. A new composite wall panel was recently proposed to improve the fire resistance rating of LSF walls, where an insulation layer was used externally between the plasterboards on both sides of the wall frame instead of using it in the cavity. A research study using both fire tests and numerical studies was undertaken to investigate the structural and thermal behaviour of load bearing LSF walls made of both conventional and the new composite panels under standard fire conditions and to determine their fire resistance rating. This paper presents the details of finite element models of LSF wall studs developed to simulate the structural performance of LSF wall panels under standard fire conditions. Finite element analyses were conducted under both steady and transient state conditions using the time-temperature profiles measured during the fire tests. The developed models were validated using the fire test results of 11 LSF wall panels with various plasterboard/insulation configurations and load ratios. They were able to predict the fire resistance rating within five minutes. The use of accurate numerical models allowed the inclusion of various complex structural and thermal effects such as local buckling, thermal bowing and neutral axis shift that occurred in thin-walled steel studs under non-uniform elevated temperature conditions. Finite element analyses also demonstrated the improvements offered by the new composite panel system over the conventional cavity insulated system.

Experimental impact and finite element analysis of a composite, portable road safety barrier

This thesis provides an experimental and computational platform for investigating the performance and behaviour of water filled, plastic portable road safety barriers in an isolated impact scenario. A schedule of experimental impact tests were conducted assessing the impact response of an existing design of road safety barrier utilising a novel horizontal impact testing system. A coupled finite element and smooth particle hydrodynamic model of the barrier system was developed and validated against the results of the experimental tests. The validated model was subsequently used to assess the effect of certain composite materials on the impact performance of the water filled, portable road safety barrier system.

Accurate pattern prediction of very closely spaced mismatched antennas using measured active element patterns

A method for prediction of the radiation pattern of N strongly coupled antennas with mismatched sources is presented. The method facilitates fast and accurate design of compact arrays. The prediction is based on the measured N-port S parameters of the coupled antennas and the N active element patterns measured in a 50 ω environment. By introducing equivalent power sources, the radiation pattern with excitation by sources with arbitrary impedances and various decoupling and matching networks (DMN) can be accurately predicted without the need for additional measurements. Two experiments were carried out for verification: pattern prediction for parasitic antennas with different loads and for antennas with DMN. The difference between measured and predicted patterns was within 1 to 2 dB.

Finite element analysis of hollow flange beams with web stiffeners

A new cold-formed and resistance welded section known as the Hollow Flange Beam (HFB) has been developed recently in Australia. In contrast to the common lateral torsional buckling mode of I-beams, this unique section comprising two stiff triangular flanges and a slender web is susceptible to a lateral distortional buckling mode of failure involving lateral deflection, twist, and cross-section change due to web distortion. This lateral distortional buckling behavior has been shown to cause significant reduction of the available flexural capacity of HFBs. An investigation using finite element analyses and large scale experiments was carried out into the use of transverse web plate stiffeners to improve the lateral buckling capacity of HFBs. This paper presents the details of the finite element model and analytical results. The experimental procedure and results are outlined in a companion paper at this conference.

Finite-element analysis of hollow flange beams with web stiffeners

A new cold-formed and resistance-welded section known as the hollow flange beam (HFB) has been developed recently in Australia. In contrast to the common lateral-torsional buckling mode of I-beams, this unique section comprising two stiff triangular flanges and a slender web is susceptible to a lateral-distortional buckling mode of failure involving lateral deflection, twist, and cross-section change due to web distortion. This lateral-distortional buckling behavior has been shown to cause significant reduction of the available flexural capacity of HFBs. An investigation using finite-element analyses and large-scale experiments was carried out into the use of transverse web plate stiffeners to improve the lateral buckling capacity of HFBs. This paper presents the details of the finite-element model and analytical results. The experimental procedure and results are outlined in a companion paper.

Predicting crack initiation due to ratchetting in rail heads using critical element analysis

This paper presents a strategy to predict the lifetime of rails subjected to large rolling contact loads that induce ratchetting strains in the rail head. A critical element concept is used to calculate the number of loading cycles needed for crack initiation to occur in the rail head surface. In this technique the finite element method (FEM) is used to determine the maximum equivalent ratchetting strain per load cycle, which is calculated by combining longitudinal and shear stains in the critical element. This technique builds on a previously developed critical plane concept that has been used to calculate the number of cycles to crack initiation in rolling contact fatigue under ratchetting failure conditions. The critical element concept simplifies the analytical difficulties of critical plane analysis. Finite element analysis (FEA) is used to identify the critical element in the mesh, and then the strain values of the critical element are used to calculate the ratchetting rate analytically. Finally, a ratchetting criterion is used to calculate the number of cycles to crack initiation from the ratchetting rate calculated.

Development of a bi-material representative volume element using damaged homogenisation approach

Most civil engineering structures are formed using a number of materials that are bonded to each other with their surface-to-surface interaction playing key role on the overall response of the structure. Unfortunately these interactions are extremely variable; simplified and extremely detailed models trialed to date prove quite complex. Models that assume perfect interaction, on the other hand, predict unsafe behavior. In this paper a damage mechanics based interaction between two materials of different softening properties is developed using homogenisation approach. This paper describes the process of developing a bi-material representative volume element (RVE) using damaged homogenisation approach. The novelty in this paper is the development of non-local transient damage identification algorithm. Numerical examples prove the stability of the approach for a simplified RVE and encourage application to other shapes of RVEs.

Trace-element modeling of the magmatic evolution of rare-earth-rich carbonatite from the Miaoya deposit, Central China

Carbonatites are known to contain the highest concentrations of rare-earth elements (REE) among all igneous rocks. The REE distribution of carbonatites is commonly believed to be controlled by that of the rock forming Ca minerals (i.e., calcite, dolomite, and ankerite) and apatite because of their high modal content and tolerance for the substitution of Ca by light REE (LREE). Contrary to this conjecture, calcite from the Miaoya carbonatite (China), analyzed in situ by laser-ablation inductively-coupled-plasma mass-spectrometry, is characterized by low REE contents (100–260 ppm) and relatively !at chondrite-normalized REE distribution patterns [average (La/Yb)CN=1.6]. The carbonatite contains abundant REE-rich minerals, including monazite and !uorapatite, both precipitated earlier than the REE-poor calcite, and REE-fluorocarbonates that postdated the calcite. Hydrothermal REE-bearing !uorite and barite veins are not observed at Miaoya. The textural and analytical evidence indicates that the initially high concentrations of REE and P in the carbonatitic magma facilitated early precipitation of REE-rich phosphates. Subsequent crystallization of REE-poor calcite led to enrichment of the residual liquid in REE, particularly LREE. This implies that REE are generally incompatible with respect to calcite and the calcite/melt partition coefficients for heavy REE (HREE) are significantly greater than those for LREE. Precipitation of REE-fluorocarbonates late in the evolutionary history resulted in depletion of the residual liquid in LREE, as manifested by the development of HREE-enriched late-stage calcite [(La/Yb)CN=0.7] in syenites associated with the carbonatite. The observed variations of REE distribution between calcite and whole rocks are interpreted to arise from multistage fractional crystallization (phosphates!calcite!REE-!uorocarbonates) from an initially REE-rich carbonatitic liquid.

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.

Array of subarrays using adaptive element patterns

This paper explores the use of subarrays as array elements. Benefits of such a concept include improved gain in any direction without significantly increasing the overall size of the array and enhanced pattern control. The architecture for an array of subarrays will be discussed via a systems approach. Individual system designs are explored in further details and proof of principle is illustrated through a manufactured examples.