Generalized element load method for first- and second-order element solutions with element load effect

The finite element method in principle adaptively divides the continuous domain with complex geometry into discrete simple subdomain by using an approximate element function, and the continuous element loads are also converted into the nodal load by means of the traditional lumping and consistent load methods, which can standardise a plethora of element loads into a typical numerical procedure, but element load effect is restricted to the nodal solution. It in turn means the accurate continuous element solutions with the element load effects are merely restricted to element nodes discretely, and further limited to either displacement or force field depending on which type of approximate function is derived. On the other hand, the analytical stability functions can give the accurate continuous element solutions due to element loads. Unfortunately, the expressions of stability functions are very diverse and distinct when subjected to different element loads that deter the numerical routine for practical applications. To this end, this paper presents a displacement-based finite element function (generalised element load method) with a plethora of element load effects in the similar fashion that never be achieved by the stability function, as well as it can generate the continuous first- and second-order elastic displacement and force solutions along an element without loss of accuracy considerably as the analytical approach that never be achieved by neither the lumping nor consistent load methods. Hence, the salient and unique features of this paper (generalised element load method) embody its robustness, versatility and accuracy in continuous element solutions when subjected to the great diversity of transverse element loads.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Static load bearing exercises during rehabilitation of individuals with transfemoral amputation fitted with osseointegrated implant: Load compliance

Osseointegration has been introduced in the orthopaedic surgery in the 1990’s in Gothenburg (Sweden). To date, there are two frequently used commercially available human implants: the OPRA (Integrum, Sweden) and ILP (Orthodynamics, Germany) systems. The rehabilitation program with both systems include some form of static load bearing exercises. These latter involved following a load progression that is monitored by the bathroom scale, providing only the load applied on the vertical axis. The loading data could be analysed through different biomechanical variables. For instance, the load compliance, corresponding to the difference between the load recommended (LR) and the load actually applied on the implant, will be presented here.

Description of body posture during Static load bearing exercises for individuals with transfemoral amputation fitted with bone-anchored prosthesis

The rehabilitation programs of bone-anchorage prostheses relying either on the OPRA (Integrum, Sweden) or the ILP (Orthodynamics, Germany) fixation involve some forms of static load bearing exercises (LBE). So far, most of biomechanical studies of these static LBEs focused on the direct measurements of the actual forces and moments applied on the OPRA fixation of individuals with transfemoral amputation (TFA). To date, the proof-of-concept of an apparatus to conduct these kinetic measurements has been presented, along with some preliminary data. The understanding of the kinetic data is essential to improve rehabilitation programs as well as the design of upcoming loading frames. However, kinetic information alone is difficult to interpret without concomitant kinematic data. The purpose of this preliminary study was to introduce a qualitative analysis describing the different body postures during LBE for a group of TFAs.

Load bearing exercises and functional outcome of individuals with transfemoral amputation fitted with OPRA fixation

Individuals with lower limb amputation fitted with an OPRA osseointegrated fixation are facing an extensive rehabilitation program including static load bearing exercises (LBE). The application of a suitable amount of stress stimulates osseointegration and prepares the bone to tolerate the forces and moments that will be incurred during activities of daily living (ADL. At present, the monitoring is typically carried out using a normal bathroom weighing scale. This scale provides information only on the magnitude of the vertical component of the applied force. The moment around the long axis of the fixation when the femur is perpendicular to the ground is not assessed and neither are the components of force and moment generated on the other two axes.

Static load bearing exercises during rehabilitation of individuals with transfemoral amputation fitted with osseointegrated implant: Kinetic analysis

The desire to solve problems caused by socket prostheses in transfemoral amputees and the acquired success of osseointegration in the dental application has led to the introduction of osseointegration in the orthopedic surgery. Since its first introduction in 1990 in Gothenburg Sweden the osseointegrated (OI) orthopedic fixation has proven several benefits[1]. The surgery consists of two surgical procedures followed by a lengthy rehabilitation program. The rehabilitation program after an OI implant includes a specific training period with a short training prosthesis. Since mechanical loading is considered to be one of the key factors that influence bone mass and the osseointegration of bone-anchored implants, the rehabilitation program will also need to include some form of load bearing exercises (LBE). To date there are two frequently used commercially available human implants. We can find proof in the literature that load bearing exercises are performed by patients with both types of OI implants. We refer to two articles, a first one written by Dr. Aschoff and all and published in 2010 in the Journal of Bone and Joint Surgery.[2] The second one presented by Hagberg et al in 2009 gives a very thorough description of the rehabilitation program of TFA fitted with an OPRA implant. The progression of the load however is determined individually according to the residual skeleton’s quality, pain level and body weight of the participant.[1] Patients are using a classical bathroom weighing scale to control the load on the implant during the course of their rehabilitation. The bathroom scale is an affordable and easy-to-use device but it has some important shortcomings. The scale provides instantaneous feedback to the patient only on the magnitude of the vertical component of the applied force. The forces and moments applied along and around the three axes of the implant are unknown. Although there are different ways to assess the load on the implant for instance through inverse dynamics in a motion analysis laboratory [3-6] this assessment is challenging. A recent proof- of-concept study by Frossard et al (2009) showed that the shortcomings of the weighing scale can be overcome by a portable kinetic system based on a commercial transducer[7].

Static load bearing exercises of individuals with transfemoral amputation fitted with an osseointegrated implant: Reliability of kinetic data

This study aimed at presenting the intra-tester reliability of the static load bearing exercises (LBEs) performed by individuals with transfemoral amputation (TFA) fitted with an osseointegrated implant to stimulate the bone remodelling process. There is a need for a better understanding of the implementation of these exercises particularly the reliability. The intra-tester reliability is discussed with a particular emphasis on inter-load prescribed, inter-axis and inter-component reliabilities as well as the effect of body weight normalisation. Eleven unilateral TFAs fitted with an OPRA implant performed five trials in four loading conditions. The forces and moments on the three axes of the implant were measured directly with an instrumented pylon including a six-channel transducer. Reliability of loading variables was assessed using intraclass correlation coefficients (ICCs) and percentage standard error of measurement values (%SEMs). The ICCs of all variables were above 0.9 and the %SEM values ranged between 0 and 87%. This study showed a high between-participants’ variance highlighting the lack of loading consistency typical of symptomatic population as well as a high reliability between the loading sessions indicating a plausible correct repetition of the LBE by the participants. However, these outcomes must be understood within the framework of the proposed experimental protocol.

A comparative study of prognostic model for bearing failure

An effective prognostics program will provide ample lead time for maintenance engineers to schedule a repair and to acquire replacement components before catastrophic failures occur. This paper presents a technique for accurate assessment of the remnant life of machines based on health state probability estimation technique. For comparative study of the proposed model with the proportional hazard model (PHM), experimental bearing failure data from an accelerated bearing test rig were used. The result shows that the proposed prognostic model based on health state probability estimation can provide a more accurate prediction capability than the commonly used PHM in bearing failure case study.

Local buckling studies of cold-formed steel compression members at elevated temperatures

Cold-formed steel members have been widely used in residential and commercial buildings as primary load bearing structural elements. They are often made of thin steel sheets and hence they are more susceptible to local buckling. The buckling behaviour of cold-formed steel compression members under fire conditions is not fully investigated yet and hence there is a lack of knowledge on the fire performance of cold-formed steel compression members. Current cold-formed steel design standards do not provide adequate design guidelines for the fire design of cold-formed steel compression members. Therefore a research project based on extensive experimental and numerical studies was undertaken to investigate the local buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. First a series of 91 local buckling tests was conducted at ambient and uniform elevated temperatures up to 700oC on cold-formed lipped and unlipped channels. Suitable finite element models were then developed to simulate the behaviour of tested columns and were validated using test results. All the ultimate load capacity results for local buckling were compared with the predictions from the available design rules based on AS/NZS 4600, BS 5950 Part 5, Eurocode 3 Parts 1.2 and 1.3 and the direct strength method (DSM), based on which suitable recommendations have been made for the fire design of cold-formed steel compression members subject to local buckling at uniform elevated temperatures.

Raman and infrared spectroscopic characterization of the arsenate-bearing mineral tangdanite– and in comparison with the discredited mineral clinotyrolite

The minerals clinotyrolite and fuxiaotuite are discredited in terms of the mineral tangdanite. The mixed anion mineral tangdanite Ca2Cu9(AsO4)4(SO4)0.5(OH)9 9H2O has been studied using a combination of Raman and infrared spectroscopy. Characteristic bands associated with arsenate, sulphate and hydroxyl units are identified. Broad bands in the OH stretching region are observed and are resolved into component bands. These bands are assigned to water and hydroxyl stretching vibrations. Two intense Raman bands at 837 and approximately 734 cm−1 are assigned to the ν1 (AsO4)3− symmetric stretching and ν3 (AsO4)3− antisymmetric stretching modes. Infrared bands at 1023 cm−1 are assigned to the (SO4)2− ν1 symmetric stretching mode, and infrared bands at 1052, 1110 and 1132 cm−1 assigned to (SO4)2− ν3 antisymmetric stretching modes, confirming the presence of the sulphate anion in the tangdanite structure. Raman bands at 593 and 628 cm−1 are attributed to the (SO4)2− ν4 bending modes. Low-intensity Raman bands found at 457 and 472 cm−1 are assigned to the (AsO4)3− ν2 bending modes. A comparison is made with the previously obtained spectral data on the discredited mineral clinotyrolite.

Infrared and Raman spectroscopic characterization of the carbonate bearing silicate mineral aerinite – Implications for the molecular structure

The mineral aerinite is an interesting mineral because it contains both silicate and carbonate units which is unusual. It is also a highly colored mineral being bright blue/purple. We have studied aerinite using a combination of techniques which included scanning electron microscopy, energy dispersive X-ray analysis, Raman and infrared spectroscopy. Raman bands at 1049 and 1072 cm−1 are assigned to the carbonate symmetric stretching mode. This observation supports the concept of the non-equivalence of the carbonate units in the structure of aerinite. Multiple infrared bands at 1354, 1390 and 1450 cm−1 supports this concept. Raman bands at 933 and 974 cm−1 are assigned to silicon–oxygen stretching vibrations. Multiple hydroxyl stretching and bending vibrations show that water is in different molecular environments in the aerinite structure.

Mechanical behavior of circular and square concrete filled steel tube stub columns under local compression

This paper presents a combined experimental and numerical study on the behaviour of both circular and square concrete-filled steel tube (CFT) stub columns under local compression. Twelve circular and eight square CFT stub columns were tested to study their bearing capacity and the key influential parameters. A 3D finite element model was established for simulation and parametric study to investigate the structural behaviour of the stub columns. The numerical results agreed well with the experimental results. In addition, analytical formulas were proposed to calculate the load bearing capacity of CFT stub columns under local compression.

A finite element modelling method for thin layer mortared masonry systems

This paper deals with a finite element modelling method for thin layer mortared masonry systems. In this method, the mortar layers including the interfaces are represented using a zero thickness interface element and the masonry units are modelled using an elasto-plastic, damaging solid element. The interface element is formulated using two regimes; i) shear-tension and ii) shearcompression. In the shear-tension regime, the failure of joint is consiedered through an eliptical failure criteria and in shear-compression it is considered through Mohr Coulomb type failure criterion. An explicit integration scheme is used in an implicit finite element framework for the formulation of the interface element. The model is calibrated with an experimental dataset from thin layer mortared masonry prism subjected to uniaxial compression, a triplet subjected to shear loads a beam subjected to flexural loads and used to predict the response of thin layer mortared masonry wallettes under orthotropic loading. The model is found to simulate the behaviour of a thin layer mortated masonry shear wall tested under pre-compression and inplane shear quite adequately. The model is shown to reproduce the failure of masonry panels under uniform biaxial state of stresses.

Evaluation of a patient-specific finite-element model to simulate conservative treatment in adolescent idiopathic scoliosis

Study design Retrospective validation study. Objectives To propose a method to evaluate, from a clinical standpoint, the ability of a finite-element model (FEM) of the trunk to simulate orthotic correction of spinal deformity and to apply it to validate a previously described FEM. Summary of background data Several FEMs of the scoliotic spine have been described in the literature. These models can prove useful in understanding the mechanisms of scoliosis progression and in optimizing its treatment, but their validation has often been lacking or incomplete. Methods Three-dimensional (3D) geometries of 10 patients before and during conservative treatment were reconstructed from biplanar radiographs. The effect of bracing was simulated by modeling displacements induced by the brace pads. Simulated clinical indices (Cobb angle, T1–T12 and T4–T12 kyphosis, L1–L5 lordosis, apical vertebral rotation, torsion, rib hump) and vertebral orientations and positions were compared to those measured in the patients' 3D geometries. Results Errors in clinical indices were of the same order of magnitude as the uncertainties due to 3D reconstruction; for instance, Cobb angle was simulated with a root mean square error of 5.7°, and rib hump error was 5.6°. Vertebral orientation was simulated with a root mean square error of 4.8° and vertebral position with an error of 2.5 mm. Conclusions The methodology proposed here allowed in-depth evaluation of subject-specific simulations, confirming that FEMs of the trunk have the potential to accurately simulate brace action. These promising results provide a basis for ongoing 3D model development, toward the design of more efficient orthoses.

Heat-producing element enrichment in granitic rocks, the role of crustal composition and evolution

This study greatly enhanced our knowledge of the potential for geothermal energy development in Queensland as a viable clean energy source in the coming decades. Key outcomes of the project were understanding the first-order controls on the concentration of the heat-producing elements: uranium, thorium and potassium in granitic rocks, and constraining where rocks with the greatest heat-producing potential lie at depth in Queensland. Importantly, new temperature and heat flow maps for southwest Queensland were developed that will greatly assist future exploration efforts.