A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs.

An enriched radial point interpolation method based on weak-form and strong-form

In this article, an enriched radial point interpolation method (e-RPIM) is developed for computational mechanics. The conventional radial basis function (RBF) interpolation is novelly augmented by the suitable basis functions to reflect the natural properties of deformation. The performance of the enriched meshless RBF shape functions is first investigated using the surface fitting. The surface fitting results have proven that, compared with the conventional RBF, the enriched RBF interpolation has a much better accuracy to fit a complex surface than the conventional RBF interpolation. It has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF interpolation, but also can accurately reflect the deformation properties of problems. The system of equations for two-dimensional solids is then derived based on the enriched RBF shape function and both of the meshless strong-form and weak-form. A numerical example of a bar is presented to study the effectiveness and efficiency of e-RPIM. As an important application, the newly developed e-RPIM, which is augmented by selected trigonometric basis functions, is applied to crack problems. It has been demonstrated that the present e-RPIM is very accurate and stable for fracture mechanics problems.

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Mechanical properties of thin sol-gel films

This thesis presents a study of the mechanical properties of thin films. The main aim was to determine the properties of sol-gel derived coatings. These films are used in a range of different applications and are known to be quite porous. Very little work has been carried out in this area and in order to study the mechanical properties of sol-gel films, some of the work was carried out on magnetron sputtered metal coatings in order to validate the techniques developed in this work. The main part of the work has concentrated on the development of various bending techniques to study the elastic modulus of the thin films, including both a small scale three-point bending, as well as a novel bi-axial bending technique based on a disk resting on three supporting balls. The bending techniques involve a load being applied to the sample being tested and the bending response to this force being recorded. These experiments were carried out using an ultra micro indentation system with very sensitive force and depth recording capabilities. By analysing the result of these forces and deflections using existing theories of elasticity, the elastic modulus may be determined. In addition to the bi-axial bending study, a finite element analysis of the stress distribution in a disk during bending was carried out. The results from the bi-axial bending tests of the magnetron sputtered films was confirmed by ultra micro indentation tests, giving information of the hardness and elastic modulus of the films. It was found that while the three point bending method gave acceptable results for uncoated steel substrates, it was very susceptible to slight deformations of the substrate. Improvements were made by more careful preparation of the substrates in order to avoid deformation. However the technique still failed to give reasonable results for coated specimens. In contrast, biaxial bending gave very reliable results even for very thin films and this technique was also found to be useful for determination of the properties of sol-gel coatings. In addition, an ultra micro indentation study of the hardness and elastic modulus of sol-gel films was conducted. This study included conventionally fired films as well as films ion implanted in a range of doses. The indentation tests showed that for implantation of H⁺ ions at doses exceeding 3x10¹⁶ ions/cm², the mechanical properties closely resembled those of films that were conventionally fired to 450°C.

Traffic queue estimation for metered motorway on-ramps through use of loop detector time occupancies

The primary objective of this study is to develop a robust queue estimation algorithm for motorway on-ramps. Real-time queue information is a vital input for dynamic queue management on metered on-ramps. Accurate and reliable queue information enables the management of on-ramp queue in an adaptive manner to the actual traffic queue size and thus minimises the adverse impacts of queue flush while increasing the benefit of ramp metering. The proposed algorithm is developed based on the Kalman filter framework. The fundamental conservation model is used to estimate the system state (queue size) with the flow-in and flow-out measurements. This projection results are updated with the measurement equation using the time occupancies from mid-link and link-entrance loop detectors. This study also proposes a novel single point correction method. This method resets the estimated system state to eliminate the counting errors that accumulate over time. In the performance evaluation, the proposed algorithm demonstrated accurate and reliable performances and consistently outperformed the benchmarked Single Occupancy Kalman filter (SOKF) method. The improvements over SOKF are 62% and 63% in average in terms of the estimation accuracy (MAE) and reliability (RMSE), respectively. The benefit of the innovative concepts of the algorithm is well justified by the improved estimation performance in congested ramp traffic conditions where long queues may significantly compromise the benchmark algorithm’s performance.

A Kalman filter based queue estimation algorithm using time occupancies for motorway on-ramps

The primary objective of this study is to develop a robust queue estimation algorithm for motorway on-ramps. Real-time queue information is the most vital input for a dynamic queue management that can treat long queues on metered on-ramps more sophistically. The proposed algorithm is developed based on the Kalman filter framework. The fundamental conservation model is used to estimate the system state (queue size) with the flow-in and flow-out measurements. This projection results are updated with the measurement equation using the time occupancies from mid-link and link-entrance loop detectors. This study also proposes a novel single point correction method. This method resets the estimated system state to eliminate the counting errors that accumulate over time. In the performance evaluation, the proposed algorithm demonstrated accurate and reliable performances and consistently outperformed the benchmarked Single Occupancy Kalman filter (SOKF) method. The improvements over SOKF are 62% and 63% in average in terms of the estimation accuracy (MAE) and reliability (RMSE), respectively. The benefit of the innovative concepts of the algorithm is well justified by the improved estimation performance in the congested ramp traffic conditions where long queues may significantly compromise the benchmark algorithm’s performance.

The birds of the Bush Heritage, Cravens Peak Reserve

Bird communities were studied in two subregional areas of Cravens Peak, the Toko Plains and the Simpson-Strzelecki Dunefields, using the point counts method. A total of 42 2ha 20 minute surveys, 46 five-hundred metre radius area surveys and 170 5km drive through area surveys were conducted and observations made. Bird species were identified, counted and recorded. The data were compared in the two subregions and, as a whole, considering species groups according to land system on which the ecosystem occurs, the specific ecosystem and according to their general feeding habits (insectivore, omnivore, frugivore, granivore, nectarivore and carnivore). Species richness and species relative abundance were compared using Simpson’s Diversity Index and the data revealed that species are distributed largely on the basis of habitat. In general, areas with a greater number of vegetation strata recorded greater species diversity. Overall, the Tall Open Acacia georginae Shrubland on alluvial floodplains has a greater diversity of birds in a 2ha area (0.87, Simpson’s Index of Diversity 1-D) compared to the other survey sites.

Birds : indicators of environmental repair in oil affected coastlines

Bird coastal communities were studied along Bribie Island and Moreton Island, two islands within Moreton Bay, Brisbane, Queensland, Australia, using the point counts method. A total of 128 five-hundred metre radius area surveys and 81 beach drive surveys were conducted and observations made over four seasons. Bird species were identified, counted and recorded. The data was compared between the two islands and, between sites on each island as oil-spill affected sites to non-oil spill affected sites. Species such as waders, shorebirds, terns/gulls and raptors were identified as species at most risk from an oil spill and the data was selected to look mainly at these species. The data indicated that sites affected by the oil spill contained 50% less oil-affected species than sites not affected by the oil spill. Bribie Island held on average 5 species per site in the oil affected sites compared to 12 species in non-oil affected sites. This same trend was observed on Moreton Island which held 6 species compared to 14 species. Bird data will continue to be counted over several years to determine whether the observed data is a true reflection of the affects of an oil spill on the habitat of shorebirds.