Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Simulation of AE wave propagation in thin plate for source identification

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in wide spectrum areas, ranging from non-destructive testing for the detection of materials defects to monitoring of microeismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary/longitudinal waves), S waves (shear/transverse waves) and Rayleight (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use the acoustic emission technique for accurate identification of source location, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Multi-modal deformable medical image registration

Non-rigid image registration is an essential tool required for overcoming the inherent local anatomical variations that exist between images acquired from different individuals or atlases. Furthermore, certain applications require this type of registration to operate across images acquired from different imaging modalities. One popular local approach for estimating this registration is a block matching procedure utilising the mutual information criterion. However, previous block matching procedures generate a sparse deformation field containing displacement estimates at uniformly spaced locations. This neglects to make use of the evidence that block matching results are dependent on the amount of local information content. This paper presents a solution to this drawback by proposing the use of a Reversible Jump Markov Chain Monte Carlo statistical procedure to optimally select grid points of interest. Three different methods are then compared to propagate the estimated sparse deformation field to the entire image including a thin-plate spline warp, Gaussian convolution, and a hybrid fluid technique. Results show that non-rigid registration can be improved by using the proposed algorithm to optimally select grid points of interest.

The development of virtual leaf surface models for interactive agrichemical spray applications

This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered.

Identification of acoustic emission wave modes for accurate source location in plate-like structures

Acoustic emission (AE) technique is a popular tool used for structural health monitoring of civil, mechanical and aerospace structures. It is a non-destructive method based on rapid release of energy within a material by crack initiation or growth in the form of stress waves. Recording of these waves by means of sensors and subsequent analysis of the recorded signals convey information about the nature of the source. Ability to locate the source of stress waves is an important advantage of AE technique; but as AE waves travel in various modes and may undergo mode conversions, understanding of the modes (‘modal analysis’) is often necessary in order to determine source location accurately. This paper presents results of experiments aimed at finding locations of artificial AE sources on a thin plate and identifying wave modes in the recorded signal waveforms. Different source locating techniques will be investigated and importance of wave mode identification will be explored.

Generation of a 3D proximal femur shape from a single projection 2D radiographic image.

Summary Generalized Procrustes analysis and thin plate splines were employed to create an average 3D shape template of the proximal femur that was warped to the size and shape of a single 2D radiographic image of a subject. Mean absolute depth errors are comparable with previous approaches utilising multiple 2D input projections. Introduction Several approaches have been adopted to derive volumetric density (g cm-3) from a conventional 2D representation of areal bone mineral density (BMD, g cm-2). Such approaches have generally aimed at deriving an average depth across the areal projection rather than creating a formal 3D shape of the bone. Methods Generalized Procrustes analysis and thin plate splines were employed to create an average 3D shape template of the proximal femur that was subsequently warped to suit the size and shape of a single 2D radiographic image of a subject. CT scans of excised human femora, 18 and 24 scanned at pixel resolutions of 1.08 mm and 0.674 mm, respectively, were equally split into training (created 3D shape template) and test cohorts. Results The mean absolute depth errors of 3.4 mm and 1.73 mm, respectively, for the two CT pixel sizes are comparable with previous approaches based upon multiple 2D input projections. Conclusions This technique has the potential to derive volumetric density from BMD and to facilitate 3D finite element analysis for prediction of the mechanical integrity of the proximal femur. It may further be applied to other anatomical bone sites such as the distal radius and lumbar spine.

Thin-film elemental analyses for precise characterization of minerals

The Analytical Electron Microscope (AEM), with which secondary X-ray emission from a thin (<150nm), electron-transparent material is measured, has rapidly become a versatile instrument for qualitative and quantitative elemental analyses of many materials, including minerals. With due regard for sources of error in experimental procedures, it is possible to obtain high spatial resolution (~20nm diameter) and precise elemental analyses (~3% to 5% relative) from many silicate minerals. In addition, by utilizing the orientational dependence of X-ray emission for certain multi-substituted crystal structures, site occupancies for individual elements within a unit cell can be determined though with lower spatial resolution. The relative ease with which many of these compositional data may be obtained depends in part on the nature of the sample, but, in general, is comparable to other solid state analytical techniques such as X-ray diffraction and electron microprobe analysis. However, the improvement in spatial resolution obtained with the AEM (up to two orders of magnitude in analysis diameter) significantly enhances interpretation of fine-grained assemblages in many terrestrial or extraterrestrial rocks.

Determination of elastic modulus of thin coating materials using nanoindentation and finite element analysis

A deconvolution method that combines nanoindentation and finite element analysis was developed to determine elastic modulus of thin coating layer in a coating-substrate bilayer system. In this method, the nanoindentation experiments were conducted to obtain the modulus of both the bilayer system and the substrate. The finite element analysis was then applied to deconvolve the elastic modulus of the coating. The results demonstrated that the elastic modulus obtained using the developed method was in good agreement with that reported in literature.

Computational fluid dynamics analysis of a flat plate photocatalytic reactor for storm and wastewater reuse

A computational fluid dynamics (CFD) analysis has been performed for a flat plate photocatalytic reactor using CFD code FLUENT. Under the simulated conditions (Reynolds number, Re around 2650), a detailed time accurate computation shows the different stages of flow evolution and the effects of finite length of the reactor in creating flow instability, which is important to improve the performance of the reactor for storm and wastewater reuse. The efficiency of a photocatalytic reactor for pollutant decontamination depends on reactor hydrodynamics and configurations. This study aims to investigate the role of different parameters on the optimization of the reactor design for its improved performance. In this regard, more modelling and experimental efforts are ongoing to better understand the interplay of the parameters that influence the performance of the flat plate photocatalytic reactor.

Scaling analysis of the thermal boundary layer adjacent to an abruptly heated inclined flat plate

The natural convection thermal boundary layer adjacent to an abruptly heated inclined flat plate is investigated through a scaling analysis and verified by numerical simulations. In general, the development of the thermal flow can be characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady state stage. Major scales including the flow velocity, flow development time, and the thermal and viscous boundary layer thicknesses are established to quantify the flow development at different stages and over a wide range of flow parameters. Details of the scaling analysis and the numerical procedures are described in this paper.

Scaling analysis of the unsteady natural convection boundary layer adjacent to an inclined plate for Pr > 1 following instantaneous heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method

The details of an application of the finite strip method to the elastic buckling analysis of thin-walled structures with various boundary conditions and subjected to single or combined loadings of longitudinal compression, transverse compression, bending and shear are presented. The presence of shear loading is accounted for by modifying the displacement functions which are commonly used in cases when shear is absent. A program based on the finite strip method was used to obtain the elastic buckling stress, buckling plot and buckling mode of thin-walled structures and some of these results are presented.

Local plastic mechanisms in thin steel plates under in-plane compression

Thin-walled steel plates subjected to in-plane compression develop two types of local plastic mechanism, namely the roof-shaped mechanism and the so-called flip-disc mechanism, but the intriguing question of why two mechanisms should develop was not answered until recently. It was considered that the location of first yield point shifted from the centre of the plate to the midpoint of the longitudinal edge depending on the b/t ratio, imperfection level, and yield stress of steel, which then decided the type of mechanism. This paper has verified this hypothesis using analysis and laboratory experiments. An elastic analysis using Galerkin's method to solve Marguerre's equations was first used to determine the first yield point, based on which the local plastic mechanism/imperfection tolerance tables have been developed which give the type of mechanism as a function of b/t ratio, imperfection level and yield stress of steel. Laboratory experiments of thin-walled columns verified the imperfection tolerance tables and thus indirectly the hypothesis. Elastic and rigid-plastic curves were them used to predict the effect on the ultimate load due to the change of mechanism. A finite element analysis of selected cases also confirmed the results from simple analyses and experiments.