The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

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.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

An exact analysis of free vibrations of simply-supported viscoelastic plates

In this paper an exact three-dimensional analysis for free vibrations of a class of simply-supported viscoelastic rectangular plates is given. The characteristic equation defining the eigenvalues is of closed form. Some numerical results are presented for standard linear solids. Results from thin plate and Mindlin theories are also given for the purpose of comparison.

Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers

The active structural component of a capacitive micromachined ultrasonic transducer (CMUT) is the top plate which vibrates under the influence of a time-varying electrostatic force thereby producing ultrasound waves of the desired frequency in the surrounding medium. Analysis of MEMS devices which rely on electrostatic actuation is complicated due to the fact that the structural deformations alter the electrostatic forces, which redistribute and modify the applied loads. Hence, it becomes imperative to consider the electrostatics-structure coupling aspect in the design of these devices. This paper presents an approximate analytical solution for the static deflection of a thin, clamped circular plate caused by electrostatic forces which are inherently nonlinear. Traditionally, finite element simulations using some commercial software such as ANSYS are employed to determine the structural deflections caused by electrostatic forces. Since the structural deformation alters the electrostatic field, a coupled-field simulation is required wherein the electrostatic mesh is continuously updated to coincide with the deflection of the structure. Such simulations are extremely time consuming, in addition to being nontransparent and somewhat hard to implement. We employ the classical thin-plate theory which is adequate when the ratio of the diameter to thickness of the plate is very large, a situation commonly prevalent in many MEMS devices, especially the CMUTs. We solve the thin-plate electrostatic-elastic equation using the Galerkin-weighted residual technique, under the assumption that the deflections are small in comparison to the thickness of the plate. The evaluation of the electrostatic force between the two plates is simplified due to the fact that the electrostatic gap is much smaller than the lateral dimensions of the device. The results obtained are compared to those found from ANSYS simulations and an excellent agreement is observed between the two. The pull-in voltage predicted by our model is close to the value predicted by ANSYS simulations.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.

Plastic limit solution for the response of plate anchors under combined translational and torsional undrained loading

Plate anchors are increasingly being used to moor large floating offshore structures in deep and ultradeep water. These facilities impart substantial vertical uplift loading to plate anchors. However, extreme operating conditions such as hurricane loading often result in partial system failures, with significant change in the orientation of the remaining intact mooring lines. The purpose of this study is to investigate the undrained pure translational (parallel to plate) and torsional bearing capacity of anchor plates idealized as square and rectangular shaped plates. Moreover, the interaction response of plate anchors under combined translational and torsional loading is studied using a modified plastic limit analysis (PLA) approach. The previous PLA formulation which did not account for shear-normal force interaction on the vertical end faces of the plate provides an exact solution to the idealized problem of an infinitely thin plate but only an approximate solution to the problem of a plate of finite thickness. This is also confirmed by the three-dimensional finite element (FE) results, since the PLA values exceed FE results as the thickness of the plate increases. By incorporating the shear-normal interaction relationship in the modified solution, the torsional bearing capacity factors, as well as the plate interaction responses are enhanced as they show satisfactory agreement with the FE results. The interaction relationship is then obtained for square and rectangular plates of different aspect ratios and thicknesses. The new interaction relationships could also be used as an associated plastic failure locus for combined shear and torsional loading to predict plastic displacements and rotations in translational and torsional loading modes as well. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Non-linear analysis of composite structures with integrated piezoelectric sensors and actuators

This paper deals with the geometrically non linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuors or sensors layers and/or patches.The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings. the finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of fredom for the generalized displacements and one eçlectrical potential degree of freedom for each piezoelectric layer or patch. An updated Lagrangian formulation associated to Newton-Raphson technique is used to solve incrementally and iteratively the equilibrium equation.The model is applied in the solution of four illustrative cases, and the results are compared and discussedwith alternative solutions when available.

Strength Predictions of Hat Stiffened Plate

Hat Stiffened Plates are used in composite ships and are gaining popularity in metallic ship construction due to its high strength-to-weight ratio. Light weight structures will result in greater payload, higher speeds, reduced fuel consumption and environmental emissions. Numerical Investigations have been carried out using the commercial Finite Element software ANSYS 12 to substantiate the high strength-to-weight ratio of Hat Stiffened Plates over other open section stiffeners which are commonly used in ship building. Analysis of stiffened plate has always been a matter of concern for the structural engineers since it has been rather difficult to quantify the actual load sharing between stiffeners and plating. Finite Element Method has been accepted as an efficient tool for the analysis of stiffened plated structure. Best results using the Finite Element Method for the analysis of thin plated structures are obtained when both the stiffeners and the plate are modeled using thin plate elements having six degrees of freedom per node. However, one serious problem encountered with this design and analysis process is that the generation of the finite element models for a complex configuration is time consuming and laborious. In order to overcome these difficulties two different methods viz., Orthotropic Plate Model and Superelement for Hat Stiffened Plate have been suggested in the present work. In the Orthotropic Plate Model geometric orthotropy is converted to material orthotropy i.e., the stiffeners are smeared and they vanish from the field of analysis and the structure can be analysed using any commercial Finite Element software which has orthotropic elements in its element library. The Orthotropic Plate Model developed has predicted deflection, stress and linear buckling load with sufficiently good accuracy in the case of all four edges simply supported boundary condition. Whereas, in the case of two edges fixed and other two edges simply supported boundary condition even though the stress has been predicted with good accuracy there has been large variation in the deflection predicted. This variation in the deflection predicted is because, for the Orthotropic Plate Model the rigidity is uniform throughout the plate whereas in the actual Hat Stiffened Plate the rigidity along the line of attachment of the stiffeners to the plate is large as compared to the unsupported portion of the plate. The Superelement technique is a method of treating a portion of the structure as if it were a single element even though it is made up of many individual elements. The Superelement has predicted the deflection and in-plane stress of Hat Stiffened Plate with sufficiently good accuracy for different boundary conditions. Formulation of Superelement for composite Hat Stiffened Plate has also been presented in the thesis. The capability of Orthotropic Plate Model and Superelement to handle typical boundary conditions and characteristic loads in a ship structure has been demonstrated through numerical investigations.

Landmark-based morphometric analysis in selected species of serranid fishes (Perciformes : Teleostei)

Morphological differences among 6 species of marine fishes belonging to 2 subfamilies of the family Serranidae (Serraninae: Dules auriga, Diplectrum formosum, and D, radiale; Epinephelinae: Epinephelus marginatus, Mycteroperca acutirostris, and M. bonaci) were studied by the geometric morphometric method of thin-plate splines and multivariate analysis of partial-warp scores. The decomposition of shape variation into uniform and nonaffine components of shape change indicate that major differences among species are related to both components of shape variation. Significant differences were found among species with respect to the uniform components, but there is no clear separation of taxonomic groups related to these components, and species are instead separated on the basis of body height and caudal peduncle length. Non-uniform changes in body shape, in turn, clearly differentiate the species of Serraninae and Epinephelinae. These shape changes are probably related to differences in habitat and feeding habits among the species.

A comparative analysis between FEM and Boundary Methods in bending of Plates

Two different methods of analysis of plate bending, FEM and BM are discussed in this paper. The plate behaviour is assumed to be represented by using the linear thin plate theory where the Poisson-Kirchoff assumption holds. The BM based in a weighted mean square error technique produced good results for the problem of plate bending. The computational effort demanded in the BM is smaller than the one needed in a FEM analysis for the same level of accuracy. The general application of the FEM cannot be matched by the BM. Particularly, different types of geometry (plates of arbitrary geometry) need a similar but not identical treatment in the BM. However, this loss of generality is counterbalanced by the computational efficiency gained in the BM in the solution achievement

Analysis of plate bending by means of high order finite hyperelements

The possibilities and limitations of high order hyperelements in plate bending analysis are discussed. Explicit shape functions for some types of triangular elements are given. These elements are applied to simple cases to assess their computational efficiency.

Application of the dynamic models to the detection of imperfections in plate Structures

This paper is part of a set of publications related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. The first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment, particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection of the first class of imperfections, i.e. cracks and it is the object of the present paper. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With this group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally, in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present and a numerical application has been shown.

Linking finite-element analysis and computer-aided drafting processes

The aim of this research was to investigate the integration of computer-aided drafting and finite-element analysis in a linked computer-aided design procedure and to develop the necessary software. The Be'zier surface patch for surface representation was used to bridge the gap between the rather separate fields of drafting and finite-element analysis because the surfaces are defined by analytical functions which allow systematic and controlled variation of the shape and provide continuous derivatives up to any required degree. The objectives of this research were achieved by establishing : (i) A package which interpretes the engineering drawings of plate and shell structures and prepares the Be'zier net necessary for surface representation. (ii) A general purpose stand-alone meshed-surface modelling package for surface representation of plates and shells using the Be'zier surface patch technique. (iii) A translator which adapts the geometric description of plate and shell structures as given by the meshed-surface modeller to the form needed by the finite-element analysis package. The translator was extended to suit fan impellers by taking advantage of their sectorial symmetry. The linking processes were carried out for simple test structures, simplified and actual fan impellers to verify the flexibility and usefulness of the linking technique adopted. Finite-element results for thin plate and shell structures showed excellent agreement with those obtained by other investigators while results for the simplified and actual fan impellers also showed good agreement with those obtained in an earlier investigation where finite-element analysis input data were manually prepared. Some extensions of this work have also been discussed.

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.