Deformation Interpolation Research Articles

Numerical Study of 3-D Liquid Sloshing in an Elastic Tank by MPS-FEM Coupled Method

The sloshing phenomenon in a partially loaded oil tanker or liquid natural gas ship is a typical fluid-structure interaction problem involving multi-physics, violent free-surface flow, and nonlinear structural response. In the past decades, the complex phenomenon has been commonly investigated without consideration of the hydro-elastic behaviors of the bulkheads. In our previous work, the liquid sloshing phenomenon in a two-dimensional (2-D) elastic tank was numerically studied. However, the bulkheads of the tank will deform within the three-dimensional (3-D) space in reality. So, it is necessary to study the 3-D sloshing problem in an elastic tank. In this article, a hybrid approach is developed within the Lagrangian system. The moving particle semiimplicit (MPS) method is used to simulate the evolution of 3-D flow with a violent free surface, and the finite element method (FEM) is used for the numerical analysis of structural response due to the impact loads of the sloshing flow. To couple the MPS method and the FEM method, an interpolation scheme based on the kernel function of the particle method is proposed for the communication on the isomerous interface between the fluid and structure domains. The reliability of force and deformation interpolation modules is validated by two tests. Then, the sloshing phenomenon in a 3-D elastic tank is numerically investigated and compared against the previous published 2-D results. By varying the Young's modulus of the tank walls, characteristics regarding the evolutions of free surface, variation of impact pressures, and dynamic responses of the structures are presented. 1. Introduction To support the transportation demands of natural resources, more and more vessels, such as the very large crude carriers and the liquid natural gas carriers, are manufactured. For these huge structures, risks such as local deformation or even damage of cargo-containment systems resulting from sloshing phenomena subsequently increase. Therefore, it is necessary to take the elasticity of the tank walls into account in the research of sloshing phenomena (Dias & Ghidaglia 2018). However, the phenomena involving the vibrations of the tank walls are complex. In the process of sloshing wave interacting with elastic bulkheads, the fragmentation, splash, and fusion of water are observed. Meanwhile, the structures vibrate nonlinearly under the impact loads resulting from the sloshing wave. These phenomena are hard to simulate realistically by the traditional mesh-based methods.

Learning statistical correlation for fast prostate registration in image‐guided radiotherapy

In adaptive radiation therapy of prostate cancer, fast and accurate registration between the planning image and treatment images of the patient is of essential importance. With the authors' recently developed deformable surface model, prostate boundaries in each treatment image can be rapidly segmented and their correspondences (or relative deformations) to the prostate boundaries in the planning image are also established automatically. However, the dense correspondences on the nonboundary regions, which are important especially for transforming the treatment plan designed in the planning image space to each treatment image space, are remained unresolved. This paper presents a novel approach to learn the statistical correlation between deformations of prostate boundary and nonboundary regions, for rapidly estimating deformations of the nonboundary regions when given the deformations of the prostate boundary at a new treatment image. The main contributions of the proposed method lie in the following aspects. First, the statistical deformation correlation will be learned from both current patient and other training patients, and further updated adaptively during the radiotherapy. Specifically, in the initial treatment stage when the number of treatment images collected from the current patient is small, the statistical deformation correlation is mainly learned from other training patients. As more treatment images are collected from the current patient, the patient-specific information will play a more important role in learning patient-specific statistical deformation correlation to effectively reflect prostate deformation of the current patient during the treatment. Eventually, only the patient-specific statistical deformation correlation is used to estimate dense correspondences when a sufficient number of treatment images have been acquired from the current patient. Second, the statistical deformation correlation will be learned by using a multiple linear regression (MLR) model, i.e., ridge regression (RR) model, which has the best prediction accuracy than other MLR models such as canonical correlation analysis (CCA) and principal component regression (PCR). To demonstrate the performance of the proposed method, we first evaluate its registration accuracy by comparing the deformation field predicted by our method with the deformation field estimated by the thin plate spline (TPS) based correspondence interpolation method on 306 serial prostate CT images of 24 patients. The average predictive error on the voxels around 5 mm of prostate boundary is 0.38 mm for our method of RR-based correlation model. Also, the corresponding maximum error is 2.89 mm. We then compare the speed for deformation interpolation by different methods. When considering the larger region of interest (ROI) with the size of 512 × 512 × 61, our method takes 24.41 seconds to interpolate the dense deformation field while TPS method needs 6.7 minutes; when considering a small ROI (surrounding prostate) with size of 112 × 110 × 93, our method takes 1.80 seconds, while TPS method needs 25 seconds. Experimental results show that the proposed method can achieve much faster registration speed yet with comparable registration accuracy, compared to the TPS-based correspondence (or deformation) interpolation approach.

TPS-HAMMER: Improving HAMMER registration algorithm by soft correspondence matching and thin-plate splines based deformation interpolation

TPS-HAMMER: Improving HAMMER registration algorithm by soft correspondence matching and thin-plate splines based deformation interpolation

TPS-HAMMER: Improving HAMMER registration algorithm by soft correspondence matching and thin-plate splines based deformation interpolation

We present an improved MR brain image registration algorithm, called TPS-HAMMER, which is based on the concepts of attribute vectors and hierarchical landmark selection scheme proposed in the highly successful HAMMER registration algorithm. We demonstrate that TPS-HAMMER algorithm yields better registration accuracy, robustness, and speed over HAMMER owing to (1) the employment of soft correspondence matching and (2) the utilization of thin-plate splines (TPS) for sparse-to-dense deformation field generation. These two aspects can be integrated into a unified framework to refine the registration iteratively by alternating between soft correspondence matching and dense deformation field estimation. Compared with HAMMER, TPS-HAMMER affords several advantages: (1) unlike the Gaussian propagation mechanism employed in HAMMER, which can be slow and often leaves unreached blotches in the deformation field, the deformation interpolation in the non-landmark points can be obtained immediately with TPS in our algorithm; (2) the smoothness of deformation field is preserved due to the nice properties of TPS; (3) possible misalignments can be alleviated by allowing the matching of the landmarks with a number of possible candidate points and enforcing more exact matches in the final stages of the registration. Extensive experiments have been conducted, using the original HAMMER as a comparison baseline, to validate the merits of TPS-HAMMER. The results show that TPS-HAMMER yields significant improvement in both accuracy and speed, indicating high applicability for the clinical scenario.

A multi-body system approach for finite-element modelling of rail flexibility in railroad vehicle applications

In this investigation, a non-linear finite-element formulation for modelling the rail structural flexibility in multi-body railroad vehicle systems is presented. Two different types of interpolations are used in the kinematic equations developed in this study; the geometry interpolation and the deformation interpolation. In the proposed formulation, the rails can have arbitrary geometry, which is described using the isoparametric geometric interpolation. The coordinates of the polynomials used in this interpolation represent constant position and gradient coordinates, which can be used to describe accurately the rail geometry. On the other hand, the rail deflections are described using the deformation interpolation and the non-linear finite-element floating frame of reference formulation. In the formulation proposed in this investigation, the rail tangent and normal vectors as well as other geometric parameters such as the curvature and torsion at the wheel/rail contact points are expressed in terms of the rail deformation coordinates. The non-linear dynamic coupling between the rail geometry and the vehicle dynamics is also considered in the formulation proposed in this paper. In particular, the coupling between the rail deformation and geometry, contact coordinates, and the non-linear vehicle dynamics is taken into consideration. Furthermore, the longitudinal, lateral, and spin creepages are expressed in terms of the rail deformations, which are the result of the wheel/rail contact forces. This non-linear coupled analysis allows for more accurate prediction of the railroad vehicle dynamics. The main outcome of this study is the development of a new procedure that allows building a complex track model that includes significant details using a finite-element preprocessor computer program. The detailed track model can be used as an input to a general purpose flexible multi-body computer program for a non-linear analysis that accounts for the dynamic coupling between the track flexibility and the vehicle coordinates. Numerical results are presented in order to demonstrate the use of the formulation proposed in this study.

Surface Splines Generalization and Large Deflection Interpolation

T HE surface spline presented by Harder and Desmarais [1] ingeniously has been generally applied in aeroelastic analysis since the comment by Rodden et al. [2], and has been a standard method of function interpolation [3]. It is based on the smalldeflection equation of an infinite plate, and so is also called infiniteplate spline (IPS). However, as a mathematical approach of data fitting, it is not limited to the hypothesis of small deflection. In this paper, we give a generalization of IPS to fit a vector value function with arbitrary number of variables, and apply it to the deformation interpolation of large deflection structures. In [2], Rodden et al. presented the importance of interpolation methods concerning the coupling of aerodynamic/structure by quoting the words of Hitch, and reviewed the development of 2-D interpolation methods before 1970s. After that, there are two major progresses in the surface spline method. The first one is called the finite-surface spline by Appa [4], which is based upon the finite element method of a finite plate. It improves the extrapolation of the infinite-surface spline, but it is less applicable in aeroelastic analysis. The other is a kind of generalized IPS, named thin-plate spline (TPS), which extends the number of variables from two to three [5], and is applied in ZAERO [6]. The deformation of a very flexible structure has more than one component, and so amethod to interpolate a vector function has to be established. In this note, the data fitting method between arbitrary dimension spaces is carried out by the further generalization of TPS. The transformation matrix defines a mapping from the original structure configuration to the set of displacement, or to the final configuration. Through the interpolation, the tangentmapping can be obtained as well to calculate the tangent or normal vectors of the configuration. This method provides a general interpolation scheme not limited to the structural and aerodynamic interface, but also applicable to interpolate any smooth data and curve/surface reconstruct. II. Mathematical Analysis

Simple CSRBF animation system with movement interpolation and collision detection

In this paper we propose that CSRBFs offer a mechanism to get extrapolated points of a deformed surface for various parts of an object under consideration and demonstrate plausible deformations. The paper extends the work of Kojekine et al. [1]. where software tools based on compactly supported radial based functions (CSRBF), were designed and applied for surface reconstruction of 3D geometric objects. We consider shape transformation (3D warping) as a general type of operation to create new shapes. Examples of applications can be found in animation, i.e. motion and deformation interpolation. A novel collision-detection method is also introduced. This new method allows fast collision query response. Most algorithms described in the literature deal with rigid bodies and are based on some kind of hierarchical representations. We present the alternative approach. The algorithm relies on the idea of "sensor particles": interacting particles distributed on a surface. Two types of particles that interact in a special way are used for determining the minimum distance between two models.

Application of the Mohr-circle construction to problems of inhomogeneous deformation

Off-axis Mohr circles are used to represent asymmetric second-order tensor quantities that describe deformation with homogeneous position gradients or flow with homogeneous velocity gradients. The validity of this representation is demonstrated. Several applications to problems of inhomogeneous deformation are explored by considering neighboring domains A and B that are homogeneously but differently deformed or flowing. The compatibility condition in Mohr space is that the circles for A and B should intersect in a point that represents the material line of the A/B boundary. In the first application it is assumed that the stretch tensor is known for each domain, and a Mohr construction is used to find the orientation of a compatible A/B boundary and the rotation of one domain with respect to the other. The second application is similar but involves the instantaneous state of a system. Non-parallel simple shearing at known rates is assumed in A and B, and a construction is used to find the instantaneous orientation of a compatible boundary and the spin of one domain with respect to the other. The third and fourth applications apply Mohr circles to problems of deformation interpolation and deformation averaging. In the former a deformation and shape is found for a domain C that lies between A and B, themselves incompatible, such that the A/C and C/B boundaries are both compatible.