Mesh Deformation Research Articles

Model-based registration for pneumothorax deformation analysis using intraoperative cone-beam CT images.

Because the lung deforms during surgery because of pneumothorax, it is important to be able to track the location of a tumor. Deformation of the whole lung can be estimated using intraoperative cone-beam CT (CBCT) images. In this study, we used deformable mesh registration methods for paired CBCT images in the inflated and deflated states, and analyzed their deformation. We proposed a deformable mesh registration framework for deformations of partial organ shapes involving large deformation and rotation. Experimental results showed that the proposed methods reduced errors in point-to-point correspondence. As a result of registration using surgical clips placed on the lung surface during imaging, it was confirmed that an average error of 3.9 mm occurred in eight cases. The result of analysis showed that both tissue rotation and contraction had large effects on displacement.

Automated Mesh Deformation for Computer-Aided Design Models That Exhibit Boundary Topology Changes

This paper describes an automated approach to deform an analysis mesh applied to a computer-aided design (CAD) model in response to a change in the shape of the CAD model. The process has been used to overcome a key issue that occurs during the shape optimization process. It is an advance over existing techniques because it works even when the boundary topology of the CAD model changes during the shape change, which other approaches cannot generally accommodate. To achieve the deformation, an analysis topology representation is created for each model, such that there is a one-to-one mapping between the analysis topology representing the models before and after the shape change. Strategies are presented to parameterize the superset entities in the analysis topology that have no global mathematical definition. The surface mesh is deformed in a way that allows the underlying surface/edge parameterizations to change, and it is shown how the domain mesh can be updated based on the surface mesh deformation. If the models before and after shape change have the same genus, then a small dimensional change in the shape of the model will result in meshes with the same topology, even if the topology of the underlying CAD representation has changed. This is highly desirable when evaluating sensitivities to a design change during an optimization.

Multiresolution analysis relying on Beta wavelet transform and multi-mother wavelet network for a novel 3D mesh alignment and deformation technique

In this paper, we propose a new 3D high mesh deformation technique to extract intuitive and interpretable deformation and alignment components. Our framework is based on a fast Beta wavelet transform for a multi-resolution analysis relying on multi-library wavelet neural network architecture. The main drawback of 3D high mesh deformation is the large number of triangles necessary to characterize a smooth surface; the majority of these techniques impose a very high computational cost. Our approach is based on the idea of combining the decomposition technique of multi-resolution analysis by Beta wavelet transform for each level of deformation process and a multi-mother wavelet network structure to construct an effective 3D alignment algorithm. We use, in our experiment, only the approximation coefficients at a chosen decomposition level to reduce the complexity of the mesh and to facilitate the alignment until reaching the target mesh, for the purpose of improving various executions and obtaining an optimal solution while reducing the error between the original and the reconstructed object to create a well-formed object. Then, to enhance the performance of wavelet networks, a novel learning algorithm based on multi-mother wavelet neural network architecture using trust region spherical is employed as an approximation tool for feature alignment between the source and the target models. This network architecture ensures the use of several mother wavelets to solve the problem of high mesh deformation utilizing the best wavelet mother that well models the object. Extensive experimental results demonstrate that the progressive deformation processes aim at avoiding the weaknesses of traditional approaches such as the slowness and the difficulty of finding an exact reconstruction.

A Mesh Deformation Method for CFD-Based Hull form Optimization

Computational fluid dynamics (CFD) is an effective tool for ship resistance prediction and hull form optimization. A three-dimensional volume mesh is essential for CFD simulation, and mesh generation requires much time and effort. Mesh deformation can reduce the time for mesh generation and simulation. The radial basis function (RBF) and inverse distance weighted (IDW) methods are well-known mesh deformation methods. In this study, the two methods are compared and a novel mesh deformation method for hull form optimization is proposed. For the comparison, a circular cylinder polyhedral mesh was deformed to the National Advisory Committee for Aeronautics (NACA) 0012 mesh. The results showed that the RBF method is faster than the IDW method, but the deformed mesh quality using the IDW method is better than that using the RBF method. Thus, the RBF method was modified to improve the deformed mesh quality. The centroids of the boundary layer cells were added to the control points, and the displacements of the centroids were calculated using the IDW method. The cells far from the ship were aligned to the free surface to minimize the numerical diffusion of the volume of fluid function. Therefore, the deformable region was limited by the deformed boundary, which reduced the time required for mesh deformation. To validate its applicability, the proposed method was applied for varying the bow shape of Japan Bulk Carrier (JBC). The resistances were calculated with the deformed meshes. The calculation time was reduced to approximately one-third using the result of the initial hull form as the initial condition. Thus, the proposed mesh deformation method is efficient and effective enough for CFD-based hull form optimization.

Tetrahedral mesh deformation with positional constraints

Deforming a tetrahedral mesh to conform to geometry modifications is a useful process in applications. This paper presents a method for tetrahedral mesh deformation driven by displacement of partial vertices of the mesh. The basic techniques behind the method are radial basis function (RBF)-based interpolation and adaptive mesh refinement. The method is realized by a warping process that transforms the mesh via iterative RBF-based interpolation to avoid the inversion of tetrahedra. Adaptive refinement by locally bisecting potentially inverted tetrahedra is also introduced to assure sufficiently large warping stepsizes. The refinement is performed on both the input mesh and the warped meshes concurrently to maintain the consistency of the topology. As a result, the method can effectively produce an inversion-free and topology compatible deformation mesh that satisfies hard positional constraints. Experimental results show the effectiveness of the method.

In vivo performance of intraperitoneal onlay mesh after ventral hernia repair

BackgroundVentral hernia repair needs to be improved since recurrence, postoperative pain and other complications are still reported in many patients. The behavior of implants in vivo is not sufficiently understood to design a surgical mesh mechanically compatible with the human abdominal wall. MethodsThis analysis was based on radiological pictures of patients who underwent laparoscopic ventral hernia repair. The pictures show the trunk of the patient at rest in a standing position and under side bending. The change in the distance between different tacks due to trunk movement was analyzed, which allowed us to determine the in vivo elongation of the mesh incorporated into the abdominal wall. FindingsThe relative elongations of the surgical mesh varied from a few percent to greater than 100% in two cases. The median of the median relative elongations obtained for all patients is 9.5%, and the median of the maximum relative elongations for all patients is 32.6%. The maximum elongation occurs between tacks that are next to each other. Trunk movement causes implant deformation, and this study provides quantitative information regarding changes in the distance between fasteners. InterpretationThe physiological movement of the human abdomen must be regarded as a very important factor in mesh deformation and should be considered in surgical practice to reduce the hernia recurrence rate and postoperative pain.

A new topology optimization framework for stiffness design of beam structures based on the transformable triangular mesh algorithm

Abstract This paper presents an explicit topology optimization method based on the so called Transformable Triangular Mesh (TTM) approach. It improves a general weakness of the traditional explicit approaches in the sense that the genus of initial geometry no longer affects the design result. In the proposed method, we first triangulate the initial geometry and organize it with the halfedge data structure. Then we employ the Laplacian energy controlled mesh deformation algorithm to realize smooth transition from the initial TTM. Furthermore, three geometrical mesh processing techniques (mesh subdivision, mesh split, and mesh refinement) are adopted to realize surface genus change. Respectively, the mesh subdivision is beneficial for the increase of mesh control hot points to obtain more degree of freedoms, the mesh split is able to rip connected triangles such that holes can be generated both inside a mesh and on the border, and the mesh refinement unifies the sizes and shapes of each triangle in the mesh such that no large distortion and self-intersection exist. To enhance the computational efficiency, we realize the above algorithm parallelly using CUDA. Finally, some benchmark examples (a cantilever beam, an MBB beam, and a cantilever beam with a fixed hole) are used to validate the algorithm. By comparing with state-of-the-art algorithms, our method proves to be reliable, accurate, and advanced.

Linear geometric algebra rotor estimator for efficient mesh deformation

The authors solve the problem of estimating the best rotation aligning two sets of corresponding vectors (also known as Wahba's problem or point cloud registration). The proposed method is among the fastest methods reported in recent literatures, moreover it is robust to noise, accurate and simpler than most other methods. It is based on solving the linear equations derived from the formulation of the problem in Euclidean Geometric Algebra. The authors show its efficiency in two applications: the as-rigid-as-possible (ARAP) surface modelling and the more smooth rotation enhanced ARAP mesh animation which is the only method capable of deforming surface modes with quality of tetrahedral models. Mesh deformation is a key technique in games, automated construction and robotics. The ARAP technique along with its improved variants, although have been extensively studied, can still not be achieved efficiently. Linear geometric algebra based rotor solution proposed in this study gives another perspective of the kernel problem. This, however, not only improves the real performance of the three-dimensional mesh deformation, but also provides a brand new computationally efficient solution to the Wahba's problem and point cloud registration, which has been closely related to the automation science and engineering.

Shape Optimization of Blended-Wing-Body Underwater Gliders Based on Free-Form Deformation

Currently developed underwater gliders can be roughly divided into the two types:traditional configuration and unconventional configuration. As a type of underwater gliders with unconventional configuration, a blended-wing-body (BWB) underwater glider has better fluid dynamic performances because of its unique shape. However, it is difficult to design the shape of the BWB underwater glider that has excellent hydrodynamic performances. Therefore, it is of great significance to optimize its shape, which this paper carries out by using the free-form deformation (FFD). The complete and automatic shape optimization framework is established by jointly using FFD parameterization method, CFD solver, optimization algorithm and mesh deformation method. The framework is used to optimize the shape of a BWB underwater glider. The average drag coefficient of the BWB underwater glider during its sinking and floating in one working period is used as the objective function to optimize its shape, with the volume constraints considered. The optimization results show that the gliding performance of the BWB underwater glider is remarkably enhanced.

Influence of Annular/Pocket Groove on the Static and Rotordynamic Characteristics of Hole-Pattern Seals

Abstract Annular damper seals, such as hole-pattern seals, are widely used to control leakage and enhance rotordynamic stability in turbomachinery, especially, for the balance-piston seal in the straight-through multistage centrifugal compressor, and the center seal in the back-to-back compressor. To avoid negative static stiffness (zero frequency), annular grooves on seal stator have been used to increase the direct static stiffness of hole-pattern seals by dividing a long seal to several shorter seal sections. However, few literatures are available for understanding the influences of grooves on seal static and rotordynamic characteristics. To comprehensively understand the effects of grooves on the static and rotordynamic characteristics of annular damper seals, a proposed three-dimensional (3D) transient CFD-based method was used to predict the rotordynamic characteristics of annular damper seals, based on the multifrequency one-dimensional rotor whirling model and mesh deformation technique. Moreover, a 3D steady CFD-based method based on the mesh deformation technique was also proposed to predict the static characteristics of annular damper seals. The accuracy and reliability of the present transient CFD-based method were demonstrated with the experimental data of frequency-dependent rotordynamic force coefficients for an experimental hole-pattern seal at three inlet preswirl conditions (μ0 = −0.244, 0, 0.598). Numerical results such as leakage flowrates, static and rotordynamic force coefficients were presented and compared for a conventional straight-through hole-pattern seal (without grooves, HPS) and two types of grooved hole-pattern seals (one with annular groove on stator, HPS-AG; one with pocket groove on stator, HPS-PG) with three groove positions (20%, 40%, 60% of seal axial length), at zero (μ0 = 0) and positive (μ0 = 0.598) inlet preswirl conditions. These seals are long (L/D = 0.75), with a diameter of 114.5 mm and a radial clearance of 0.2 mm. The effects of groove types (annular and pocket) and groove positions on seal's static and rotordynamic force coefficients were numerically discussed. Results show that compared to the conventional HPS seal, two types of grooves (annular and pocket) both produce a significant increase (20–150%, especially for the larger rotor eccentric ratios) in static direct stiffness, and the HPS-PG seal possesses the relatively optimal static stability. Two types of grooves (annular and pocket) both result in a slight increase (less than 5%) in seal leakage. The annular groove will significantly weaken the seal dynamic stiffness capability, however, the pocket groove shows only very weak influences. Compared to the conventional HPS seal, the HPS-PG seal possesses the similar increasing effective damping and decreasing crossover frequency with the HPS-AG seal. This suggests that the pocket groove is a more suitable design to improve the seal static and rotordynamic characteristics. The rotordynamic force coefficients show a strong dependence on the groove location for the HPS-AG seal, but which is insensitive for the HPS-PG seal. The optimal location of annular groove is strongly related to the inlet preswirl conditions.

Evolution of Sliding Contact Wear Between Deformable Conducting Bodies via a Multiphysics Framework

AbstractA multiphysics computational framework is introduced and exercised to predict the wear behavior of two deformable, heat-conducting bodies under conditions of sliding contact. This framework enables the solution of a coupled system of partial differential equations (PDEs) expressing the conservation of energy and momentum along with two ordinary differential equations (ODEs) expressing mass conservation. This system is intended to capture wear evolution for each of the bodies forming a wear pair, in a self-consistent manner. Furthermore, an arbitrary-Lagrangian-Eulerian approach has been integrated to enable tracking the evolution of the wear fronts on both elements of the sliding contact pair through physics-informed mesh deformation. A theorem and a corollary are proved to indicate that most existing models describing wear that are expressed in the form of an ODE are actually manifestations of the law of conservation of mass. The framework is applied for two distinct slider-base pairs. The first involves an aluminum alloy slider and a copper alloy base. The second pair is identical to the first except it contains a thin strip of soda-lime glass embedded in the surface of the base. The effects of this glass layer on the wear of all participating bodies in comparison to the pair that does not contain this layer are presented. They indicate that while the glass layer has a wear mitigation effect for the stationary base it slightly increases the wear of the slider when compared with the respective bodies when the glass is not present.

Image stitching with positional relationship constraints of feature points and lines

The elimination of parallax and the processing of natural issue in complex scenes are challenging tasks for image stitching. In this paper, an image stitching method with positional relationship constraints of feature points and lines, which can accomplish accurate alignment and reduce projection distortion, is proposed. At first, to reduce the computational cost and the number of outliers on subsequent feature matching, we combine the template matching to propose a quick way for detecting overlapping regions. Then, the appropriate reference image is determined to mitigate the projection distortion that the image warping is in the cases of non-planar geometry of the scenes. Furthermore, a local mesh model based on dual features is established to guide the mesh deformation. And an energy function is designed to refine alignment. In addition to alignment error terms, a novel positional relationship constraint term is proposed to improve quality of naturalness of final stitching results. Finally, experimental results demonstrate that our approach is superior to the existing image stitching algorithms in improving quality of the stitched image naturalness.

Displacement‐Correlated XFEM for Simulating Brittle Fracture

AbstractWe present a remeshing‐free brittle fracture simulation method under the assumption of quasi‐static linear elastic fracture mechanics (LEFM). To achieve this, we devise two algorithms. First, we develop an approximate volumetric simulation, based on the extended Finite Element Method (XFEM), to initialize and propagate Lagrangian crack‐fronts. We model the geometry of fracture explicitly as a surface mesh, which allows us to generate high‐resolution crack surfaces that are decoupled from the resolution of the deformation mesh. Our second contribution is a mesh cutting algorithm, which produces fragments of the input mesh using the fracture surface. We do this by directly operating on the half‐edge data structures of two surface meshes, which enables us to cut general surface meshes including those of concave polyhedra and meshes with abutting concave polygons. Since we avoid triangulation for cutting, the connectivity of the resulting fragments is identical to the (uncut) input mesh except at edges introduced by the cut. We evaluate our simulation and cutting algorithms and show that they outperform state‐of‐the‐art approaches both qualitatively and quantitatively.

A thermomechanical model for mesh deflection calculation of crown spur gear pair

An analytical model of evaluating tooth pair deflection along the line of contact is proposed in this paper to preliminarily determine the load distribution between tooth pairs contacting instantaneously for crown spur gears. Further, a three-dimensional thermomechanical point contact method is introduced for modeling the normal approach of two contacting teeth. Combined with tooth and fillet-foundation deflections, a coupled thermoelastic mesh deformation model for crown gears is developed. The influence of load, angular velocity and friction coefficient on the normal approach of the contact, load sharing ratio and transmission error during meshing are respectively investigated. It is suggested that without considering thermal influence, the vibration excitation of gears can be underestimated. Considering the coupled thermoelastic deformation of meshing gears may result in a better evaluation of transmission error and facilitate the subsequent tooth modification design and dynamic study.

Residue-Pole Methods for Variability Analysis of S-parameters of Microwave Devices with 3D FEM and Mesh Deformation

Residue-Pole Methods for Variability Analysis of S-parameters of Microwave Devices with 3D FEM and Mesh Deformation

Spring‐network model of red blood cell: From membrane mechanics to validation

SummaryRed blood cell membrane is highly elastic and proper modeling of this elasticity is essential for biomedical applications that involve computational experiments with blood flow. Inseparable and often some of the most difficult parts of modeling process are verification and validation. In this work, we present a revised model, which uses a spring network to represent the cell membrane immersed in a fluid and has been successfully used in blood flow simulations. We demonstrate the validation steps by first deriving the theoretical relations between the bulk properties of elastic membranes—shear modulus and area compressibility modulus—and parameters of the model that enter the nonlinear stretching and local area conservation computational moduli. We verify the theoretically derived relations using computer simulations of deformable triangular mesh. We calibrate the model by performing a computational version of the optical tweezers experiment. And finally, we validate the modeled cell behavior by investigating the cell rotation frequency when it is subjected to shear flow and cell deformation in narrow channels. The supplementary material contains an extensive dataset that can be used for setting different elastic properties for each cell in simulations of dense suspensions, while still conforming to the biological data. This work contains a complete model development process: From modelling of basic mechanical concepts (the spring network) and advanced biomechanical concepts (such as elasticity of the membrane), through calibration process towards the final stage of model validation.

A particle finite element-based model for droplet spreading analysis

A particle finite element method-based model is proposed to analyze droplet dynamics problems, particularly droplet spreading on solid substrates (wetting). The model uses an updated Lagrangian framework to formulate the governing equations of the liquid. The curvature of the liquid surface is tracked accurately using a deforming boundary mesh. In order to predict the spreading rate of the droplet on the solid substrate and track the corresponding contact angle evolution, dissipative forces at the contact line are included in the formulation in addition to the Navier-slip boundary conditions at the solid–liquid interface. The inclusion of these boundary conditions makes it possible to account for the induced Young’s stress at the contact line and for the viscous dissipation along the solid–liquid interfacial region. These are found to be essential to obtain a mesh-independent physical solution. The temporal evolution of the contact angle and the contact line velocity of the proposed model are compared with spreading droplets and micro-sessile droplet injection experiments and are shown to be in good agreement.

Aerodynamics Design for Automotive Shape based on Approximate Optimization Algorithm

Since it is difficult to find the optimal solution directly by the traditional CFD optimization method due to its strong dependence on the designer’s experience, an automatic aerodynamic optimization design platform for automotive shape was built based on mesh deformation technology, surrogate model and optimization algorithm in this paper. A parameterized model of an automotive was established. Latin hypercube method was adopted to select sample points. The drag coefficients corresponding to sample points were calculated by CFD simulation, whereby the influence of each parameter on drag coefficient was obtained. By comparing the calculation time, optimization effect and optimization accuracy of 9 combinations of surrogate models and optimization algorithms, the combination of RBF model and NLPQL algorithm was selected as the optimal one which is the most appropriate for the aerodynamic optimization design for automotive shape

An efficient large-scale mesh deformation method based on MPI/OpenMP hybrid parallel radial basis function interpolation

An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption. Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation, the present method employs different surface points sets and influence radius for each volume point movement, accompanied with efficient geometry searching strategy. The deformed surface points, also called Control Points (CPs), are stored in each processor. The displacement of spatial points is interpolated by using only 20–50 nearest control points, and the local influence radius is set to 5–20 times the maximum displacement of control points. To shorten the searching time for the nearest control point clouds, an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique. Besides, an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications. Three 3D cases, including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements, are used to test the present mesh deformation method. The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 45° and more than 80% parallel efficiency with 1024 MPI processors. In addition, the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.

Dynamic Characteristics and Stability Prediction of Steam Turbine Rotor Based on Mesh Deformation

In order to study the steam flow excited vibration caused by the eccentricity of a rotor, three-dimensional rotor whirl motion is simulated based on mesh deformation. The mechanism of steam flow excited vibration and its influence on the dynamic characteristics of the rotor are investigated. The results show that the exciting forces change with the displacement of the rotor’s centre. Rotor dynamic coefficients are nonlinear when the rotor whirls pass the mesh deformation. The rotor dynamic coefficients and effective damping increase with the increase of whirl frequency. When the whirl frequency is 24.41 Hz, the rotor dynamic coefficients are strongly affected by rotational velocity. The maximum fluctuations of average direct stiffness, cross-coupling stiffness, direct damping and cross-coupling damping are 8.1 %, 113.2 %, 45.8 %, and 121.0 %, respectively. Effective damping fluctuates greatly when both whirl and rotational frequency are 24.41 Hz. The direct stiffness, direct damping, and effective damping increase with the increase of pressure ratio, which can improve rotor stability. The pressure fluctuation on the rotor’s surface is a primary reason for steam flow excited vibration. The stability margin of the rotor can be estimated precisely via effective damping.