Diarthrodial joint contact models: finite element model development of the human hip

The demands associated with modeling geometrically complex anatomic structures often limit the utility of musculoskeletal finite element (FE) analyses. Automated meshing routines typically rely on the use of tetrahedral elements. Hexahedral elements, however, often outperform tetrahedral elements, namely during contact analyses. Hence, a need exists for a preprocessor geared towards automated hexahedral meshing of biologic structures. Two meshing schemes for finite element mesh development of the human hip are presented: (1) a projection method, coupled with a surface smoothing algorithm, has been applied to accommodate the near spherical nature of the femoral head articular cartilage surface, while (2) a technique termed the preferential method was developed to mesh the acetabulum. The latter technique benefits from a user traced bound of the articular surface. High-quality, three-dimensional continuum models, consisting solely of hexahedral elements, were generated for the femoral head and the acetabulum. To check the validity of the meshing routines, a transient deformable–deformable contact finite element analysis was carried out. Gait cycle kinematics and kinetics from the weight-bearing stance phase were considered. The contact pressure (1.74 MPa) was in agreement with the values reported in the literature.     

A template-based approach for parallel hexahedral two-refinement

We provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3 prior to smoothing.     

Meshing complexity: predicting meshing difficulty for single part CAD models

This paper proposes a method for predicting the complexity of meshing computer aided design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of effort required to generate a valid finite element mesh on a given CAD geometry. A function is proposed to approximate the meshing complexity for single part CAD models. The function is dependent on a user defined element size as well as on data extracted from the geometry and topology of the CAD part. Several geometry and topology measures are proposed, which both characterize the shape of the CAD part and detect configurations that complicate mesh generation. Based on a test suite of CAD models, the function is demonstrated to be accurate within a certain range of error. The solution proposed here is intended to provide managers and users of meshing software a method of predicting the difficulty in meshing a CAD model. This will enable them to make decisions about model simplification and analysis approaches prior to mesh generation.     

Topological operations for editing the singularity on a hex mesh

This paper introduces topological operations for editing the singularity on a hex mesh while maintaining the connectivity of hexahedral mesh. The operations include (1) an enhanced column collapse operation that can avoid generating the poor-quality elements; (2) a column insertion operation that is the opposite operation of column collapse; (3) four semantic operations for achieving the movement of different types of singularity pairs based on column operations. To demonstrate their effectiveness, two related applications are provided. One is moving face-based hex mesh editing, in which the interface between the original mesh and the new region mesh is made structured using the semantic operations. The other is hex mesh structure simplification based on the topological operations.

     

Automated Conformal Hexahedral Meshing Constraints, Challenges and Opportunities

Automated hexahedral element meshing has been the ‘Holy Grail’ of mesh generation research for years. The rigid connectivity and shape constraints of these meshes provide the challenge. The ever-present economic pressure for automating meshing of complex geometries, difficult transitions and large mesh sizes establishes the opportunity. This paper will systematically review the requirements of the hexahedral meshing challenge, the various approaches to the solution of the problem (along with their respective attributes), and some musings about future research opportunities.     

Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm

This paper describes mesh correction techniques necessary for meshing an arbitrary volume with a completely hexahedral mesh. Specifically, it describes seams and wedges, mechanisms that overcome major hurdles encountered in the preliminary work on the plastering algorithm. The plastering algorithm iteratively projects layers of elements inward from a quadrilateral discretization of the volume's bounding faces. Seams and wedges resolve incompatibilities in the mesh and in the progressing boundary, thus ensuring the correct formation of a hexahedral mesh from the plastering algorithm.     

Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization

The combinatorial dual of a hex mesh induces a collection of mutually intersecting surfaces (dual sheets). Inspired by Campen et al.'s work on quad meshing [CBK12, CK14], we propose to directly generate such dual sheets so that, as long as the volume is properly partitioned by the dual sheets, we are guaranteed to arrive at a valid all‐hex mesh topology. Since automatically generating dual sheets seems much harder than the 2D counterpart, we chose to leave the task to the user; our system is equipped with a few simple 3D modeling tools for interactively designing dual sheets. Dual sheets are represented as implicit surfaces in our approach, greatly simplifying many of the computational steps such as finding intersections and analyzing topology. We also propose a simple algorithm for primalizing the dual graph where each dual cell, often enclosing singular edges, gets mapped onto a reference polyhedron via harmonic parameterization. Preservation of sharp features is simply achieved by modifying the boundary conditions. We demonstrate the feasibility of our approach through various modeling examples.     

Non-rigid 3D shape tracking from multiview video

We present a fast and efficient non-rigid shape tracking method for modeling dynamic 3D objects from multiview video. Starting from an initial mesh representation, the shape of a dynamic object is tracked over time, both in geometry and topology, based on multiview silhouette and 3D scene flow information. The mesh representation of each frame is obtained by deforming the mesh representation of the previous frame towards the optimal surface defined by the time-varying multiview silhouette information with the aid of 3D scene flow vectors. The whole time-varying shape is then represented as a mesh sequence which can efficiently be encoded in terms of restructuring and topological operations, and small-scale vertex displacements along with the initial model. The proposed method has the ability to deal with dynamic objects that may undergo non-rigid transformations and topological changes. The time-varying mesh representations of such non-rigid shapes, which are not necessarily of fixed connectivity, can successfully be tracked thanks to restructuring and topological operations employed in our deformation scheme. We demonstrate the performance of the proposed method both on real and synthetic sequences.     

Hexahedral mesh generation constraints

For finite element analyses within highly elastic and plastic structural domains, hexahedral meshes have historically offered some benefits over tetrahedral finite element meshes in terms of reduced error, smaller element counts, and improved reliability. However, hexahedral finite element mesh generation continues to be difficult to perform and automate, with hexahedral mesh generation taking several orders of magnitude longer than current tetrahedral mesh generators to complete. Thus, developing a better understanding of the underlying constraints that make hexahedral meshing difficult could result in dramatic reductions in the amount of time necessary to prepare a hexahedral finite element model for analysis. In this paper, we present a survey of constraints associated with hexahedral meshes (i.e., the conditions that must be satisfied to produce a hexahedral mesh). In presenting our formulation of these constraints, we will utilize the dual of a hexahedral mesh. We also discuss how incorporation of these constraints into existing hexahedral mesh generation algorithms could be utilized to extend the class of geometries to which these algorithms apply. We also describe a list of open problems in hexahedral mesh generation and give some context for future efforts in addressing these problems.     

Hexahedral mesh smoothing via local element regularization and global mesh optimization

The quality of finite element meshes is one of the key factors that affect the accuracy and reliability of finite element analysis results. In order to improve the quality of hexahedral meshes, we present a novel hexahedral mesh smoothing algorithm which combines a local regularization for each hexahedral mesh, using dual element based geometric transformation, with a global optimization operator for all hexahedral meshes. The global optimization operator is composed of three main terms, including the volumetric Laplacian operator of hexahedral meshes and the geometric constraints of surface meshes which keep the volumetric details and the surface details, and another is the transformed node displacements condition which maintains the regularity of all elements. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Several experimental results are presented to demonstrate that our method obtains higher quality results than other state-of-the-art approaches.     

Feature-based 3D morphing based on geometrically constrained spherical parameterization

Current trends in free form editing motivate the development of a novel editing paradigm for CAD models beyond traditional CAD editing of mechanical parts. To this end, we need robust and efficient 3D mesh deformation techniques such as 3D structural morphing.In this paper, we present a feature-based approach to 3D morphing of arbitrary genus-0 polyhedral objects that is appropriate for CAD editing. The technique is based on a sphere parameterization process built on an optimization technique that uses a target function to maintain the correspondence between the initial polygons and the mapped ones, while preserving topology and connectivity through a system of geometric constraints. Finally, we introduce a fully automated feature-based technique that matches surface areas (feature regions) with similar topological characteristics between the two morphed objects and performs morphing according to this feature correspondence list. Alignment is obtained without user intervention based on pattern matching between the feature graphs of the two morphed objects.     

A framework for 3D model reconstruction in reverse engineering

We present a framework for 3D model reconstruction, which has potential applications to a spectrum of engineering problems with impacts on rapid design and prototyping, shape analysis, and virtual reality. The framework, composed of four main components, provides a systematic solution to reconstruct geometric model from the surface mesh of an existing object. First, the input mesh is pre-processed to filter out noise. Second, the mesh is partitioned into segments to obtain individual geometric feature patches. Then, two integrated solutions, namely solid feature based strategy and surface feature based strategy, are exploited to reconstruct primitive features from the segmented feature patches. Finally, the modeling operations, such as solid boolean and surface trimming operations, are performed to “assemble” the primitive features into the final model. The concepts of “feature”, “constraint” and “modeling history” are introduced into the entire reconstruction process so that the design intents are retrieved and exhibited in the final model with geometrical accuracy, topological consistency and flexible editability. A variety of industrial parts have been tested to illustrate the effectiveness and robustness of our framework.     

Constrained mesh optimization on boundary

This paper presents a new mesh optimization approach aiming to improve the mesh quality on the boundary. The existing mesh untangling and smoothing algorithms (Vachal et al. in J Comput Phys 196: 627–644, 2004; Knupp in J Numer Methods Eng 48: 1165–1185, 2002), which have been proved to work well to interior mesh optimization, are enhanced by adding constrains of surface and curve shape functions that approximate the boundary geometry from the finite element mesh. The enhanced constrained optimization guarantees that the boundary nodes to be optimized always move on the approximated boundary. A dual-grid hexahedral meshing method is used to generate sample meshes for testing the proposed mesh optimization approach. As complementary treatments to the mesh optimization, appropriate mesh topology modifications, including buffering element insertion and local mesh refinement, are performed in order to eliminate concave and distorted elements on the boundary. Finally, the optimization results of some examples are given to demonstrate the effectivity of the proposed approach.     

A spatial warping method for freeform modeling based on a level-set method

Providing an intuitive and effective tool for freeform geometric modeling is important for product design. We introduce in this paper a level-set based spatial warping method for freeform modeling, allowing shape deformation to be initialed by rigid body transformations of volumetric tools. Intuitive user operations including imprinting, deformation and smoothing are developed to shield the user from the underlying geometric complexity. Unlike mesh-based spatial warping methods, the developed method represents a digital model by implicit distance field data and describes its change of geometry by the level-set method. This guarantees the generation of topologically correct triangular mesh models and circumvents the error-prone remeshing and mesh-repairing processes, thus preventing topological errors such as self-intersections. We present this method with algorithm details, numerical experiments and modeling examples.     

Fun sheet matching: towards automatic block decomposition for hexahedral meshes

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay??s algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3- and 4-valent vertices.     

New method for graded mesh generation of all hexahedral finite elements

Mapping method is widely applied by most of commercial mesh generators because of its efficiency, mesh quality. One of the obstacles to apply the mapping method and generate a graded all hexahedral mesh of high quality in an arbitrarily three-dimensional domain is the generation of hexahedral parent elements on a super-element that allows for gradations in three co-ordinate directions. This paper presents a pattern module’s method to generate the graded mesh of all hexahedral elements in a cube and thus improves the mapping method. The method requires few calculations.     

Interpolatory,solid subdivision of unstructured hexahedral meshes

This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes. To date, nearly every existing volumetric subdivision scheme is approximating, i.e., with each application of the subdivision algorithm, the geometry shrinks away from its control mesh. Often, an approximating algorithm is undesirable and inappropriate, producing unsatisfactory results for certain applications in solid modeling and engineering design (e.g., finite element meshing). We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials. We show that our algorithm is a natural generalization of the butterfly subdivision surface scheme to a tri-variate, volumetric setting.     

Creating geometry and mesh models for nuclear reactor core geometries using a lattice hierarchy-based approach

Nuclear reactor cores are constructed as rectangular or hexagonal lattices of assemblies, where each assembly is itself a lattice of fuel, control, and instrumentation pins, surrounded by water or other material that moderates neutron energy and carries away fission heat. We describe a system for generating geometry and mesh for these systems. The method takes advantage of information about repeated structures in both assembly and core lattices to simplify the overall process. The system allows targeted user intervention midway through the process, enabling modification and manipulation of models for meshing or other purposes. Starting from text files describing assemblies and core, the tool can generate geometry and mesh for these models automatically as well. Simple and complex examples of tool operation are given, with the latter demonstrating the generation of meshes with 12 million hexahedral elements in <30?min on a desktop workstation, using about 4?GB of memory. The tool is released as open source software as part of the MeshKit mesh generation library.     

A Survey of Indicators for Mesh Quality Assessment

We analyze the joint efforts made by the geometry processing and the numerical analysis communities in the last decades to define and measure the concept of “mesh quality”. Researchers have been striving to determine how, and how much, the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depends on the particular mesh adopted to model the problem, and which geometrical features of the mesh most influence the result. The goal was to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. We overview the most common quality indicators, measures, or metrics that are currently used to evaluate the goodness of a discretization and drive mesh generation or mesh coarsening/refinement processes. We analyze a number of local and global indicators, defined over two- and three-dimensional meshes with any type of elements, distinguishing between simplicial, quadrangular/hexahedral, and generic polytopal elements. We also discuss mesh optimization algorithms based on the above indicators and report common libraries for mesh analysis and quality-driven mesh optimization.     

Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and hexahedral meshes. The algorithm iteratively improves a quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a regularized algebraic distortion measure of the elements. We propose several techniques to improve the robustness and the computational efficiency of the optimization algorithm. In addition, we have adopted an object-oriented paradigm to create a common framework to smooth meshes composed by any type of elements, and using different minimization techniques. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when the initial meshes contain a large number of tangled elements.