Three-dimensional Finite Element Mesh Research Articles

Multi-Physics Three-Dimensional Component Placement and Routing Optimization Using Geometric Projection

Abstract This article presents a novel three-dimensional topology optimization framework developed for 3D spatial packaging of interconnected systems using a geometric projection method (GPM). The proposed gradient-based topology optimization method simultaneously optimizes the locations and orientations of system components (or devices) and lengths, diameters, and trajectories of interconnects to reduce the overall system volume within the prescribed 3D design domain. The optimization is subject to geometric and physics-based constraints dictated by various system specifications, suited for a wide range of transportation (aerospace or automotive), heating, ventilation, air-conditioning, and refrigeration, and other complex system applications. The system components and interconnects are represented using 3D parametric shapes such as cubes, cuboids, and cylinders. These objects are then projected onto a three-dimensional finite element mesh using the geometric projection method. Sensitivities are calculated for the objective function (bounding box volume) with various geometric and physics-based (thermal and hydraulic) constraints. Several case studies were performed with different component counts, interconnection topologies, and system boundary conditions and are presented to exhibit the capabilities of the proposed 3D multi-physics spatial packaging optimization framework.

Momentary finite element for elasticity 3D problems

A description of a new 8-node finite element in the form of a hexahedron is given for solving elasticity 3D problems. This finite element has the following features. This is a linear approximation of functions in the element, one point of integration and taking into account the moments of forces in the element. The finite element is based on “rare mesh” FEM schemes—finite element schemes in the form of n-dimensional cubes (square, cube, etc.) with templates in the form of inscribed simplexes (triangle, tetrahedron, etc.). Among the rare mesh schemes, schemes in 3-dimensional and 7-dimensional spaces are successful, in which the simplex can be arranged symmetrically with respect to the center of the n-dimensional cube. The rare mesh FEM schemes have not the hourglass instability due to the fact that the template of the finite element operator has the form of a simplex. Compared to traditional linear finite elements in the form of a simplex, rare mesh schemes are more economical and converge better, since they do not have the effect of overestimated shear stiffness. Moment FEM schemes are constructed by rare mesh schemes higher dimensional projection, respectively, on a two-dimensional or three-dimensional finite element mesh. The resulting finite elements are close to the known polylinear elements and surpass them in efficiency. The schemes contain parameters that allow you to control the convergence of numerical solutions. The possibility of applying this approach to the construction of numerical schemes for solving other problems of mathematical physics is discussed.

Finite element analysis of Tumor Treating Fields in a patient with posterior fossa glioblastoma

IntroductionTumor Treating Fields (TTFields) are alternating electric fields at 200 kHz that disrupt tumor cells as they undergo mitosis. Patient survival benefit has been demonstrated in randomized clinical trials but much of the data are available only for supratentorial glioblastomas. We investigated a series of alternative array configurations for the posterior fossa to determine the electric field coverage of a cerebellar glioblastoma.MethodsSemi-automated segmentation of neuro-anatomical structures was performed while the gross tumor volume (GTV) was manually delineated. A three-dimensional finite-element mesh was generated and then solved for field distribution.ResultsCompared to the supratentorial array configuration, the alternative array configurations consist of posterior displacement the 2 lateral opposing arrays and inferior displacement of the posteroanterior array, resulting in an average increase of 46.6% electric field coverage of the GTV as measured by the area under the curve of the electric field-volume histogram (EAUC). Hotspots, or regions of interest with the highest 5% of TTFields intensity (E5%), had an average increase of 95.6%. Of the 6 posterior fossa configurations modeled, the PAHorizontal arrangement provided the greatest field coverage at the GTV when the posteroanterior array was placed centrally along the patient’s posterior neck and horizontally parallel, along the longer axis, to the coronal plane of the patient’s head. Varying the arrays also produced hotspots proportional to TTFields coverage.ConclusionsOur finite element modeling showed that the alternative array configurations offer an improved TTFields coverage to the cerebellar tumor compared to the conventional supratentorial configuration.

An automated a priori knowledge-based p-adaptive three-dimensional finite element mesh improvement method for stress analysis of underground excavations with prismatic cross-sections

ABSTRACT With increasing modelling capabilities in geomechanics incorporating non-linear material behaviour, an increasing complexity of models representing excavation of tunnels can be analysed. Often, analysis is using finite elements, where problems size can be a controlling factor due to limited computational resources. An approach to analysing these problems is to optimise the discretisation of the differential equations by concentrating elements where solution accuracy counts the most. This paper describes a priori p-refinement method for mesh improvement for stress analysis of prismatic tunnels. The improvement results in a mesh with higher-order elements near regions of interest and lower-order elements elsewhere. The focus is on the automated insertion of transitional elements at the interface of the two regions, based on the zone of disturbance in the geomaterial. The method was incorporated into a finite element code, and its performance was tested on practical problems, where the global stiffness matrix size was reduced by 70%, and the calculation times were significantly shortened. The average difference compared to complex models without mesh improvement was less than 3%. It is anticipated that the presented method enables analysis of problems that would otherwise be beyond the current computing capabilities leading to safer and economical designs.

Three-dimensional magnetic resonance imaging of fetal head molding and brain shape changes during the second stage of labor.

To demonstrate and describe fetal head molding and brain shape changes during delivery, we used three-dimensional (3D) magnetic resonance imaging (MRI) and 3D finite element mesh reconstructions to compare the fetal head between prelabor and the second stage of labor. A total of 27 pregnant women were examined with 3D MRI sequences before going into labor using a 1 Tesla open field MRI. Seven of these patients subsequently had another set of 3D MRI sequences during the second stage of labor. Volumes of 2D images were transformed into finite element 3D reconstructions. Polygonal meshes for each part of the fetal body were used to study fetal head molding and brain shape changes. Varying degrees of fetal head molding were present in the infants of all seven patients studied during the second phase of labor compared with the images acquired before birth. The cranial deformation, however, was no longer observed after birth in five out of the seven newborns, whose post-natal cranial parameters were identical to those measured before delivery. The changing shape of the fetal brain following the molding process and constraints on the brain tissue were observed in all the fetuses. Of the three fetuses presenting the greatest molding of the skull bones and brain shape deformation, two were delivered by cesarean-section (one after a forceps failure and one for engagement default), while the fetus presenting with the greatest skull molding and brain shape deformation was born physiologically. This study demonstrates the value of 3D MRI study with 3D finite element mesh reconstruction during the second stage of labor to reveal how the fetal brain is impacted by the molding of the cranial bones. Fetal head molding was systematically observed when the fetal head was engaged between the superior pelvic strait and the middle brim.

Construction of polyhedral finite element meshes based upon marching cube algorithm

Hexahedral meshes that exhibit the superiority in terms of solution accuracy and convergence rate are preferred to other types of meshes in the finite element analysis. However, the construction of the hexahedral meshes for complex geometries is still considered troublesome due to their poor geometric adaptability. This paper presents an efficient grid-based scheme to automatically generate polyhedral meshes including the hexahedral elements, and thus to provide hexahedral-dominant meshes for three-dimensional geometry with complex shapes. On the basis of the marching cube algorithm with a background grid composed of a regular arrangement of cubes, surface topologies for the background cubes are defined to represent the three-dimensional boundaries of a given domain. Then, in order to generate a three-dimensional finite element mesh, the surface topologies of the marching cube algorithm are systematically expanded to polyhedral volume topologies. Meanwhile, a topology ambiguity problem inherent in the marching cube algorithm is effectively resolved to generate an appropriate polyhedral mesh even for an arbitrary complex geometry. Several examples including biostructure modeling demonstrate that the proposed mesh generation scheme can easily discretize complex three-dimensional domains with hexahedral-dominant meshes, which are composed of the polyhedral elements near the domain boundaries and the hexahedral elements that come from the background cubes inside the domains. Furthermore, to show the applicability and effectiveness of polyhedral meshes in the finite element analysis, some structural analyses are performed using the smoothed finite element method that can be straightforwardly adapted to polyhedral elements of arbitrary shape.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Meticulous simulation and evaluation of seepage control effects at right bank dam foundation and underground powerhouse of Jinping I hydropower station

This case study presents a systematic performance assessment of the seepage control system at the right bank abutment of Jinping I Hydropower Station. By utilizing the in-situ measurements of seepage field, the characteristics of groundwater flow behaviors in the dam foundation and around the underground powerhouse were analyzed. Based on an equivalent continuum method, an anisotropic seepage tensor model of the fractured rock mass in the dam site area was established. Considering the features of topography, geological settings and hydraulic structures, a three-dimensional finite element mesh with complex seepage control structures was generated. A numerical method combining a substructure technique, a variational inequality formulation of Signorini’s type and an adaptive penalized Heaviside function (short for SVA method) is adopted to simulate the three-dimensional seepage field at the dam site. On this basis, the distribution of seepage field during the operation period was predicted, and the performance of the seepage control system was evaluated. Besides, the influence of critically oriented fractures along the direction of NWW on the seepage control effect was also discussed. The methodology presented in this study is useful for understanding the groundwater flow behavior and the performance of the seepage control system in hydraulic engineering.

Construction of hexahedral finite element mesh capturing realistic geometries of a petroleum reserve

The three-dimensional finite element mesh capturing realistic geometries of the Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh consists of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time while maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill, Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for various civil and geological structures.

An innovative numerical modeling strategy for the structural analysis of historical monumental buildings

In this paper, an innovative numerical modeling strategy for the structural analysis of historical monumental buildings is presented. The strategy is based on a procedure that enables the semi-automatic transformation of a three-dimensional points cloud surveyed through terrestrial laser scanner or closed range photogrammetry into a three-dimensional finite element mesh, as well as its mechanical characterization. Therefore, an increase of the level of automation in the mesh generation process is attained and a large reduction in the required time in comparison with traditional modeling procedures is achieved. In order to validate the new strategy, an application to the case study of the San Felice sul Panaro (Italy) fortress is carried out. The reliability of the proposed model is assessed through a comparison between the results of structural analyses and the crack pattern experienced by the structure during the Emilia earthquake (2012). Moreover, the vulnerability assessment of the main tower of the fortress is performed through simplified pushover analyses conducted on the generated mesh.

Elasto-thermoelectric non-linear, fully coupled, and dynamic finite element analysis of pulsed thermoelectrics

This paper presents a numerical study on the influence of pulsed electric signals applied to the overcooling of thermoelectric devices. To this end, an experimental setup taken from the literature and a commercial cell are simulated using a complete, specially developed research finite element code. The electro-thermal coupling is extended to include the elastic field, demonstrating that the increment of cooling can produce mechanical failure. Numerical results are developed and the variation of overcooling versus pulse gain and versus duration is validated towards a new analytical expression and the experimental data. The issue of optimal intensity at steady-state is also newly developed. Thermal and mechanical trends are presented using constant and variable (with temperature) material properties for a single thermoelement. While some of the first trends are similar to those of published works, others are different or directly new, all closer to those of the experiments. The mechanical results have not been thoroughly studied until recently. The three-dimensional finite element mesh includes non-thermoelectric materials that are fundamental for the current study. Distribution of stresses during steady and transient states are shown inside the thermoelement, for five components and for the combined Tresca stress. Concentrations at corners of the lower side appear close to the cold face. Due to these concentrations, 27-node isoparametric, quadratic brick elements are used. It is shown that the mechanical field is an important factor in the design of pulsed thermoelectrics, since for practical applications the stress levels are close or slightly above the admissible limits.

High fidelity multidisciplinary design optimisation of an electromagnetic device

The application of multidisciplinary design optimisation is mostly confined to bi-disciplinary systems such as fluid-structure interaction problems. High fidelity models of three disciplines involving electromagnetic-thermal-structural designs are rare. Here, the multidisciplinary optimisation of such a design is presented. The device comprises a C-shaped iron core and a single coil. The problem is decomposed using a monolithic multidisciplinary feasible architecture. The multidisciplinary analyses involve a single three-dimensional finite element mesh for transient non-linear electromagnetic, non-linear-static thermal, and linear-static structural models. During each multidisciplinary iteration the mesh is linearly morphed. A gradient based optimisation algorithm in combination with a multi-start routine is applied to the constrained mass minimisation problem. Multidisciplinary feasibility is ensured by convergence of a single coupling parameter i.e. air-gap deformation. In conclusion, some multidisciplinary optimisation, analyses, and decomposition considerations are discussed.

Automated Fracture Mechanics and Fatigue Analyses Based on Three-Dimensional Finite Elements

This paper describes the structure and application of a software system that automates the fatigue initiation and crack propagation analysis based on finite element method (FEM). The system automatically performs necessary procedures to track propagation history of cracks: insertion of a crack and updating of three-dimensional (3D) finite element mesh in accordance with the crack propagation. The system is equipped with a function to automatically perform fatigue analyses using the stress–strain histories at nodes of a 3D FEM model. Some analyses for several examples were carried out for validation. The important example is the surface crack propagation in steel pipes with residual stress.

Multiscale finite element analysis of wave propagation in periodic solids

This paper reports on the application of the geometric multiscale finite element method for the analysis of wave propagation in heterogeneous periodic solids. The proposed scheme exploits multi-node elements to describe the microstructure through a local, auxiliary mesh that resolves the fine scale features, and that is used to numerically compute a set of interpolation functions employed for elements formulations at the global level. The method is applied for the analysis of the dispersion properties of, and transient wave propagation in domains featuring periodicity in two dimensions. Band diagram calculations, wave velocities and time domain computations are conducted on solids discretized using two-dimensional and three-dimensional multiscale finite element meshes. Results for assemblies with periodic inclusions, phononic stubbed plates and structural lattices illustrate the effectiveness of the method. Accurate predictions of dispersion relations, wave modes and time domain simulations are obtained with significant reductions in model size. The presented examples also illustrate some of the interesting wave characteristics of the considered class of periodic structures, which include wave directionality and frequency bandgaps.

OSCAR statement of methods

OSCAR (Outil de Simulation du CAptage pour la Reconnaissance des défauts) is the pantograph–catenary dynamic software developed by Société Nationale des Chemins de fer Français (SNCF) since 2004. A three-dimensional finite element (FE) mesh allows the modelling of any catenary type: alternating current (AC) or direct current (DC) designs, and conventional or high-speed lines. It is a representative of the real overhead line geometry, with contact wire (CW) irregularities, staggered alignment of the CW, dropper spacing, wire tension, etc. Nonlinearities, such as slackening of droppers and unilateral contact between the pantograph and the CW, are taken into account. Several pantograph models can be used, with a complexity level growing from the three-lumped-mass model to the multibody model. In the second case, a cosimulation between the FE method catenary and the multibody pantograph models has been developed. Industrial features for pre- and post-treatments were developed to increase robustness of results and optimise computation time. Recent developments include volume meshing of the CW for stress computation or statistical analysis and lead to new fields of studies such as fatigue failure or design optimisation. OSCAR was fully validated against in-line measurements for its different AC and DC catenary models as well as its different pantograph models (with independent strips for instance) and has continuously been certified against EN50318 since 2008.

On the performance of anisotropic mesh adaptation for scroll wave turbulence dynamics in reaction–diffusion systems

Nonlinear reaction–diffusion systems are widely employed to study the spatio-temporal chaotic behavior that occurs in excitable media such as cardiac tissue where sufficiently strong perturbations can excite nonlinear propagating waves which can form spiral waves in two dimensions or scroll waves in three dimensions. The numerical simulation of these waves calls for grids that are extremely fine over the whole computational domain to accurately predict the trajectories and multiplication of wave fronts and therefore leads to huge computational challenges. Mesh adaptation methods can reduce the number of degrees of freedom required for a given accuracy but they also have a cost and it is not clear if they are competitive with respect to very fine uniform meshes. Previous mesh adaptation techniques applied to spatio-temporal chaotic behavior have been mostly limited to the two-dimensional case. The purpose of this paper is to explore the efficiency of a three-dimensional anisotropic finite element mesh adaptivity for simulating scroll wave turbulence. The computational efficiency of the proposed method is assessed using reference solutions obtained on a uniform refined mesh with more than 44 millions degrees of freedom. The proposed method reduces significantly the number of elements leading to huge saving in memory as well as in computational time. Examples of the dynamics of ventricular fibrillation in cardiac tissue will be presented illustrating the performance of the overall methodology.

Numerical model for mechanical behavior of lightweight concrete and for the prediction of local stress concentration

In this study a numerical approach to simulate elastic behavior of lightweight concrete, is presented, at mesoscopic level. Concrete is considered as a bi-phasic material, composed of a granular skeleton dispersed in a mortar. Aggregates generation should respect a granular model where a maximum distance between aggregates is imposed. The granular media is also defined by a granular curve and a compacity. A numerical concrete sample is carried out, using three-dimensional finite element mesh. Here lightweight concretes are considered, where Young’s modulus of natural sand based mortar is higher than the modulus of the lightweight coarse aggregates. Different concretes are carried out, according to experimental studies from literature, in order to distinguish the influence of Young’s modulus contrast, and of the concrete compacity, on mechanical behavior. Then numerical compressive tests are realized until an experimental value of compressive strength, and the local stress and strain distribution around aggregates is studied, still remaining in the elastic domain. According to these results, breaking of this kind of concrete occurs when the maximum strain is reached in the lightweight aggregates surrounded mortar.

Researches on the Generation of Three-Dimensional Manifold Element under FEM Mesh Cover

Three-dimensional manifold element generation and contact detection algorithm between blocks are the bottleneck for the development of three-dimensional numerical manifold method (NMM). For building mathematics cover, the technology of three-dimensional finite element mesh generation is utilized in the paper. Aiming at the characteristics of complex formation and difficult identification of three-dimensional manifold block, three-dimensional manifold cutting technology is developed. It is important to achieve the coding of mathematical cover (MC) and physical cover (PC) for NMM, which directly determines the correctness of three-dimensional manifold element generation. Based on the character that the coding of three-dimensional manifold is the same as two-dimensional field essentially, coding algorithm of PC system proposed by Dr. Shi is extended to be three-dimensional. A three-dimensional manifold cutting program 3D MC.f90 is developed in this paper, which can generate an arbitrary three-dimensional manifold element under tetrahedral and hexahedral mesh cover. Several examples are made, and results show that three-dimensional manifold block shape and the coding of manifold node and element generated by three-dimensional manifold cutting program all agree well with the definition of three-dimensional manifold element.

An algorithm for discrete booleans with applications to finite element modeling of complex systems

In this paper we describe a robust algorithm for three-dimensional boolean operations between boundary representation objects whose geometry is given by discrete (faceted) data. The algorithm presents a new approach for computing the intersection graph which is critical for robustness. It uses elementary computational-geometry operations such as, facet–segment intersection, point containment in simplices and edge recovery in a plane, to produce high-level boolean operations including union, intersection, difference as well as the imprint of the boundary of one object onto another. We also demonstrate the extension and application of the algorithm to mesh-based volumes. We show the robustness and efficacy of our algorithm by employing it to model complex three-dimensional finite element mesh models such as a complete ship where some of the model components are defined in a CAD-based system while others come from legacy mesh-based facetized representations. Use of our algorithm has enabled automation of modeling of very complex configurations reducing the turnaround time for analyses-ready numerical representations from several months to hours or less.

A combined algorithm for characteristic edge match of hexahedral meshes based on priority nodes and relative position relationships

Boundary matching is an important problem in automatic generation of three-dimensional finite element meshes. In this paper, a combined algorithm for characteristic edge match of hexahedral meshes based on priority nodes and relative position relationships was proposed. The geometric and topologic conditions for characteristic edge (C-edge) match were firstly introduced. Seven types of free facet configurations and corresponding matching rules were established. A C-edge matching algorithm which combined priority nodes with relative position relationships was proposed by introducing priority nodes into the relative position relationship method. The identification method for each level of priority nodes was presented. The basic algorithms and implementation strategies of the combined method were introduced in detail. An effective method for characteristic point (C-point) match was also proposed on the basis of geometric topology and priority nodes. In addition, a method for treating the special sub-surface that intersected itself on a boundary line was proposed. A correction method was correspondingly proposed to deal with the nodes matched on unreasonable C-edges. Several examples of automatic meshing for hexahedral elements were provided to demonstrate the accuracy and effectiveness of the boundary matching algorithms proposed in this paper. The results show that the newly proposed algorithms not only can realize accurate match of mesh boundaries, but also establish reasonable geometric and topologic relationships of matched nodes.