Irregular Meshes Research Articles

An outline of the natural force density method and its extension to quadrilateral elements

The Natural Force Density Method (NFDM) is a convenient method for finding configurations of membranes and funicular shell structures, providing viable equilibrium geometries in a single linear equilibrium analysis. It is an extension of the Force Density Method (FDM), first proposed by Linkwitz in 1971, as convenient alternative for finding configurations of cable nets, which became ubiquitous in the field of membrane design, serving as basis of several successful computer programs. However, the equivalence between a network of force density elements and a continuous membrane is far from obvious, and it may become quite dubious which force densities should be prescribed, to achieve a desired configuration, comprising a geometric shape and an associate stress field. This is seldom remarked in papers about the method, and even less aware of that might be the general users the of programs based on it. The NFDM, first proposed by Pauletti in 2006, treats directly the continuous problem, overcoming the difficulties of FDM to deal with irregular meshes. Nevertheless, the NFDM was originally proposed considering the triangular membrane element introduced by Argyris in 1974, and thus required a fully triangular tessellation of a reference domain. In this paper we present a more concise deduction and systematic outline of the NFDM, as well as a simple extension of the method to quadrangular elements, allowing the use of more general mesh generators for the initial references meshes, and selection of a broader class of membrane or shell finite elements, afterwards.

Continuum modeling of crushing of low density foams

Under compression deformation in low-density foams localizes into narrow bands of crushed cells. Crushing spreads at nearly constant stress with crushed and relatively undeformed material coexisting. The material returns to homogeneous deformation with increasing stress when the crushing has spread over the whole specimen. This paper presents a first attempt at representing the inhomogeneous behavior exhibited by open-cell aluminum alloy foams with relative density of 8%. A plasticity model is presented with a compressible yield function calibrated to a set of multiaxial foam crushing tests coupled with a non-associated flow rule. An essential component of the modeling effort is the introduction of a softening branch to the material stress-strain response. A cubical finite element model with an irregular mesh of solid elements is used to simulate a set of numerical crushing tests on micromechanically accurate foam models performed in a true triaxial apparatus in Yang and Kyriakides (2019). Small geometric imperfections are used to trigger localized deformation in the form of planar bands of high strain normal to the loading directions of compression. The bands broaden with the stresses tracing plateaus that mimic the random foam test results. The predicted mean stress–change in volume responses perform equally well up to a volume reduction of about 50%. At higher compressions, the stresses exhibit the gradual increase characteristic of foams in the densification regime. These parts of the stress–displacement trajectories, and mean stress–change in volume responses under-predict to some degree those recorded in the random foams. The material hardening in the densification regime appears to be deformation-dependent causing this difference.

Assessment of groundwater depletion caused by excessive extraction through groundwater flow modeling: the Celaya aquifer in central Mexico

A numerical groundwater flow model was developed for the Celaya aquifer in central Mexico to assess the potential impacts of excessive groundwater use in the region. The numerical simulations were made with the program FEFLOW, which allowed the use of an irregular mesh that was adjusted to boundaries with irregular geometries and refined in wells and streams. Considering mountain block hydrology, both diffuse and stream-focused recharges were simulated. Hydraulic properties were assigned according to the three-dimensional distribution of lithologic units, which were estimated using geological information from the region. The model was calibrated using static water level measurements in wells and qualitative information of some hydrological processes. Some of the trends observed in the residuals were related to time-constant boundary conditions which can only be solved by developing a regional groundwater flow model. The simulations were undertaken for predevelopment, present, and future scenarios, up to the year 2030. The future simulations considered two possible scenarios: (1) future extractions are equal to current extractions; and (2) future extractions increase gradually in time. The results show that current groundwater extractions are not sustainable in the long term and decreases in extraction rates are required to achieve sustainable groundwater use in the region.

Scalable Wavelet-Based Coding of Irregular Meshes With Interactive Region-of-Interest Support

This paper proposes a novel functionality in wavelet-based irregular mesh coding, which is interactive region-of-interest (ROI) support. The proposed approach enables the user to define the arbitrary ROIs at the decoder side and to prioritize and decode these regions at arbitrarily high-granularity levels. In this context, a novel adaptive wavelet transform for irregular meshes is proposed, which enables: 1) varying the resolution across the surface at arbitrarily fine-granularity levels and 2) dynamic tiling, which adapts the tile sizes to the local sampling densities at each resolution level. The proposed tiling approach enables a rate-distortion-optimal distribution of rate across spatial regions. When limiting the highest resolution ROI to the visible regions, the fine granularity of the proposed adaptive wavelet transform reduces the required amount of graphics memory by up to 50%. Furthermore, the required graphics memory for an arbitrary small ROI becomes negligible compared to rendering without ROI support, independent of any tiling decisions. Random access is provided by a novel dynamic tiling approach, which proves to be particularly beneficial for large models of over 106 ~ 107 vertices. The experiments show that the dynamic tiling introduces a limited lossless rate penalty compared to an equivalent codec without ROI support. Additionally, rate savings up to 85% are observed while decoding ROIs of tens of thousands of vertices.

Canonical Correlation between Soil Attributes and Foliar of Conilon Coffee Trees

The nutritional status of the coffee tree is influenced by the concentration of nutrients in the soil of the growing area. The objective of this work was to evaluate, using canonical correlation, the linear relationships between chemical attributes of soil and nutrients of leaf tissues in seminal coffee. The work was developed in a commercial crop located in the municipality of Cachoeiro de Itapemirim, the southern region of the state of Espírito Santo. In the crop, an irregular sampling mesh was constructed, totalling 80 georeferenced points. The canonical correlation analysis was performed considering the original data observed in two consecutive conilon coffee harvests, 2015/16 and 2016/17, to verify the associations between a (dependent) group formed by foliar nutrients (N, P, K, Ca, Mg, S, B, Cu, Fe, Mn, and Zn) and an independent group formed by soil chemical attributes (pH, Ca, Al, K, S, P, Cu, Fe, Mn and Zn). Even if nutrients are available, that is, available in a satisfactory amount in the soil, it can happen that it does not reach the leaf tissue, resulting in a deficiency for some nutrients. There was a direct relationship between the concentration of K in the leaf tissue and K in the soil in the two harvests. Other soil attributes, such as Organic Matter, Fe, Mn, and S, also influenced this relationship, showing that the soil attributes in the independent group interact together on the nutrients in the leaf tissue. There is an inverse relationship between the concentrations of K in the leaf tissue and the Mn in the soil in the two harvests, showing that the excess of Mn in the soil is influencing the K deficiency in the leaf tissue.

Mathematical Modeling of Spatial Wave Responses by Grid-characteristic Method on Irregular Computational Meshes

The aim of this article is representing of mathematical modeling results in spatial exploration seismology problems, in particular the problem of seismic waves propagation in fractured layers with fractures of different dimensions. The modeling was produced by grid-characteristic method with use of irregular computational meshes (triangle in 2D-case and tetrahedral in 3D-case). The use of such numerical method takes into consideration the characteristic physical properties of describing processes and give us possibility to construct correct algorithms on boundaries and contact boundaries in integrational domain. By the use of unstructured meshes we can produce computations of wave processes in any areas of different complex shapes.

Use of Drones for the Topo-Bathymetric Monitoring of the Reservoirs of the Segura River Basin

The Segura River Basin (SRB), located in the South East of Spain, has the lowest percentage of renewable water resources of all the Spanish basins. Therefore, knowledge of the annual rate of water reservoir sedimentation is an important issue to be resolved in one of the most water-stressed regions in the western Mediterranean basin. This paper describes the sensors developed in collaboration with technology-based enterprises (aerial drone, floating drone, and underwater drone), and the methodology for integration of the different types of data acquired to monitor the reservoirs of the SRB. The proposed solution was applied to 21 reservoirs of the SRB. The proposed methodology is based on the use of unmanned aerial vehicles (UAV) for photogrammetry of the reservoir surface area. For each reservoir, two flights were completed, with 20 cm and 5 cm resolution, respectively. Then, a triangular irregular network mesh was generated by GIS techniques. Surface water vehicles (USV) and underwater remote-operated vehicles (ROV) were used to undertake bathymetric surveys. In addition, water quality measurements were made with an ROV device. The main results consist of topographic and bathymetric measurements for each reservoir, obtained by using equipment based on OpenSource technology. According to the results, the annual rate of storage capacity loss of water resources in the SRB´s reservoirs is 0.33%.

Перспективные методы цифровой обработки многомерных сигналов на основе применения нерегулярных сеток

The article considers sparse representation of signals based on using irregular meshes, which is one of prospective lines in digital processing of multidimensional signals. Application of irregular meshes has been seen for several decades as a promising field of investigations opening the possibility of using high efficiency of representing a signal carrier in combination with well-developed approximation methods used in solving boundary-value problems. However, lack of tools suitable for solving typical digital signal processing problems with the use of irregular meshes (e.g., for computing orthogonal discrete transforms) had resulted in that any noticeable and practically significant results are lacking in this area. Nevertheless, the recent years have seen a growth of interest in using irregular meshes. The article presents the results of investigations in this field that were carried out at the MPEI Chair for Computers, Systems and Networks. Matters concerned with generation of irregular meshes adapted to the specific features of multidimensional signals are addressed. Algorithms intended for carrying out interpolation, for making a shift from a regular carrier (a uniform regular mesh) to an irregular one, and for computing discrete transformations for a signal with an irregular carrier are presented. Solutions for arranging intellectual signal processing, such as pattern recognition and motion detection, are suggested.

Tension‐Compression Damage Model with Consistent Crack Bandwidths for Concrete Materials

This paper proposes a tension‐compression damage model for concrete materials, formulated within the framework of thermodynamics of irreversible processes. The aim of this work is to solve the following problems: the premature divergence of numerical solutions under general loading conditions due to the conflict of tensile and compressive damage bounding surfaces, which is a result of the application of the spectral decomposition method to distinguish tension and compression, and the unsatisfactory reproduction of distinct tension‐compression behaviors of concrete by strain‐driven damage models. The former is solved by the sign of the volumetric deformation, while the latter is solved via two separated dissipation mechanisms. Moreover, of specific interest is an improved solution to the problem of mesh‐size dependency using consistent crack bandwidths, which takes into account situations with irregular meshes and arbitrary crack directions in the context of the crack band approach. The performance of the model is validated by the well‐documented experimental data. The simplicity and the explicit integration of the constitutive equations render the model well suitable for large‐scale computations.

Variational integrators for anelastic and pseudo-incompressible flows

The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper, we derive and test structure-preserving numerical schemes for these two systems. The derivations are based on a discrete version of the Euler-Poincare variational method. This approach relies on a finite dimensional approximation of the (Lie) group of diffeomorphisms that preserve weighted-volume forms. These weights describe the background stratification of the fluid and correspond to the weighted velocity fields for anelastic and pseudo-incompressible approximations. In particular, we identify to these discrete Lie group configurations the associated Lie algebras such that elements of the latter correspond to weighted velocity fields that satisfy the divergence-free conditions for both systems. Defining discrete Lagrangians in terms of these Lie algebras, the discrete equations follow by means of variational principles. Descending from variational principles, the schemes exhibit further a discrete version of Kelvin circulation theorem, are applicable to irregular meshes, and show excellent long term energy behavior. We illustrate the properties of the schemes by performing preliminary test cases.

Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations

This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It systematically extends work previously made for incompressible fluids to the compressible case. We consider in detail the numerical scheme on 2D irregular simplicial meshes and evaluate the scheme numerically for the rotating shallow water equations. In particular, we investigate whether the scheme conserves stationary solutions, represents well the nonlinear dynamics, and approximates well the frequency relations of the continuous equations, while preserving conservation laws such as mass and total energy.

Improvements in Shear Locking and Spurious Zero Energy Modes Using Chebyshev Finite Element Method

In this paper, the authors present Chebyshev finite element (CFE) method for the analysis of Reissner–Mindlin (RM) plates and shells. Chebyshev polynomials are a sequence of orthogonal polynomials that are defined recursively. The values of the polynomials belong to the interval [−1,1] and vanish at the Gauss points (GPs). Therefore, high-order shape functions, which satisfy the interpolation condition at the points, can be performed with Chebyshev polynomials. Full gauss quadrature rule was used for stiffness matrix, mass matrix and load vector calculations. Static and free vibration analyses of thick and thin plates and shells of different shapes subjected to different boundary conditions were conducted. Both regular and irregular meshes were considered. The results showed that by increasing the order of the shape functions, CFE automatically overcomes shear locking without the formation of spurious zero energy modes. Moreover, the results of CFE are in close agreement with the exact solutions even for coarse and irregular meshes.

Deterministic method for calculating fusion neutron emission probability distribution in tokamak through mesh mapping

The high-fidelity 3D neutronics analysis of fusion systems has been enabled by advanced computer-aided design (CAD)-based simulation tools, and is being driven by an increasing desire to couple the analysis results with other physical field analyses. With increase in the level of output detail, the effects of the fusion neutron source spatial distribution have become increasingly important. The current fine-resolution neutron source model was established based on the Monte Carlo (MC) method, which is a time-consuming approach to reduce the deviations at low-intensity positions. This work presents a deterministic method to calculate the fusion neutron emission probability (FNEP) distribution in a tokamak machine with high resolution. In this deterministic method, the mesh-mapping technique is utilized to transfer neutron intensity data from an irregular (a, φ) mesh to a structured or unstructured (R, Z) mesh. The intensity data on (R, Z) mesh can be used directly by a deterministic neutronics code, or further be integrated and normalized in every grid to obtain the FNEP for an MC neutronics code. This deterministic scheme was implemented in the code EDITON, and the neutron source map can be generated subsequently by this code. EDITON exhibited high efficiency, and its accuracy was verified by comparing the obtained FNEP distribution and neutron wall loading (NWL) with the corresponding data from the TRANSGEN code, which is a tokamak fusion neutron spatial distribution calculation code based on the MC method.

Boundary integral equation method for simulation scattering of elastic waves obliquely incident to a doubly periodic array of interface delaminations

The paper proposes a novel computational method for simulating diffraction of obliquely incident plane waves by a doubly periodic array of arbitrarily shaped planar delaminations in elastic layered structures. The presented approach is an extension of the boundary integral equation method (BIEM) based on the boundary integral approach. Periodically situated delaminations are simulated via spring boundary conditions (SBCs), which allows considering bridged cracks. A boundary integral equation is formulated for a reference delamination based on SBCs in terms of the Fourier transform of Green's matrix and solved using Galerkin method. Two modifications of the method are proposed: the spectral BIEM applied only for rectangular delaminations and the meshless BIEM with axisymmetric basis functions, which is applied for delaminations of arbitrary shapes. The effectiveness of regular and irregular meshes is studied for the meshless BIEM. Comparison of both modifications of the BIEM is provided for open and bridged cracks. The proposed method allows considering specific wave phenomena such as a band-gap formation or opening of an interface for wave propagation in elastic layered structures with a doubly periodic array of inhomogeneities (e.g. phononic crystals and damaged interfaces).

Modelling Spatiotemporal Dynamics of Large Wood Recruitment, Transport, and Deposition at the River Reach Scale during Extreme Floods

Large wood (LW) can lead to clogging at bridges and thus cause obstruction, followed by floodplain inundation. Moreover, colliding logs can cause severe damage to bridges, defense structures, and other infrastructure elements. The factors influencing spatiotemporal LW dynamics (LWD) during extreme floods vary remarkably across river basins and flood scenarios. However, there is a lack of methods to estimate the amount of LW in rivers during extreme floods. Modelling approaches allow for a reliable assessment of LW dynamics during extreme flood events by determining LW recruitment, transport, and deposition patterns. Here, we present a method for simulating LWD on a river reach scale implemented in R (LWDsimR). We extended a previously developed LW transport model with a tree recognition model on the basis of Light Detection and Ranging (LiDAR) data for LW recruitment simulation. In addition, we coupled the LWD simulation model with the hydrodynamic simulation model Basic Simulation Environment for Computation of Environmental Flow and Natural Hazard Simulation (BASEMENT-ETH) by adapting the existing LW transport model to be used on irregular meshes. The model has been applied in the Aare River basin (Switzerland) to quantify mobilized LW volumes and the associated flow paths in a probable maximum flood scenario.

Scale-specific analysis of fMRI data on the irregular cortical surface

To fully characterize the activity patterns on the cerebral cortex as measured with fMRI, the spatial scale of the patterns must be ascertained. Here we address this problem by constructing steerable bandpass filters on the discrete, irregular cortical mesh, using an improved Gaussian smoothing in combination with differential operators of directional derivatives. We demonstrate the utility of the algorithm in two ways. First, using modelling we show that our algorithm yields superior results in numerical precision and spatial uniformity of filter kernels compared to the most widely adopted approach for cortical smoothing. As the effective scales of information differ from the nominal filter sizes applied to extract them, we evaluated the effective scales empirically for different filters to make subsequent comparisons well calibrated. Second, we applied the algorithm to an fMRI dataset to assess the scale and pattern form of cortical encoding of information about visual objects in the ventral visual pathway. We found that filtering by our method improved the detection of discriminant information about experimental conditions over previous methods, that the level of categorization (subordinate versus superordinate) of objects was differentially related to the spatial scale of fMRI patterns, and that the spatial scale at which information was encoded increased along the ventral visual pathway. In sum, our results indicate that the proposed algorithm is particularly suited to assess and detect scale-specific information encoding in cortex, and promises further insight into the topography of cortical encoding in the human brain.

Tube microstructure and formation in some feather duster worms (Polychaeta, Sabellidae)

Species of the sabellid polychaete genera Anamobaea, and Notaulax, are some of the most attractive sabellid polychaetes from coral reef areas due to their large colorful radiolar crowns. Tube microstructures of Anamobaea orstedi, Notaulax tenuitorques, and Notaulax sp. nov. are described. The studied sabellid tubes have three different types of microstructure. Most simple is irregular mesh microstructure which is composed of thin, long, and variously curved fibers of somewhat chaotic orientation (Notaulax tenuitorques). The irregular mesh microstructure could be plesiomorphic among sabellid tube structures. Oriented fibers in homogeneous matrix microstructure involves some kind of chemical control mechanisms that asserts the same orientation of all fibers (Notaulax sp. nov.). Anamobaea orstedi shows the most advanced pattern, a regular plywood structure, which is composed of thin subparallel or parallel to each other fibers that have different orientation in adjacent lamellae. Regular plywood structure has apparently greatest strength among organic tube structures of sabellids combined with good flexibility. Organic sabellid tube microstructures are likely species specific and have a taxonomic value.

Antishear Stress Bionic Carbon Nanotube Mesh Coating with Intracellular Controlled Drug Delivery Constructing Small-Diameter Tissue-Engineered Vascular Grafts.

Small-diameter (<6 mm) tissue-engineered blood vessels (TEBVs) have a low patency rate due to chronic inflammation mediated intimal hyperplasia. Functional coating with drug release is a promising solution, but preventing the released drug from being rushed away by blood flow remains a great challenge. A single-walled carboxylic acid functionalized carbon nanotube (C-SWCNT) is used to build an irregular mesh for TEBV coating. However, an interaction between the released drug and the cells is still insufficient due to the blood flow. Thus, an intracellular drug delivery system mediated by macrophage cellular uptake is designed. Resveratrol (RSV) modified CNT is used for macrophage uptake. M1 macrophage uptakes CNT-RSV and then converts to the M2 phenotype upon intracellular RSV release. Prohealing M2 macrophage inhibits the chronic inflammation thus maintains the contractile phenotype of the vascular smooth muscle cell (VSMC), which reduces intimal hyperplasia. Additionally, RSV released from the mesh coating also directly protects the contractile VSMCs from being converted to a secretory phenotype. Through antishear stress coating and macrophage-based intracellular drug delivery, CNT-RSV TEBVs exhibit a long-term anti-intimal hyperplasia function. Animal transplantation studies show that the patency rate remains high until day 90 after grafting in rat carotid arteries.

Masked 3D conditional generative adversarial network for rock mesh generation

3D-GAN (Wu et al. in: Advances in Neural Information Processing Systems, pp. 82–90, 2016) has been introduced as a novel way to generate 3D models. In this paper, we propose a 3D-Masked-CGAN approach to apply in the generation of irregular 3D mesh geometry such as rocks. While there are many ways to generate 3D objects, the generation of irregular 3D models has its own peculiarity. To make a model realistic is extremely time-consuming and in high cost. In order to control the shape of generated 3D models, we extend 3D-GAN by adding conditional information into both the generator and discriminator. It is shown that that this model can generate 3D rock models with effective control over the shapes of generated models.

Application of subdivision surfaces in ship hull form modeling

The restriction of tensor-product B-splines to regular control meshes and thus four-sided surfaces is the reason that hull form modeling is still a challenge. This limitation is addressed by subdivision surfaces as they originate from the idea to define B-spline surfaces on irregular control meshes. Often subdivision is considered as a method to refine polygon meshes, but the linear nature of polygon meshes is generally not qualified for hull form representation. Therefore an introduction to the theory of generalized B-splines is given which employs the notion of subdivision to define smooth B-spline surfaces on irregular control meshes.This article covers the application of generalized B-splines for the representation of hull forms. It is possible to represent hull forms with a single B-spline surface. The main advantage is, however, the ability to use the control mesh for modeling. It is shown that the structure of a control mesh and the principles to define a control mesh are essentially the same as for curve networks which are mostly used to define hull surfaces. In contrast to the common belief in the industry, it is analyzed that the approximation-based definition of a hull surface in terms of a control mesh simplifies modeling and improves the robustness compared to interpolation-based methods such as the commonly found interpolation of curve networks.