Nodal Connectivity Research Articles

The anisotropic elasto-plastic analysis using a natural neighbour RPIM version

In this work, the natural neighbour radial point interpolation method (NNRPIM), an advanced discretization meshless technique, is used to study several solid mechanics benchmark examples considering an elasto-plastic approach. The NNRPIM combines the radial point interpolators (RPI) with the natural neighbour geometric concept. The nodal connectivity and the background integration mesh depend entirely on the nodal discretization and are both achieved using mathematic concepts, such as the Voronoi diagram and the Delaunay tessellation. The obtained interpolation functions, used in the Galerkin weak form, are constructed with the RPI and possess the delta Kronecker property, which facilitates the imposition of the natural and essential boundary conditions. Due to the organic procedure employed to impose the nodal connectivity, the obtained displacement and the stress field are smooth and accurate. Since the scope of this work is to extend and validate the NNRPIM in the anisotropic elasto-plastic analysis, it is used as nonlinear solution algorithm, the modified Newton–Raphson initial stiffness method. The efficient “backward-Euler” procedure is considered to return the stress to the Hill anisotropic yield surface. The elasto-plastic algorithm of solution is described. Several benchmark two-dimensional problems are solved, considering anisotropic elasto-plastic materials with anisotropic hardening, and the obtained solutions are compared with finite-element solutions, showing that the meshless approach developed is efficient and accurate.

Periodic truss structures

Despite the recognition of the enormous potential of periodic trusses for use in a broad range of technologies, there are no widely-accepted descriptors of their structure. The terminology has been based loosely either on geometry of polyhedra or of point lattices: neither of which, on its own, has an appropriate structure to fully define periodic trusses. The present article lays out a system for classification of truss structure types. The system employs concepts from crystallography and geometry to describe nodal locations and connectivity of struts. Through a series of illustrative examples of progressively increasing complexity, a rational taxonomy of truss structure is developed. Its conceptual evolution begins with elementary cubic trusses, increasing in complexity with non-cubic and compound trusses as well as supertrusses, and, finally, with complex trusses. The conventions and terminology adopted to define truss structure yield concise yet unambiguous descriptions of structure types and of specific (finite) trusses. The utility of the taxonomy is demonstrated by bringing into alignment a disparate set of ad hoc and incomplete truss designations previously employed in a broad range of science and engineering fields. Additionally, the merits of a particular compound truss (comprising two interpenetrating elementary trusses) is shown to be superior to the octet truss for applications requiring high stiffness and elastic isotropy. By systematically stepping through and analyzing the finite number of structure types identified through the present classification system, optimal structures for prescribed mechanical and functional requirements are expected to be ascertained in an expeditious manner.

The Natural Neighbor Radial Point Interpolation Method Extended to the Crack Growth Simulation

In the present work, the Natural Neighbor Radial Point Interpolation Method (NNRPIM) is used to simulate the crack growth phenomenon in brittle materials. In order to discretize the problem domain, the NNRPIM only requires an unstructured nodal distribution. With the spatial information of the computational nodes, the NNRPIM is capable to automatically establish the nodal connectivity and to construct the interpolation functions. Additionally, using the natural neighbor geometrical concept, the NNRPIM is able to obtain, from the unstructured nodal distribution, the integration background mesh required to numerically integrate the integro-differential equations ruling the studied physical phenomenon. In this work, a crack opening path algorithm is adapted and combined with the NNRPIM. The developed algorithm is able to predict the crack growth by relocating iteratively the crack tip. The stress field in the vicinity of the crack tip is determined in each iteration and then, using the maximum circumferential stress criterion, the direction of the crack propagation is calculated. Here, the repositioning of the crack tip requires a local re-meshing. However, due to the flexibility of the natural neighbor concept, the local re-meshing do not represent a numerical difficulty. Additionally, in order to show the efficiency of the proposed approach, several demanding crack growth benchmark examples are solved.

Scale-Dependent Variability and Quantitative Regimes in Graph-Theoretic Representations of Human Cortical Networks.

Studying brain connectivity is important due to potential differences in brain circuitry between health and disease. One drawback of graph-theoretic approaches to this is that their results are dependent on the spatial scale at which brain circuitry is examined and explicitly on how vertices and edges are defined in network models. To investigate this, magnetic resonance and diffusion tensor images were acquired from 136 healthy adults, and each subject's cortex was parceled into as many as 50,000 regions. Regions were represented as nodes in a reconstructed network representation, and interregional connectivity was inferred via deterministic tractography. Network model behavior was explored as a function of nodal number and connectivity weighing. Three distinct regimes of quantitative behavior assumed by network models as a function of spatial scale are identified, and their existence may be modulated by the spatial folding scale of the cortex. The maximum number of network nodes used to model human brain circuitry in this study (∼50,000) is larger than in previous macroscale neuroimaging studies. Results suggest that network model properties vary appreciably as a function of vertex assignment convention and edge weighing scheme and that graph-theoretic analysis results should not be compared across spatial scales without appropriate understanding of how spatial scale and model topology modulate network model properties. These findings have implications for comparing macro- to mesoscale studies of brain network models and understanding how choosing network-theoretic parameters affects the interpretation of brain connectivity studies.

The Axisymmetric Analysis of Circular Plates Using the Radial Point Interpolation Method

This work extends the radial point interpolation method (RPIM) to the elasto-static analysis of circular plates. Instead using a plate bending theory, the 2D axisymmetric deformation theory is assumed. The RPIM enforces the nodal connectivity with the influence-domain concept and integrates numerically the integro-differential equations governing the studied phenomenon using a background integration mesh. Thus, both concepts are revised and more adequate parameters are found for the axisymmetric RPIM approach. Several benchmark circular plate examples are solved and the results are compared with other numerical approaches, showing that the RPIM is capable to obtain accurate and smooth variable fields.

Computation of the effective mechanical response of biological networks accounting for large configuration changes

The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with FE simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes.

Crack path prediction using the natural neighbour radial point interpolation method

One of the most challenging problems in computational mechanics is the prediction of the crack propagation path. In this work, the Natural Neighbour Radial Point Interpolation Method (NNRPIM), an efficient meshless method, is extended to the field of fracture mechanics. Since the NNRPIM relies on the Natural Neighbour mathematical concept to obtain the integration mesh and establish the nodal connectivity, the NNRPIM only requires a computational nodal distribution to fully discretise the problem domain. The Radial Point Interpolators (RPI) are used to construct the NNRPIM interpolation functions.Taking advantage of the unique features of the NNRPIM, in this work, the crack propagation path is numerically simulated using an adapted crack path opening algorithm, in which the crack is iteratively extended in line segments. In each iteration, using the obtained stress field, the crack propagation direction is determined using the maximum circumferential stress criterion. Due to the flexibility of the natural neighbour concept, the increase of the domain discontinuities do not represent a numerical difficulty. In the end, several crack opening path benchmark examples are solved in order to show the efficiency of the proposed numerical approach.

Direct collocation meshless method for vector radiative transfer in scattering media

A direct collocation meshless method based on a moving least-squares approximation is presented to solve polarized radiative transfer in scattering media. Contrasted with methods such as the finite volume and finite element methods that rely on mesh structures (e.g. elements, faces and sides), meshless methods utilize an approximation space based only on the scattered nodes, and no predefined nodal connectivity is required. Several classical cases are examined to verify the numerical performance of the method, including polarized radiative transfer in atmospheric aerosols and clouds with phase functions that are highly elongated in the forward direction. Numerical results show that the collocation meshless method is accurate, flexible and effective in solving one-dimensional polarized radiative transfer in scattering media. Finally, a two-dimensional case of polarized radiative transfer is investigated and analyzed.

The Elasto-plastic Response of the Bone Tissue Due to the Insertion of Dental Implants

In this work, the elasto-plastic behaviour of the bone tissue, in the presence of dental implants, is numerically obtained using a discrete meshless method - the Natural Neighbour Radial Point Interpolation Method (NNRPIM). Within the NNRPIM the nodal connectivity is enforced using the Natural Neighbour concept. Additionally, using the same mathematical concept, it is possible to obtain the background integration mesh. The NNRPIM is a truly meshless method, because the construction of the nodal connectivity and the integration mesh depends uniquely on the nodal mesh discretizing the problem. No other spatial information is required. The integration mesh is used in the numerical integration of the integro-differential equations governing the physic phenomenon. The NNRPIM interpolation functions are constructed using the Radial Point Interpolators (RPIs). These functions are used as the trial functions of the Galerkin weak form, which permits to define the discrete system of equations. The obtained interpolation functions possess the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. Since in this work it is performed an elasto-plastic analysis of the bone tissue, a non-linear solution algorithm must be adopted. In this work the Newton-Raphson initial stiffness method is considered. Additionally, the efficient “forward-Euler” procedure is used in order to return the stress to the yield surface. Experimental studies reveal that the bone tissue show a distinctive yielding followed by a constant nominal stress plateau for both uniaxial and confined compression, which can be represented with a classic “linear elastic – linear plastic” material behaviour. Thus, in this work, it is used the von-Mises yield surface to characterize the plastic behaviour of trabecular bone.

Assessing dynamic brain graphs of time-varying connectivity in fMRI data: Application to healthy controls and patients with schizophrenia

Graph theory-based analysis has been widely employed in brain imaging studies, and altered topological properties of brain connectivity have emerged as important features of mental diseases such as schizophrenia. However, most previous studies have focused on graph metrics of stationary brain graphs, ignoring that brain connectivity exhibits fluctuations over time. Here we develop a new framework for accessing dynamic graph properties of time-varying functional brain connectivity in resting-state fMRI data and apply it to healthy controls (HCs) and patients with schizophrenia (SZs). Specifically, nodes of brain graphs are defined by intrinsic connectivity networks (ICNs) identified by group independent component analysis (ICA). Dynamic graph metrics of the time-varying brain connectivity estimated by the correlation of sliding time-windowed ICA time courses of ICNs are calculated. First- and second-level connectivity states are detected based on the correlation of nodal connectivity strength between time-varying brain graphs. Our results indicate that SZs show decreased variance in the dynamic graph metrics. Consistent with prior stationary functional brain connectivity works, graph measures of identified first-level connectivity states show lower values in SZs. In addition, more first-level connectivity states are disassociated with the second-level connectivity state which resembles the stationary connectivity pattern computed by the entire scan. Collectively, the findings provide new evidence about altered dynamic brain graphs in schizophrenia, which may underscore the abnormal brain performance in this mental illness.

Identifying and Mapping Connectivity Patterns of Brain Network Hubs in Alzheimer's Disease.

Alzheimer's disease (AD) is associated not only with regional gray matter damages, but also with abnormalities in functional integration between brain regions. Here, we employed resting-state functional magnetic resonance imaging data and voxel-based graph-theory analysis to systematically investigate intrinsic functional connectivity patterns of whole-brain networks in 32 AD patients and 38 healthy controls (HCs). We found that AD selectively targeted highly connected hub regions (in terms of nodal functional connectivity strength) of brain networks, involving the medial and lateral prefrontal and parietal cortices, insula, and thalamus. This impairment was connectivity distance-dependent (Euclidean), with the most prominent disruptions appearing in the long-range connections (e.g., 100-130 mm). Moreover, AD also disrupted functional connections within the default-mode, salience and executive-control modules, and connections between the salience and executive-control modules. These disruptions of hub connectivity and modular integrity significantly correlated with the patients' cognitive performance. Finally, the nodal connectivity strength in the posteromedial cortex exhibited a highly discriminative power in distinguishing individuals with AD from HCs. Taken together, our results emphasize AD-related degeneration of specific brain hubs, thus providing novel insights into the pathophysiological mechanisms of connectivity dysfunction in AD and suggesting the potential of using network hub connectivity as a diagnostic biomarker.

A Global Numerical analysis of the "central incisor/local maxillary bone" system using a meshless method.

In this work the maxillary central incisor is numerically analysed with an advance discretization technique--Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM permits to organically determine the nodal connectivity, which is essential to construct the interpolation functions. The NNRPIM procedure, based uniquely in the computational nodal mesh discretizing the problem domain, allows to obtain autonomously the required integration mesh, permitting to numerically integrate the differential equations ruling the studied physical phenomenon. A numerical analysis of a tooth structure using a meshless method is presented for the first time. A two-dimensional model of the maxillary central incisor, based on the clinical literature, is established and two distinct analyses are performed. First, a complete elasto-static analysis of the incisor/maxillary structure using the NNRPIM is evaluated and then a non-linear iterative bone tissue remodelling analysis of the maxillary bone, surrounding the central incisive, is performed. The obtained NNRPIM solutions are compared with other numerical methods solutions available in the literature and with clinical cases. The results show that the NNRPIM is a suitable numerical method to analyse numerically dental biomechanics problems.

Method for Generating Statically Determinate Cable Net Topology Configurations of Deployable Mesh Antennas

AbstractLarge deployable high-frequency mesh antennas are being envisioned for future space missions. The static determinacy is required to ensure the long-term dimensional stability of cable net reflectors of mesh antennas under extreme space environments. In this paper, the design methodologies for creating statically determinate cable net topology configurations of AstroMesh and umbrella-type antennas are proposed on the basis of the generalized Maxwell’s rule, respectively. To generate these configurations, the number of subdivisions of mesh reflectors is first determined by the allowable surface accuracy. Then, by introducing the concept of nodal connectivity, the cable net topology configurations of AstroMesh antennas are deduced from a general analytical solution of linear algebraic theory. The desired topology configurations of umbrella-type antennas are obtained by adjusting the number of nodes, cables, and kinematic constraints under uncertain supporting boundary conditions. Some novel cable net...

차분진화알고리즘을 이용한 네트워크 돔의 정삼각형 메쉬 모델링에 관한 연구

This paper aimed at modeling a triangular mesh for network dome by using differential evolution algorithm. For this purpose, an optimization process to find a regular triangular mesh on the curved surface was proposed and a program for this was developed. The objective function consisted of the standard deviations of the area and the boundary length of each triangle, and the design variables were regulated by the upper and lower boundary conditions which were calculated depending on the nodal connectivity. Plate model and triangular network dome model, which initially had consisted of irregular triangular meshes, were selected as target examples. In the case of the plate model its final mesh corresponded with the regular triangular mesh exactly. In network dome model, its result was very approached to the minimum standard deviation of the area and theboundary length of each triangle, too. Additionally, the more rise-span ratio of the dome decreased, the more the standard deviation of the mesh modeling decreased.

Form-finding of tensegrity structures with arbitrary strut and cable members

An advanced form-finding method for tensegrity structures is presented. In the present study, determining an appropriate candidate for strut members using the discontinuity condition of struts is performed. Additionally, the self-equilibrium and stability properties of tensegrity structures are obtained by using the force density method combined with a genetic algorithm. The proposed algorithm is effectively capable of searching for appropriate strut candidates with limited information in nodal connectivity. Appropriate member types and a feasible set of the nodal coordinates and the force densities can be found efficiently. Based on numerical examples, it is found that the proposed method is very efficient and robust in searching the self-equilibrium configuration of tensegrity structures.

Locally constrained nodal connectivity refinement procedures for unstructured triangular finite element meshes

This paper presents specific procedures for locally refining nodal connectivity of two-dimensional unstructured triangular meshes to improve the quality of the mesh as well as to increase solution accuracy and computational speed. Details of the procedure are outlined along with a discussion of similar work, and an example problem from hydrodynamics is shown.

Análise de vigas laminadas utilizando o natural neighbour radial point interpolation method

In this work, a meshless method, “natural neighbour radial point interpolation method” (NNRPIM), is applied to the one‐dimensional analysis of laminated beams, considering the theory of Timoshenko.The NNRPIM combines the mathematical concept of natural neighbours with the radial point interpolation. Voronoï diagrams allows to impose the nodal connectivity and the construction of a background mesh for integration purposes, via influence cells. The construction of the NNRPIM interpolation functions is shown, and, for this, it is used the multiquadratic radial basis function. The generated interpolation functions possess infinite continuity and the delta Kronecker property, which facilitates the enforcement of boundary conditions, since these can be directly imposed, as in the finite element method (FEM).In order to obtain the displacements and the deformation fields, it is considered the Timoshenko theory for beams under transverse efforts. Several numerical examples of isotropic beams and laminated beams are presented in order to demonstrate the convergence and accuracy of the proposed application. The results obtained are compared with analytical solutions available in the literature.

Meshless natural neighbor Galerkin method for the bending and vibration analysis of composite plates

In the present work we present a meshless natural neighbor Galerkin method for the bending and vibration analysis of plates and laminates. The method has distinct advantages of geometric flexibility of meshless method. The compact support and the connectivity between the nodes forming the compact support are performed dynamically at the run time using the natural neighbor concept. By this method the nodal connectivity is imposed through nodal sets with reduced size, reducing significantly the computational effort in construction of the shape functions. Smooth non-polynomial type interpolation functions are used for the approximation of inplane and out of plane primary variables. The use of non-polynomial type interpolants has distinct advantage that the order of interpolation can be easily elevated through a degree elevation algorithm, thereby making them suitable also for higher order shear deformation theories. The evaluation of the integrals is made by use of Gaussian quadrature defined on background integration cells. The plate formulation is based on first order shear deformation plate theory. The application of natural neighbor Galerkin method formulation has been made for the bending and free vibration analysis of plates and laminates. Numerical examples are presented to demonstrate the efficacy of the present numerical method in calculating deflections, stresses and natural frequencies in comparison to the Finite element method, analytical methods and other meshless methods available in the literature.

Survivable Network Design and Optimization with Network Families

In modeling communication networks for simulation of survivability schemes, one goal is often to implement these schemes across varying degrees of nodal connectivity to get unbiased performance results. Abstractions of real networks, simple random networks, and families of networks are the most common categories of these sample networks. This paper looks at how using the network family concept provides a solid unbiased foundation to compare different network protection models. The network family provides an advantage over random networks by requiring one solution per average nodal degree, as opposed to having to solve many, which could take a significant amount of time. Also, because the network family looks at a protection scheme across a variety of average nodal connectivities, a clearer picture of the scheme’s performance is gained compared to just running the simulation on a single network or select few networks.

Analysis of thick plates by the natural radial element method

An innovative numerical approach, combining the simplicity of low-order finite elements connectivity with the geometric flexibility of Meshless methods, is extended to the elastostatic analysis of thick plates. The nodal connectivity is enforced using the natural neighbour mathematical concept and the background integration mesh is constructed uniquely depending on the nodal mesh. The nodal connectivity is imposed through nodal sets with reduced size, reducing significantly the test function construction cost. The interpolation functions are constructed using Euclidean norms and easily obtained. It is considered as the Reissner–Mindlin plate shear deformation theory. Several thick plate elastostatic benchmark examples are solved.