Element Nodes Research Articles

Numerical modelling of mode-I cracking in asphalt concrete

This paper presents a numerical model to simulate mode-I fracture in asphalt concrete. The phase field method is used to simulate diffuse damage in asphalt concrete. In addition to the displacement degrees of freedom, a scalar damage degree of freedom is added at each node of a finite element. Evolution of the damage variable is governed by a crack potential which regularizes a sharp crack over a finite volume. The phase field method does not suffer from mesh dependency problem like the continuum damage models and therefore preferred for damage analysis. A single edge notch beam is analysed to show the performance of the model. The damage pattern as well as load versus crack mouth opening displacement graph is compared with the experimental data. The numerical results show good agreement with the experimental observations.

Nearly Incompressible Large Deformation Analysis using 4-node Tetrahedral Strain Smoothing Element (SSE-T4)

A novel finite element formulation using 4-node tetrahedral elements is presented for large deformation analysis of nearly incompressible solids. The present method is a straightforward extension of the strain smoothing element (SSE) or the edge center-based SSE (EC-SSE) using selective reduced integration (SRI) to avoid volumetric locking. The deviatoric strain distribution of the present method is piecewise linear, whereas the volumetric one is piecewise constant. The suppression effect of spurious low-energy modes and pressure checkerboarding with the present method will be discussed at the conference.

Electromagnetic eigen analysis: Performance comparison of four node and four edge quadrilateral elements with the effect of distortion

In edge finite elements, electric fields are obtained across edges of each element instead of nodal output as obtained in nodal finite element. In the nodal framework, the potential formulation provides required tangential continuity and normal discontinuity for electromagnetic analysis whereas this continuity requirement is directly attained in the edge framework. In this work, we have used the conversion technique to transfrom four node quadrilateral element to four edge quadrilateral element. Then, we have compared the performance of these elements by performing the eigenvalue analysis for two standard examples. Finally, we also analyzed the effect of distortion in those elements.

О применении моделей грунта Soft Soil и Hardening Soil Small-Strain в рамках задачи фильтрационной консолидации на различных этапах возведения и эксплуатации здания в условиях слабых грунтов

The article considers the problem of stage-by-stage construction of a framed structure building on a slab foundation in conditions of soft soils. The calculation was carried out within the frame of the filtration consolidation problem in the numerical formulation. A comparative analysis is submitted (within the frame of Soft Soil model and Hardening Soil Small-Strain model) for the resulting deformations of the base and the slab, the forces in the nodal structural elements, and the distribution of pore pressure in the base at various stages of the building`s construction and operation.

АЛГОРИТМ КОНСЕРВАТИВНОГО СГЛАЖИВАНИЯ РАЗРЫВНЫХ ВОЛН НАПРЯЖЕНИЙ В МКЭ

Three-dimensional geometrically and physically nonlinear problems of nonstationary deformation of structures are considered. The defining system of equations is formulated in Lagrange variables. The equation of motion is derived from the balance of virtual work capacities. The elastic-plastic deformation of structural materials is described by the relations of the flow theory with isotropic hardening. The solution of the problem is based on the moment scheme of the finite element method. The discretization of the problem by spatial variables is carried out by eight nodal finite elements with multilinear functions of the approximation form of the displacement velocity. Time integration is performed according to an explicit finite-difference scheme of the “cross” type, which does not have the monotonicity property. Due to the dispersion in the vicinity of the gap, it generates non-physical oscillations, which significantly limits the scope of its applicability. In this paper, to suppress high-frequency oscillations, it is proposed to use an algorithm for conservative smoothing of a numerical solution with a space-time monotony analyzer. Based on it, software modules have been developed for the “Dynamics-3” computing complex. Verification of the developed technique and its software implementation was carried out by solving a one-dimensional problem in a three-dimensional formulation of the compression wave passing through a fixed elastic layer. For comparison, the results of numerical solution of the problem according to the “cross” scheme without smoothing, with linear viscosity, with conservative smoothing using spatial and spatiotemporal monotonicity analyzers are obtained. The problem of penetration of an elastic cylinder into a round steel plate is solved in a three-dimensional formulation. It is shown that the developed technique not only suppresses high-frequency oscillations, but also prevents the occurrence of zero-energy modes. So, in the second problem, without using the procedure of conservative smoothing of the numerical solution, the final elements of the plate in the collision zone are significantly distorted, which leads to an early interruption of the calculation.

2D finite elements for the computational analysis of crack propagation in brittle materials and the handling of double discontinuities

Crack growth simulations by way of the traditional Finite Element Method claim progressive remeshing to fit the geometry of the fracture, severely increasing the computational effort. Methods such as the eXtended Finite Element Method (XFEM) allow to overcome this limitation by means of nodal shape functions multiplied by Heaviside step function to enrich finite element nodes. Through the medium of a discontinuous field, the entire geometry of the discontinuity can be modelled regardless of the mesh, avoiding remeshing. In this paper two shell-type XFEM elements (a three-node triangular element and a four-node quadrangular element) to evaluate crack propagation in brittle materials are presented. These elements have been implemented into the widespread opensource framework OpenSees to evaluate crack propagation into a plane shell subjected to monotonically increasing loads. Moreover, in the perspective of fracture propagation simulations, the problem of managing multiple cracks without remeshing or operating subdivisions on the integration domain has been investigated and a four-node quadrangular finite element for the computational analysis of double crossed discontinuities by the means of equivalent polynomials is presented in this paper. Equivalent polynomials allow to overcome inaccuracies on the results when performing standard numerical integration (e.g. Gauss-Legendre quadrature rule) over the entire domain of XFEM elements, without the need of defining integration subdomains. The presented work and the computational strategy behind it may be extremely useful not only in the field of fracture mechanics, but also to solve complex geometry problems or material discontinuities.

Study on the Vector Quadrilateral Isoparametric Shell Element with Shear Deformation

Based on the linear superposition of the quadrilateral isoparametric membrane element and quadrilateral Mindlin plate element, basic vector formulas for the quadrilateral isoparametric shell element with the shear deformation is derived. Two different coordinate modes for updating the particle displacement and the element node internal force are put forward. The uniform numerical solution for an irregular quadrilateral element is realized by the isoparametric integral scheme along the element plane. Then, the bilinear elastoplastic constitutive of material is introduced into the vector finite shell element, and the nonlinear effect of the material is realized based on the integral method along the thickness. On this basis, the nonlinear calculation and analysis program of the quadrilateral isoparametric shell element is developed. Numerical example results show that the static and dynamic analysis, large deformation and large rotation analysis, and buckling analysis can all be well performed for the shell structures by the developed program, which verifies the validity of theoretical derivation and computer program.

Oscillation-free nodal discontinuous spectral element method for the simulation of compressible multicomponent flows

The nodal discontinuous spectral element method (DSEM) is improved to avoid pressure and velocity oscillations from material interfaces in the solution of multi-component compressible flows. A novel double flux method compatible with the DSEM scheme is developed to account for variations in the specific heats ratio at material interfaces. The double flux method consists of a modified Harten-Lax-van Leer-Contact (HLLC) Riemann solver and an averaging technique to freeze the temperature-dependent specific heats ratio during the solution update to remove oscillations. The double flux model is combined with a conservative method of calculating the convective flux function to avoid unnecessary energy conservation error at shock fronts. Numerical diffusion terms are also introduced for capturing a shock wave, contact discontinuity, and material interface, without inducing oscillations at the material interface. A series of one- and two-dimensional tests are conducted to evaluate the efficacy of the numerical scheme in capturing sharp discontinuities, as well as vortices, without introducing significant conservation error. According to the benchmark results, the new approach maintains the pressure, velocity, and temperature equilibriums across material interfaces. Artificial diffusion is added to the equation in a controlled manner that enables a higher Courant-Friedrichs-Lewy (CFL) number for high polynomial orders. The present scheme's performance is validated by comparing the spatiotemporal evolution of characteristic points in the shock-bubble interaction and Richtmyer-Meshokov's instability problems.

BLOOD FLOW IN ARTERIAL BIFURCATION CALCULATED BY TURBULENT FINITE ELEMENT MODEL

In this paper, turbulent fluid flow is analyzed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results shows that a cardiologist can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries.

Lock-in prediction for vortex-induced vibrations of a long hanged and weighted riser in internal fluid flow and external currents

The occurrence of lock-in, a local synchronization between the vortex shedding and cross-flow (CF) structural vibration frequencies, is investigated for a long flexible riser, of which the top is hanged and bottom is weighted and moveable in both the in-line (IL) and CF directions, conveying internal fluid flow (IF) and immersed in uniform, and linear shear currents (flows). Our established models are used to conduct a numerical simulation, in which unsteady hydrodynamic forces associated with wake dynamics are described using two van der Pol wake oscillators in both the IL and CF directions that are coupled with the riser. The riser is discretized into a string of spatial slender beam elements, and the wake oscillators are distributed on every immersed element nodes. MATLAB (R2014a) is used to establish a computational program, which is verified using existing experimental data. The lock-in frequency and location are captured by comparing the CF oscillation frequency of the wake model with the CF vibration frequency of the riser at every node of the finite element system when both coincide with each other at the frequency as well as location. The influences of the oncoming flow velocity (OFV), IF velocity (IFV) and bottom hanging weight (BHW) on the lock-in frequency, as well as the lock-in distribution along the riser axis are discussed. In UF, a high IFV (4.5 m/s) makes lock-in occurrence in riser’s “whole oncoming velocity region” in a single-frequency mode but a zero or low IFV (1.5 m/s) makes it null. In linear shear flow, a zero or low IFV (1.5 m/s) makes the lock-in occurrence in riser’s “low and middle oncoming velocity region” in a single-frequency mode and a high IFV (4.5 m/s) makes it in the “whole oncoming velocity region” in the multi-frequency modes, the lock-in frequency mode (but not the lock-in amount) is regardless of OFV and BHW in the context of this paper.

STRESS DISTRIBUTION IN THE HOLLOW STIFFENED HYBRID LAMINATED COMPOSITE PANELS IN SHIP STRUCTURES UNDER SINUSOIDAL LOADING

A simplified hollow stiffened hybrid laminated plate model has been developed for the marine structures. The detailed stress analysis through the thickness of the stiffened plate based on the higher order shear deformation theory has been carried out under sinusoidal loading. The hybrid laminates are made by wrapping the GFRP laminates with CFRP at the outermost layers of the stiffened panel. This hybridization technique can be an optimum solution from the point of view of cost reduction as well as enhancement of strength properties. The layer-wise stresses for the stiffened plate have been calculated in the present paper. A 3D polynomial curve fitting technique has been used to obtain higher accuracy and consistency in the computation of stresses. The computer code has been developed using MATLAB considering the plates as eight noded isoparametric plate bending element and the stiffener has been modeled as three noded isoparametric beam element. The stiffened panel has also been analysed using the ANSYS14.0 software package considering 2D model. The results obtained from the present formulation have been compared with those available in the published literature to validate the present formulation. The stiffened panels made of GFRP, CFRP and GFRP-CFRP hybrid laminates have been studied here. An extensive parametric study has been carried out with varying fibre content in the laminates.

Moving least-squares aided finite element method (MLS-FEM): A powerful means to consider simultaneously velocity and pressure discontinuities of multi-phase flow fields

We suggest a strategy to consider discontinuities in the two-phase flow calculations. Our approach comprises enhancing the shape functions of the finite element method (FEM) with the moving least-squares (MLS) interpolation functions. The new shape functions correlate a parameter at any arbitrary point to its surrounding nodes instead of an element's nodes. We name this strategy the "moving least-squares" aided "finite element method" (MLS-FEM).In a previous paper Mostafaiyan et al., we have employed the concept of the MLS-FEM to develop the PMLS (pressure shape function enhanced by the MLS interpolation functions) method, which predicts pressure discontinuities due to the surface tension forces. We take another additional step to consider velocity and pressure discontinuities in a domain with two different fluids. Therefore, we use the MLS technique to enhance the pressure (P) and velocity (V) shape functions. We name this scheme PVMLS (pressure and velocity shape functions enhanced by the MLS technique).We validate the PVMLS method with a stationary drop problem (as a benchmark). We show that the previous PMLS method fails to predict an accurate pressure or smooth streamlines by increasing the Capillary number and deviating from the unit viscosity ratio. However, the PVMLS method provides more accurate results since it considers velocity as a discontinuous parameter. Also, we compare the results of the PVMLS method at very high viscosity ratios (undeformable fluid) with a boundary-fitted single-phase problem. The reported similarities between the predicted pressure values and streamlines in both strategies demonstrate the reliability of the PVMLS method. Finally, we discuss that by employing the PVMLS method to calculate the velocity field, the interface advection will be more mass-conservative.

Galerkin finite element analysis for peristaltic flow of micropolar fluid through porous soaked inclined tube independent of wavelength

In this novel numerical investigation, the application of well-renowned numerical technique known as Galerkin finite element method on full form of Navier-Stokes equations presented peristaltic flow of non-Newtonian fluid confined by a uniformly saturated porous medium. The rheological aspects of non-Newtonian material are discussed by considering micropolar fluid. The flow model consists of system of nonlinear partial differential equations with mixed boundary condition. The flow also experienced an externally applied magnetic field. The effects of inertial forces and the results independent of wavelength are obtained by dropping the presumptions of lubrication theory in modelling the governing equations. The numerical solution for formulated problem in terms of partial differential expressions is worked out via Galerkin finite technique in view of six nodal triangular elements. The enhancement in the inertial forces gives impressive pressure enhancement against wavelength while opposed the fluid flow in the vicinity of peristaltic walls of the tube but supported the fluid flow in the central region of the tube. The present results are also compared with the available results after applying lubrication theory and found in reliable agreement.

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

Risk and Opportunity Analysis of Tesla Motors Inc. Marketing Strategy and Business Ethics Study

Winning the Top 500 World Brands in 2018, Tesla is working hard to cover a variety of categories including high-end sports cars and luxury cars. As a leader in the "new car movement", Tesla from Silicon Valley is committed to building cars with IT concepts, and it is not a traditional car manufacturer's thinking represented by Detroit. This paper undertakes a full marketing audit to evaluate Tesla’s strengths, weaknesses, opportunities and threats to many other car manufacturers using PEST, SWOT and USP models. Based on the above issues, the business process of external supply chain management is proposed: information-technology outreach, upstream management of docking, overall coordination and co-existence, and analysis of node elements and evaluation schemes are feasible. Besides, the recent accidents regarding the brake caliper bolts failure, battery charging, and pilot driving are also mentioned in this review. Corresponding recommendations are also provided for the improvement of moral images in the end.

Vibration response analysis of a gear-rotor-bearing system considering steady-state temperature

Thermal effect is a crucial factor leading to failure of gear system. However, the lack of comprehensive nonlinear dynamics model limits the further study of thermal effects. The constitutive relation of beam element considering steady-state temperature is reconstructed, and thermal node load is formulated. Considering the influences of thermal expansion and temperature on material properties, a more comprehensive dynamic model of gear-rotor-bearing system is established based on the finite element node method. Nonlinear friction, high-speed gyroscopic effect, thermal-related time-varying meshing stiffness (TVMS) and thermal backlash are included in the model. The effects of temperature and bearing type on the vibration response of gear system are analyzed. The results show that the system motion changes from period to chaos with the temperature increase in part of the speed range. The appropriate backlash could restrain the chaotic motion caused by temperature rise. Moreover, the temperature significantly increases the axial bearing force, and the appropriate bearing could reduce the axial displacement. This research can further understand the influence of temperature on the dynamic response of gear system and guide the design of gear system.

Stress-strain distribution in intact L4-L5 vertebrae under the influence of physiological movements: A finite element (FE) investigation

This study is aimed at finding the stress and strain distribution in functional spinal unit of L4-L5 occurring due to physiological body movements under five loading conditions, namely compression, flexion, extension, lateral bending and torsion. To this purpose, 3D finite element (FE) model has been generated using 4-noded unstructured tetrahedral elements considered both for bones and intervertebral disc, and 1D tension-only spring elements for ligaments. The analyses were performed for a compression load of 500 N and for other load cases, a moment of 10 N-m along with a preload of 500 N was applied. The model was validated against in-vitro experimental data obtained from literature and FE analysis data for a range of motion (RoM) corresponding to various loading conditions. The highest stress was predicted in the case of torsion though the angular deformation was highest in case of flexion.

Solving the hourglass instability problem using rare mesh variation-difference schemes

The hourglass instability effect is characteristic of the Wilkins explicit difference scheme or similar schemes based on two-dimensional 4-node or three-dimensional 8-node finite elements with one integration point in the element. The hourglass effect is absent in schemes with cells in the form of simplexes (triangles in two-dimensional case, tetrahedrons in three-dimensional case). But they have another well-known drawback - slow convergence. One of the authors proposed a rare mesh scheme, in which elements in the form of a tetrahedron are located one at a time in the centers of the cells of a hexahedral grid. This scheme showed the absence “hourglass” effect and other drawbacks with high efficiency. This approach was further developed for solving 2D and 3D problems.

The diameter vulnerability of two-dimensional optimal circulant networks

This paper studies the effect of changing the diameter of the network in circulant networks of dimension two with unreliable elements (nodes, links). The well-known (Δ,D,D′, s)-problem is to find (Δ, D)-graphs with maximum degree Δ and diameter D such that the subgraphs obtained from the original graph by deleting any set of up to s vertices (edges) have diameter at most D′. For a family of optimal circulants of degree four we found the ranges of the orders of the graphs that preserve the diameter of the graph for one (two) vertex or edge failures. It is proved that in the investigated circulant networks in case of failure of one or two edges (vertices), the diameter can increase by no more than one, and in case of failure of three elements by no more than two (edge failures) or three (vertex failures). It is shown that two-dimensional optimal circulants, in comparison with two-dimensional tori, have a better diameter in case of element failures.

ARCHITECTURAL AND PLANNING ORGANIZATION OF SERVICE OBJECTS LOCATED ON TRANSPORT HUBS

The article discusses the main aspects of the architectural and planning organization of service facilities for transport hubs. The main blocks of the functional planning structure of transport interchange hubs (T.I.HUB), elements of their structure and principles of placement in the structure of large cities have been formed in the center, in the structure of residential areas, in historical city centers, and in the contact zone of urban and suburban development. The work substantiates the relevance of the development regarding the design of transport hubs (T.HUB)s in the structure of modern cities, which are constantly and systematically developing, increasing the need for the transportation of an increasing number of passengers.
 The dynamic development of modern infrastructural cities, especially large ones, require a revision of the norms and dimensions of transfer stations, the landing front of stops, the reorganization of the inner spaces of the transport hubs (T.HUB), etc. The design and construction of transport hubs can be carried out in a completely new construction, reconstruction or reconstruction with modernization, or in the difficult conditions. Already today, many big cities are suffering from traffic jams bordering on collapse, especially during peak hours. Therefore, this problem must be solved in all possible ways, especially attention should be paid to the architectural and planning organization of service facilities, which are located at the transport hub (T.HUB). A transport interchange hub is a nodal element of the city's planning structure, which allows organizational transfer of passengers between various types of urban and external (intercity, international) passenger transport or between different lines of the same type of transport in an urban structure. For example, transport hubs (T.HUB) are possible in the structure of the functioning of a railway transport hub from one railway line to another. Transport interchange hubs (T.I.HUB)can be specialized or multifunctional, and include a number of facilities for passing passenger services and social infrastructure: accumulative lobbies in front of the entrance group ("entrance" - "exit"), a foyer with digital validation of electronic tickets and cards on different routes of passengers; cargo and goods rooms for baggage claim (at airports, river stations and railway stations); customs premises (if we are talking about international flights departing from transport hubs (T.HUB); intercepting parking lots and taxi and bus stands; public service facilities; shops, catering establishments; financial institutions, etc.
 As noted earlier, we can talk about six types of transport hubs (T.HUB) in the structure of the designed and existing nodes on land, underground, river, rail, sea and air transport. Thus, modern transport hubs can be organized not only in the city structure, but also in ports, railways. railway stations and airports, which can significantly expand their typological range of service facilities.