Finite Element Method Code Research Articles

Dynamic site response analysis in the face of uncertainty–an approach based on response surface method

AbstractAlthough advanced modeling techniques such as the finite element method (FEM) have been used successfully in dynamic site response analysis, the high computational expense has hindered the incorporation of input parameter uncertainty in such analysis. Thus, when the variation of the peak ground acceleration (PGA) at the ground surface, which is the outcome of the site response analysis, has to be evaluated in the face of uncertainty, a surrogate model such as Response Surface Method (RSM) model is often used in lieu of the FEM model. In this paper, the RSM surrogate model was implemented in the context of seismic site response analysis to evaluate the variation (or uncertainty) of the PGA due to the propagation of input parameter uncertainty. The engineering implication of the variation of the surface PGA is significant as this knowledge is required for such tasks as reliability analysis of soil liquefaction and probabilistic seismic risk analysis. To derive the RSM model specifically for a site response analysis, a parametric study of the dynamic site responses using FEM code ABAQUS with the modified Davidenkov soil constitutive model implemented as a user‐defined material subroutine is first conducted. The input parameters, including the soil profile, soil properties, and input ground motion, in a typical dynamic site response analysis are then characterized and screened for their suitability to be included in the RSM model. For a given site response problem in the face of uncertainty, representative “samples” are taken for site response analysis using ABAQUS, and the analyses are carried out and finally the response surface is constructed using the outcomes of the ABAQUS numerical experimentations. The accuracy of the developed RSM model is then validated using the results of ABAQUS on cases not used in the development of the RSM model. Once the RSM model is deemed satisfactory, the reliability‐based formulation for evaluating the mean and standard deviation of the surface PGA is established. Example is provided to illustrate the RSM approach for dynamic site response analysis in the face of input parameter uncertainty.

Building an Integrated Drilling Geomechanics Model Using a Machine-Learning-Assisted Poro-Elasto-Plastic Finite Element Method

SummaryThe petroleum industry has long relied on predrilling geomechanics models to generate static representations of the allowable mud weight limits. These models rely on simplifying assumptions such as linear elasticity, a uniform wellbore shape, and generalized failure criteria to predict failure and determine a safe mud weight. These assumptions lead to inaccurate results, and they fail to reflect the effect of different routing drilling events. Thus, this paper’s main objective is to improve the process for predicting the wellbore rock failure while drilling. This work overcomes the limitations by using a new and integrated modeling scheme.Wellbore failure prediction is improved through the use of an integrated modeling scheme that involves an elasto-plastic finite element method (FEM) model, machine learning (ML) algorithms, and real-time drilling data, such as image logs from a logging while drilling (LWD) tool that accurately describes the current shape of the wellbore. Available offset well data are modeled in the FEM code and are then used to train the ML algorithms. The produced integrated model of FEM and ML is used to predict failure limits for new wells. This improved failure prediction can be updated with the occurrence of different drilling events such as induced fractures and wellbore enlargements. The values are captured from real-time data and reflected in the integrated model to produce a dynamic representation of the drilling window.The integrated modeling scheme was first applied to laboratory experimental results to provide a proof of concept and validation. This application showed improvement in rock-failure prediction when compared with conventional failure criteria such as Mohr-Coulomb. Also, offset-well data from wireline logging and drilling records are used to train and build a field-based integrated model, which is then used to show that the model output for a separate test well reasonably matches the drilling events from the test well. Application of this integrated model highlights how the allowable mud-weight limits can vary because drilling progresses in a manner that cannot be captured by the conventional predrilling models.As illustrated by a field case, the improvement in failure prediction through this modeling scheme can help avoid nonproductive time events such as wellbore enlargements, hole cleaning issues, pack-offs, stuck-pipe, and lost circulation. This efficiency is to be achieved by a real-time implementation of the model where it responds to drilling events as they occur. Also, this model enables engineers to take advantage of available data that are not routinely used by drilling.

Development and application of an interface constitutive model for fully grouted rock-bolts and cable-bolts

This paper proposes a new interface constitutive model for fully grouted rock-bolts and cable-bolts based on pull-out test results. A database was created combining published experimental data with in-house tests. By means of a comprehensive framework, a Coulomb-type failure criterion accounting for friction mobilization was defined. During the elastic phase, in which the interface joint is not yet created, the proposed model provides zero radial displacement, and once the interface joint is created, interface dilatancy is modeled using a non-associated plastic potential inspired from the behavior of rock joints. The results predicted by the proposed model are in good agreement with experimental results. The model has been implemented in a finite element method (FEM) code and numerical simulations have been performed at the elementary and the structural scales. The results obtained provide confidence in the ability of the new model to assist in the design and optimization of bolting patterns. • New interface constitutive model suitable for both rock-bolts and cable-bolts. • The new model is based on laboratory pull-out test results (in-house and external). • The interface radial behavior has no elastic component. • Model has been implemented in a FEM code and successfully applied to pull-out tests.

Coupled Thermo-Hydro-Mechanical Numerical Modeling of Evolving Fractures in Rocks

We present a numerical technique capable of handling evolving fractures in rocks triggered by coupled thermo-hydro-mechanical (THM) phenomena. The approach is formulated in the context of the finite-element method (FEM) and consists in introducing especial (high-aspect ratio) finite elements in-between the regular (bulk) finite elements. We called this method the mesh fragmentation technique (MFT). The MFT has been successfully used to model mechanical and hydro-mechanical problems related to drying cracks in soils, fractures in concrete, and hydraulic fractures in rocks. In this paper, we extend the MFT for tackling non-isothermal problems in porous media. We present the main components of the mathematical formulation together with its implementation in a fully coupled THM computer code. The proposed method is verified and validated using available analytical, experimental, and numerical results. A very satisfactory performance of the proposed method is observed in all the analyzed cases. These results are encouraging and show the potential of the MFT to tackle THM applications involving fractured rocks. A clear advantage of the proposed framework is that it can be easily implemented in existing numerical FEM codes for continuous porous media to upgrade them to tackle THM engineering problems with evolving discontinuities.

Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method

The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.

Nonlocal integral elasticity based phase field modelling and simulations of nanoscale thermal- and stress-induced martensitic transformations using a boundary effect compensation kernel

In this paper, a nonlocal elasticity based phase field model is presented for thermal and stress induced martensitic phase transformations (PTs) at the nanoscale. The main drawbacks of previous kernels are resolved by introducing the compensated two-phase (CTP) kernel as a combination of the modified and the two-phase (TP) kernels which compensates the boundary effects. The finite element method and COMSOL code are used to solve‌ the coupled Ginzburg-Landau and local/nonlocal elasticity equations. Several important PT examples are presented and the results of the local elasticity and nonlocal elasticity with different kernels are compared. The thermal induced interface propagation is found almost similar for all cases. In contrast, at the equilibrium temperature, the local elasticity creates a stationary vertical interface while both kernels result in a similar 450–rotated interface and a different stress field with lower values. For the nucleus growth, similar morphology and growth rate are found for all cases except during the initial growth where the CTP kernel leads to the growth rate smaller than that of the local elasticity and larger than that of the TP kernel. For the reverse PT, with nonhomogeneous initial conditions, the austenitic embryo grows and the interface propagates until the entire sample transforms back to austenite. The role of the CTP kernel is pronounced with homogeneous initial conditions where the TP kernel represents a nonhomogeneous reverse PT while both the local elasticity and CTP kernel show a similar homogenous reverse PT with no interface. For the precipitate induced PT, in contrast to the TP kernel for which the entire sample transforms to martensite, there remains some noncomplete martensite near the precipitate for the local elasticity and CTP kernel. The CTP kernel also predicts the initial growth rate and stress concentrations between the local elasticity and TP kernel. Note that when boundary periodicity is included, the precipitate induced growth is suppressed. In the presence of a nanobubble which represents internal surfaces, the growth starts from its surface and proceeds if the boundary periodicity is removed and both kernels show a smaller growth rate than the local elasticity. The current study allows for a better understanding of the nonlocal elasticity theory and its application within the kinetics modeling of martensitic PTs and similar nanoscale phenomena.

Performance Characterization of a Kenics Static Mixer Using Slotted Elements

The pharmaceutical, biomedical, bioenergy, and consumer products industries rely heavily on the mixing of fluids. The bulk of the processes that are undergone in these industries are laminar flowing fluids with the attendant need for low-pressure losses which the Kenics static mixers are better suited for. The mixing of fluids is achieved through the splitting and shearing at successive element junctions and stretching and folding along the length of the elements. The performance of Kenics static mixers can be enhanced by optimizing the total blade twist angle, however, the blade pitch has little or no impactful effect. The device geometry optimization is a criterion for its performance enhancement. This study investigates the output mixture strength of the Kenics static mixer using slotted mixer elements solved numerically with Finite Element Method code; COMSOL Multiphysics. The Kenics static mixer performance was optimized with the use of slotted mixer elements as it was observed that the slot width size and a varying number of slots on the mixer elements had an impact on its performance.

Role of the mandrel in the variable curvature local-induction-heating bending process of B1500HS thin-walled rectangular tubes

The variable curvature local-induction-heating bending forming (VC-LIHBF) technology is commonly used in the automotive industry to lighten and stiffen the structure parts. This technology allows the simultaneously bending forming and hardening of ultrahigh strength steel tubes, and allows the tensile strength of B1500HS steel to reach 1500 MPa. By adjusting the bending curvature parameters of the experimental facility through the numerical control system, the production of the tubes with variable curvatures could be achieved without changing dies. However, the more major problem of wrinkling occurs when a small-radius bending is applied on thin-walled rectangular tubes. This paper focuses on improving of forming quality and forming limit of the thin-walled rectangular steel tube (TWRST) with mandrel supported. In this study, an analytical model of the mandrel is established and some reference formulas for the selection of the mandrel parameters are deduced. Based on the above analysis, a three-dimensional elastic-plastic finite element method (FEM) model of the LIHBF process of the B1500HS TWRST is developed using the dynamic explicit FEM code ABAQUS/Temp-disp/Explicit, and key technological problems are solved. Experiments are carried out to verify the accuracy of the analytical model and confirm the reliability of the FEM model. The influences of the mandrel on stress distribution during the local-induction-heating bending process are also investigated. The influence mechanism of the mandrel parameters on the minimum radius of the LIHBF without wrinkling and the forming quality is revealed. The appropriate process parameters for the B1500HS TWRST are obtained through experiments and simulations.

Structural assessment of the EU-DEMO WCLL Central Outboard Blanket segment under normal and off-normal operating conditions

Within the framework of the EUROfusion design activities concerning the EU-DEMO Breeding Blanket (BB) system, a research campaign has been carried out at the University of Palermo with the aim of investigating the structural behaviour of the DEMO Water-Cooled Lithium Lead (WCLL) Central Outboard Blanket (COB) segment. The assessment has been performed considering three different loading scenarios: the Normal Operation (NO), the Over-Pressurization (OP) and the Upward Vertical Displacement Event (VDE-up). In particular, NO scenario represents the loading case referring to the nominal operating conditions, whereas the OP scenario refers to the loading conditions due to an in-box LOCA accident, listed as one of the BB design basis accidental events. Lastly, the VDE-up scenario is an off-normal event reproducing the plasma disruption caused by an uncontrolled vertical motion of the plasma volume. This event brings the plasma in contact with the upper part of the plasma chamber, generating a sudden energy discharge accompanied by Electro Magnetic (EM) forces acting on the structure. The study has been carried out following a theoretical-numerical approach based on the Finite Element Method (FEM) and adopting the quoted ABAQUS v. 6.14 commercial FEM code. In particular, a detailed 3D FEM model of the whole COB segment, including the back-supporting structure and its attachment system to the vacuum vessel, has been set up. Several simulations have been run to assess the thermo-mechanical performances of the segment under the afore-mentioned loading scenarios, also taking into account the impact of the tungsten (W)-armour on the overall structural response. EM loads have been considered in all the assessed scenarios. In the first two, only magnetization forces have been taken into account, while in the VDE-up scenario Lorentz’s forces have been also taken into account. The structural response has been evaluated according to the RCC-MRx structural design rules. The obtained results are herewith presented and critically discussed.

Determination of a pre-heating sequence for the DONES Target Assembly

Within the activities promoted by the EUROfusion consortium in support of the design and construction of the DEMO Oriented NEutron Source (DONES), a mock-up of its Target Assembly (TA), based on the configuration with a “bayonet” Back-Plate (BP) and available at ENEA Brasimone labs, is being adopted for the execution of experimental activities aiming at the validation of specific aspects of the target design.Despite the “integral”-TA concept is the current reference, experimental tests concerning the TA pre-heating phase are not significantly affected by the TA concept and are still representative even though conducted on the bayonet-TA concept. Indeed, the main objective of the pre-heating phase is to raise the TA temperature up to a value close to that of the lithium flow in nominal condition (250 °C). In particular, one of the main concerns is to keep the BP at a temperature higher than 200 °C to avoid possible local lithium freezing.In order to support the afore-mentioned tests, a numerical research campaign has been launched by ENEA Brasimone in collaboration with the University of Palermo with the goal of determining an optimal design of the electrical heaters, both in terms of temperature set-points and geometrical layout. To this purpose, several configurations have been assessed following a theoretical-computational approach based on the Finite Element Method (FEM) and adopting the Abaqus FEM code. In a first phase, different electric heater layouts were assessed by means of steady state thermal analyses. Once the most promising scenario was selected, a detailed thermal transient analysis was carried out. An iterative procedure, based on the analysis of the maximum temperature achieved within the mock-up most critical components, was followed in order to determine the duty cycle of the electric heaters. The obtained numerical results are herewith reported and critically discussed.

Accurate and Efficient Thermal Analysis of Slow Wave Structures for Helix Traveling-Wave Tubes by Finite-Element Method

In slow wave structures (SWSs) for helix traveling-wave tubes, both thermal conductivities (TCs) of materials and thermal contact resistances (TCRs) are temperature-dependent, which have a great influence on the heat dissipation of helix SWSs. This article presents an accurate and efficient thermal analysis method of helix SWSs by finite-element method (FEM). In this method, a novel contact boundary condition (CBC) approach is proposed. This CBC approach can easily integrate various TCR models to simulate temperature-dependent TCRs accurately and conveniently. Specially for double nonlinearities arising from temperature-dependent TCs and TCRs within helix SWSs, a fast nonlinear solver named FMONS is also proposed to significantly improve the efficiency of the thermal simulation for helix SWSs. Based on this method, we further developed a 3-D thermal design tool for helix SWSs called TS2. Different from all the present FEM codes, for example, ANSYS, our TS2 can directly model temperature-dependent TCRs. By simulating various helix SWSs including a global model of the entire helix SWS, it is found that our TS2 has very high accuracy and efficiency in the thermal analysis of helix SWSs, which would be very useful for the design of high-power helix traveling-wave tubes.

Numerical investigation on fluid forces of piggyback circular cylinders in tandem arrangement at low Reynolds numbers

Numerical simulations of flows past the piggyback circular cylinders in tandem arrangement are performed by solving the variational multiscale formulation of the incompressible Navier–Stokes equations using in-house finite element method (FEM) codes. The effects of the gap-spacing-to-diameter (G/D) and the two diameter ratio (d/D) on the flow characteristics and the reductions of the root-mean-square (RMS) drag and lift coefficients are considered for Reynolds numbers (Res) are 100 and 200. The validation shows the fluid force coefficients obtained by the in-house FEM codes are in good agreement with the results in the existing literatures. The obtained results show that, with a proper placement of the smaller cylinder ( $$d/D=0.2$$ ) behind the larger cylinder, the RMS drag and lift coefficients largely decrease compared to those of the single circular cylinder. When $$d/D=0.2$$ , the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at $$G/D=1.2$$ as Re $$=100$$ and at $$G/D=1.0$$ as Re $$=200$$ . It is observed that the proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake, and that the different positions of the vortex shedding at two Res cause that the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at different G/D as Re is different. When d/D varies, the variation of the RMS total lift coefficient behaves differently at two Res. It decreases with d/D increasing at Re $$=100$$ , while it no longer monotonously varies with d/D, but reaches a minimum in the considered range of d/D at Re $$=200$$ . Moreover, the larger d/D results in stronger suppression and postponement of the vortex shedding in the wake. The effects of the gap-spacing-to-diameter and the two-diameter ratio on the flow characteristics and the reductions of the root-mean-square (RMS) drag and lift coefficients are investigated by stabilized finite element method. With a proper placement of the smaller cylinder behind the larger cylinder, the RMS drag and lift coefficients are smaller than those of the single circular cylinder. The proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake.

Slope Stability Analysis under Complex Stress State with Saturated and Unsaturated Seepage Flow

Seepage flow is one of the primary factors that trigger slopes and landslides’ failure. In this study, the slope stability under saturated or unsaturated conditions is analyzed. The influence of a complex stress state on the slope stability with the saturated or unsaturated seepage flow is proposed in this paper. Firstly, an elastoplastic constituted model for the soil under a complex stress state is established and as a user subroutine of the finite element method code of FLAC. Secondly, the 2D and 3D problems of slope stability influenced by the saturated or unsaturated seepage flow are analyzed via the finite difference method with the influence of the complex stress state. Finally, the influence of the intermediate principal stress and the saturated or unsaturated seepage flow on the slope stability is analyzed in this study.

An anisotropic stress-driven growth model for soft tissue based on Eulerian deformation tensor and growth potential

An anisotropic stress-driven growth model of living tissue is presented for tissue engineering based on Eulerian deformation tensor and growth potential. The evolution of growth is simply defined by the homeostatic pressure and Cauchy stress caused by the left Cauchy–Green deformation tensor that is an Eulerian deformation measure. For more generality, anisotropy is considered by proposing the concept of growth flow and growth potential that are inspired by the flow rule of plasticity theory. This method is then able to make three-dimensional anisotropic growth modeling. The Eulerian tensor-based characteristic enables easy implementation into finite element method (FEM). The presented model was implemented into an FEM code and validated by a theoretical solution of thick-walled hollow tubes of soft tissue in homeostatic state, and aortic stenting simulation was also performed for biomedical engineering application. The simulation results show good agreement with the references. The effect of the anisotropic function is also discussed with one element tension simulation. Finally, it is shown that the proposed model can capture experimental data of a growing tumor tissue, and a future work is discussed.

Automatic differentiation of strain‐energy functions in the context of user‐defined materials for the FEM

AbstractIn order to implement material models as user‐defined material subroutines into implicit finite element method (FEM) codes, a stress tensor and a fourth‐order tangent tensor are required. In the context of hyperelasticity, these tensors can be obtained as the first and second derivative of the strain‐energy function. Manual formulation and implementation of these derivatives can be tedious and error‐prone.In this contribution, we discuss automatic differentiation (AD) as an easy‐to‐use alternative to express derivatives for the FEM [1] in an efficient way and without extensive manual implementation [2]. AD is applied to automatically obtain a user‐defined material subroutine for an implicit analysis based on source code of the strain‐energy. The approach is validated by utilizing a hyperelastic anisotropic model of arterial layers [3] in ABAQUS. Additionally, a pseudo‐elastic model of the Mullins effect in filled rubber [4] is implemented to evaluate the applicability of the discussed approach for inelastic behaviors which require internal variables.

Local Refinement in Isogeometric Analysis of Complex Tire Models

AbstractThe capability of Non‐Uniform Rational B‐Splines (NURBS) to exactly represent conic sections exactly makes Isogeometric Analysis (IGA) an attractive alternative to classical Finite Element Method (FEM) for tire simulation. Application of NURBS as basis functions for geometry representation simplifies the generation of the computational mesh that can be directly obtained from the software for graphical design. NURBS‐based approximations of the field variables lead to higher convergence rates and allow higher continuity across the element boundaries. Moreover, the tensor structure of these functions permits the usage of additional advanced refinement techniques.The contribution at hand focuses on the application of hierarchically nested basis functions in tire analysis. The developed framework is based on the introduction of the global multilevel Bézier extraction operator [1]. This approach allows local refinement in the existing isoparametric FEM code without violating its architecture. Within the introduced framework, material models developed for standard FEM can be retained.Special attention is paid to the modelling of rebar elements within the framework of IGA and local refinement in particular. The from standard FEM adopted unconventional method avoids the drawbacks of smeared formulations common in tire numerical analysis and does not require an explicit definition of the reinforcing bars [2]. An additional check of the volumetric content of rebar in the material allows the compatibility of the employed concept with locally improved meshes.Numerical simulations for rolling tires using IGA are presented. The complex multilevel composite structure of tire‐models is obtained by means of CAD‐software. All simulations are performed under the consideration of steady‐state rolling within the Arbitrary Lagrangian‐Eulerian (ALE) description including finite deformations. A benchmark study of IGA and FEM for tire analysis closes this presentation.

Non-linear panel instabilities at high-subsonic and low supersonic speeds solved with strongly coupled CIRA FSI framework

Nonlinear aspects of aeroelastic stability are here investigated for two and three dimensional panels in high subsonic and low supersonic flows. The effects of edge constraints and initial conditions on post-flutter behaviour are also studied.Such phenomena are crucial for spatial launchers development, that has renewed interest due to a larger number of commercial companies in the frame of space flight access.Numerical analyses are carried out with a framework developed at CIRA, able to deal with Fluid Structure Interaction simulation in a partitioned approach. The CIRA multi-block structured flow solver for unsteady Navier–Stokes equations was updated and tightly coupled with the open-source finite element method code CalculiX in a modular approach.The results are compared in terms of static divergence and Limit Cycle Oscillations with literature results.

Resonance tuning in vocal tract acoustics from modal perturbation analysis instead of nonlinear radiation pressure

The analysis of planar wave resonances in ducts of variable cross-section is of importance in many areas of acoustics such as horn theory, the design of musical instruments or the numerical generation of voice. An interesting problem is that of modifying the tube geometry and physical parameters to move its resonances to desired target values. In vowel production, for instance, one can properly adjust the length, cross-sectional area and wall admittance of the vocal tract (VT) to change the frequency of a resonance or to bring together or set apart a group of them for achieving some natural voice effects. An optimization strategy can be implemented to that purpose, which induces small sequential variations of the VT parameters according to sensitivity functions, until one obtains the desired resonance values. The sensitivity functions are usually derived from the work done by variations in the non-linear radiation pressure within the duct. In this paper we will show that, elegant as it may be, there is in fact no need of non-linear phenomena to determine appropriate sensitivity functions. These can readily be obtained from first order modal perturbation analysis. To demonstrate that, we transform the three-dimensional (3D) problem of voice generation into a one-dimensional one (1D), driven by a Webster-type equation. Despite of the latter being 1D, we discretize it using the finite element method (FEM) to benefit from its weak formulation to deduce expressions for the sensitivity functions. The latter are recovered from a perturbation modal analysis of the discrete Webster equation for VT area, length and wall admittance variations. Several examples concerning vowel to vowel transformations are presented to illustrate the potential and limitations of the method. The herein proposed 1D approach for resonance tuning could be easily coupled to 3D FEM codes for expressive vowel production in the future.

Seismic slope stability and failure process analysis using explicit finite element method

Earthquake is one of the primary factors that triggers the failure of slopes and the landslides in the mountainous area. In this study, an efficient method for the seismic slope stability analysis and seismic failure process simulation is proposed. The seismic slope stability and the failure process of a two-dimensional slope model are analyzed via the explicit finite element method with the influence of the dynamic mechanical behavior of soil and the frictional resistance characteristic of the slope rupture surface. A dynamic visco-elasto-plastic constituted model for soil is established and written in FORTRAN as a user subroutine of the finite element method code of ABAQUS. The validation of the visco-elasto-plastic constituted model and the explicit finite element method are compared with the experimental results and the implicit method. The seismic factor of safety and the sliding distance of the soil slopes under the natural earthquake conditions are calculated via the dynamic visco-elasto-plastic constituted model and the explicit finite element method. The influence of the ground motion characteristics on the seismic slope stability is analyzed in this study via the specified elastic response acceleration spectrum. The analysis results of this paper suggest that the seismic slope stability analysis and the progressive failure process of the slope under the seismic condition can be analyzed by the explicit finite element method efficiently. The results show that the dynamic mechanical behavior of soil and the ground motion characteristics are both critical influence factors for the seismic slope stability. The frictional resistance characteristic of the slope rupture surface is the principal influence factor for the sliding distance of the slope, and it also has more influence on the sliding distance of a high slope than that of the small slope.

Effect of Cylinder Arrangement on Fluid Flow and Heat Transfer Characteristics past Four Elliptic Cylinders

Fluid flow and heat transfer characteristics past four elliptic cylinders arranged in square configuration are numerically investigated in this study. An in-house finite element method code based on streamline upwind Petrov - Galerkin algorithm has been used for simulations of two-dimensional, incompressible and laminar flow of air. Analyses are carried out by changing geometric parameters such as spacing ratio, axis ratio and incident angle. Results in terms of vorticity and temperature contours, Strouhal number, drag and lift coefficients and Nusselt number are studied for all cases. These results show that fluid flow patterns are strongly influenced by geometric parameters, based on which flow can be categorized into different types. A critical spacing ratio is found for some of the configurations, where a steep increase in drag coefficient is encountered. From this study, it is observed that incident angle 22.5 degree gives a higher heat transfer rate compared to the other two configurations (0 and 45 degree). Also, elliptic cylinders (axis ratio of 0.8 and 0.5) have similar Nusselt number value with less drag force compared to circular cylinders (axis ratio of 1.0) which justifies the utilization of elliptic cylinders as an alternative for circular ones.