Equilibrium Finite Element Research Articles

A nonlinear interval finite element method for elastic–plastic problems with spatially uncertain parameters

This paper proposes a nonlinear interval finite element method for elastic–plastic analysis of structures with spatially uncertain parameters. The spatially uncertain parameters are described by the interval field, and the variation bounds of the elastic–plastic structural responses can be calculated effectively. Quantified by the interval field, the spatially uncertain parameters are represented by the interval Karhunen–Loève (K-L) expansion, based on which the nonlinear interval finite element equilibrium equation is formulated. An interval iterative method is then presented to solve the equilibrium equation and obtain an outer solution of the variation bounds of structural responses such as displacement. In this method, the Newton-Raphson iterative method is used to transform the nonlinear problem into a linear one, and then the interval iterative method is introduced to solve the interval linear equations. Three numerical examples are employed to illustrate the feasibility and accuracy of the proposed method.

Behavior analysis of energy piles in layered transversely isotropic saturated soils

This paper conducts theoretical research on energy piles in layered saturated transversely isotropic soils under different load forms. Firstly, the Timoshenko beam coupled axial force rod elements is used to simulate the pile elements, and the finite element equilibrium equation for energy single piles is derived accordingly. Then, the extended precise integration method (EPIM) is applied to obtain the fundamental solution of soil, which is regarded as the kernel function of the boundary element method to construct the boundary integral equation. Based on the theory of the coupled finite element method - boundary element method (FEM-BEM), and combined with the equilibrium conditions of force and displacement coordination at the pile-soil interface, the boundary integral equation of soil is coupled with the finite element equilibrium equation of the pile to establish the interaction equation. The calculation results of this method are compared with theoretical solutions and in-site field tests to verify the correctness of this theory. Finally, numerical examples are designed to explore the influence of the parameters of energy piles and soils on the behavior of energy piles in layered saturated transversely isotropic soils under vertical and horizontal loadings.

Comparative Studies between Frequency Domain Analysis and Time Domain Analysis on Free-Field One-Dimensional Shear Wave Propagation

In Korea, the underground silo structure for low- and intermediate-level radioactive waste disposal facilities has been constructed and operated since 2014. Large-scale earthquakes occurred in 2016 and 2017, respectively, in Gyeongju and Pohang areas near the underground silo structures, and interest in the stability of the underground silo increased significantly. In this paper, one-dimensional free-field analyses have been carried out before the three-dimensional silo dynamic analyses subjected to earthquake loadings. As an additional study, a new form of the finite element equilibrium equation is derived in terms of relative motions, which is essentially the same equation expressed in terms of total motions where the base shear force is applied to the earthquake load. The accuracy of conventional finite element solutions is evaluated by directly comparing them with closed-form solutions by frequency domain analysis such as SHAKE91.

A 3D time-dependent backward erosion piping model

Backward erosion piping (BEP) is a failure mechanism of hydraulic structures like dams and levees on cohesionless foundations subjected to seepage flows. This article models the time-dependent development of BEP using numerical simulation of the erosion process. A 3-dimensional finite element equilibrium BEP model is extended with a formulation for the sediment transport rate. The model is compared to and calibrated with small- and large-scale experiments. Finally, a large set of simulations is analyzed to study the effects of factors such as grain size, scale (seepage length) and overloading on the rate of pipe progression. The results show that the development of BEP in the small-scale experiments is predicted well. Challenges remain for the prediction at larger scales, as calibration and validation is hard due to limited large-scale experiments with sufficiently accurate measurements. The results show that the progression rate increases with grain size and degree of overloading and decreases with seepage length, which is consistent with experimental observations. The model results provide a better physical basis for incorporating time-dependent development in the risk assessment and design of levees.

Seepage Analysis and Optimization of Reservoir Earthen Embankment with Double Textured HDPE Geo-Membrane Barrier

This research paper focuses on conducting a steady state seepage analysis along with the downstream slope factor of safety using the Modified Bishops method in a poorly compacted earthen embankment and optimizing the same reservoir earthen embankment in a case study located near Sadiyavav village in Junagadh district in Gujarat, India. The study site, situated at 21°32'06.5"N and 70°37'26.7"E, is renowned for its Asiatic lions. The analysis and optimization were performed with a double-textured High-Density Polyethylene (HDPE) Geo-membrane barrier. Previously, designs and numerical solutions proposed homogenous embankments and too poorly compacted with no drainage arrangements, which led to anisotropic conditions within the section and water seeping out, cutting the phreatic line. The paper presents the documented improvements in the factor of safety achieved through the seepage analysis and the optimization of the HDPE Geo-membrane barrier. Two improvement techniques were studied using the “Limiting Equilibrium-Finite Element Method” (LS-FEM). The first using (HDPE) Geo-membrane stabilized with gabions, and the second alternative using HDPE Geo-membrane with gabions in addition to rock toe. The study results showed improvements in the downstream slope stability for the two alternatives by 3% and 10%, respectively. Doi: 10.28991/CEJ-2023-09-11-07 Full Text: PDF

Equilibrium finite element and error estimation for frictional contact problem based on linear complementarity problem formulation

AbstractThis article proposes a novel equilibrium finite element method (EFEM) for equilibrated solution of frictional contact problem. The development of such EFEM is mainly two‐fold. On the one hand, the traction‐based equilibrium element is employed to construct the discrete equilibrated stress field. This equilibrium element, using edge tractions as basic variables, is found straightforward to deal with the friction and contact constraints on the contact surface. On the other hand, the Coulomb frictional contact problem is recast into a linear complementarity problem (LCP), with which the algebraic complementarity formulation can be obtained with the help of the constructed equilibrated stress field. A remarkable property of the proposed EFEM is that the equilibrated solution, in conjunction with the compatible solution of the traditional FEM, can provide reliable error estimation for frictional contact within the framework of dual analysis. Numerical examples are finally conducted to see the performance and the ability to reliable error estimation of the proposed EFEM.

The simplest node-based equilibrium finite element for 2D Poisson equation with exploration of the equivalence among hybrid, flux-based and stress-function-based equilibrium elements

The simplest node-based equilibrium finite element for 2D Poisson equation with exploration of the equivalence among hybrid, flux-based and stress-function-based equilibrium elements

An interval iterative method for response bounds analysis of structures with spatially uncertain parameters

Parameters with spatial uncertainties are very common in practical engineering, which could have a significant effect on structural performances. Different from the framework of probability theory, the interval field model describes the spatial uncertainty with upper and lower bounds rather than the probability distribution function or other statistical characteristics. By introducing the interval field model into finite element analysis and solving the resulting interval finite element equilibrium equation, the upper and lower bounds of structural responses can then be obtained. This paper proposes an interval iterative method for static displacement response analysis of structures with spatial uncertainties, effectively improving the overestimation existing in traditional interval analysis due to dependency problems and obtaining a compact interval envelope of the exact response bounds. Firstly, the spatially uncertain parameters described by the interval field are represented by the interval Karhunen–Loève (K-L) expansion, based on which the interval finite element equilibrium equation is formulated. Secondly, the interval finite element problem is decomposed into several subproblems, and an interval iterative method is developed for an envelope solution of the structural response bounds. Finally, the accuracy and efficiency of the proposed method are verified by several numerical examples.

Cyclic Capacity of Monopiles in Sand under Partially Drained Conditions: A Numerical Approach

Cyclic loading of saturated sand under partially drained conditions may lead to accumulated strains, pore pressure buildup, and consequently reduced effective stress, stiffness, and shear strength. This will affect the ultimate limit state capacity of monopile foundations in sand for offshore wind turbines. This paper calculates the performance of large-diameter monopile foundations, which are installed in uniform dense sand, subjected to storm loading using the partially drained cyclic accumulation model (PDCAM). The simultaneous pore pressure accumulation and dissipation is accounted for by fully coupled pore water flow and stress equilibrium (consolidation) finite element analyses. Drainage and cyclic load effects on monopile behavior are studied by comparing the PDCAM simulation results with simulation results using a hardening soil model with small strain stiffness. At the end, a simplified procedure of PDCAM, named PDCAM-S, is proposed, and the results using this approach together with PLAXIS 3D and the NGI-ADP soil model are compared with the PDCAM results.

An equilibrium finite element method for contact problem with application to strict error estimation

An equilibrium finite element method for contact problem with application to strict error estimation

Geotechnical Perspective on Dozer-Push Method in Coal Mining Operations

The rapid increase of technological development is currently playing a role in the mining industry. The dozer push exploitation method is an alternative to the conventional truck and shovel method. Heavy dozers have the ability to move large amounts of waste material in short distances at a low cost, while trucks and shovels will be more economical if over long distances. Geotechnical assessment becomes one of the critical considerations in making a decision plan and slope design for mining activities where the dozer push activities were carried out. Material conditions greatly affect slope stability, which can be defined as material behavior based on the physical and mechanical properties of the material. The slope stability analysis method used in this study was a combination of two methods, the Limit Equilibrium Method (LEM) and Finite Element Method (FEM). These two combinations of analytical methods will strengthen the justification of the geotechnical perspective. By understanding the behavior of the material on a slope, the risk of a slope failure can be controlled and minimized using a geotechnical perspective. The parameters that will be studied in this study are the physical and mechanical properties of the material against several conceptual design options

Deterministic and Probabilistic Analysis of Dasdhunga Soil Slope along Narayangarh-Mugling Road Section

Instability of slopes is usually governed by a combination of intrinsic and extrinsic factors. The inherent variability of parameters make the problem probabilistic rather than a deterministic one. This research deals with evaluation of stability of slopes with the calculation of the factor of safety of Dasdhunga soil slope along Narayangarh- Mugling road section under different rainfall conditions through the use of coupled finite element and limit equilibrium method in GeoStudio and the determination of probability of failure by sliding, modeled as infinite slopes by using Monte Carlo simulation in R-Studio. Mean, standard deviation, minimum and maximum values of the parameters like- friction angle, cohesion and unit weight were computed from eight samples of the slope. The pore water pressure developed and its corresponding statistical data for different rainfall conditions were computed from FEM based SEEP/W simulation. The above parameters are assumed to follow truncated normal probability distribution function and the geometric parameters like height and slope angle are regarded as constant parameters. It was observed that the safety factors for theslopeis low in high intensity-low duration rainfalls and the probability of failure is high. The tendency to fail increases as the return period of rainfall increases and viceversa. Sensitivity analysis performed in both deterministic and probabilistic methods showed that friction angle is the most sensitive.

Effect of geometric and magnetic boundary conditions on magnetic islands in 3D force-free ideal MHD equilibria

Three-dimensional boundary features and magnetic perturbations affect the magnetic topology of the force-free ideal MHD equilibria formed within a given volume. The use of the PSI-Tet 3D finite-element equilibrium code reveals the existence of magnetic islands inside such equilibria within boundaries with three-dimensional features in configurations that directly depend on the natures of those features. The nature and limits of the influence of such features are explored, as is the influence of flux boundary conditions to qualitatively identify the structure of magnetic islands in Taylor state equilibria with three-dimensional boundary conditions.

A semi-analytical interval method for response bounds analysis of structures with spatially uncertain loads

This paper proposes a semi-analytical interval method for static response bounds analysis of structures subjected to spatially uncertain loads. In the investigated problem, the external loads applied to the structure are spatially uncertain but bounded, which are quantified by an interval field model using upper and lower bounds. By introducing the interval field and its series expansion form into finite element analysis, the interval finite element equilibrium equations are then formulated, where the force vector is an interval vector. Solving the interval equations by the proposed method, a semi-analytical solution of the upper and lower bounds of structural static responses such as displacement and stress can be obtained efficiently. Finally, the effectiveness and accuracy of the proposed method are verified by three numerical examples.

Evaluating Landslide Remediation Methods Used in the Carpathian Mountains, Poland

ABSTRACT The aim of this study was to evaluate the results of landslide remediation in the Polish Carpathians. The research for safeguarding the roads and infrastructure was conducted in the years 2005–2018 in nine landslide areas. The interpretation of engineering geology conditions was complex due to the soil-rock nature of the flysch sediment. Movements were activated after heavy rainfalls. In two cases, triggers were connected with the undercutting of the slope or external loading. The research methods included mapping, drilling, index, oedometer, direct shear tests, ground-penetrating radar scanning, and numerical modeling. To date, 15–59 series of inclinometer and piezometer network readings in 30 locations have been taken. Three online stations have been delivering continuous, nearly real-time data since May 2010. Displacements before the remediation ranged from a few millimeters to several centimeters. The proposed remediation methods included piles, micropiles, anchors, retaining walls, and drainage systems. Six stabilization projects were prepared and checked using the limit equilibrium method and finite element method modeling. The research shows that in five landslide areas, the proposed remedial works were effective. Two other partial stabilization works limited the scope of the movements but did not eliminate the risk. At two locations, only temporary repairs were conducted. Proper identification of the landslide triggers and activity is standard for the recognition of counteraction possibilities and could lower stabilization costs. The selected methods delivered data for remedial decisions. However, effective remediation of an active Carpathian landslide is difficult. It requires individually calibrated investigations, representative monitoring, and careful design of stabilization.

A slope stability analysis for southern Wuchangping tin mine

This paper aims to provide a slope stability analysis for the southern part of Wuchangping mine. The methods of limit equilibrium analysis, finite element simulation and neural network were used to study the stability of the southern slope. The preventive measures, such as bolt reinforcement, drainage system and so on were carried out. The results are as follows. The slope angle for the lower slope of moderately weathered granite and slightly weathered granite is recommended as 60°-65°. The slope angle for the layer where locates near the ground of full weathered granite is recommended as 30°-32°. When the thickness of fully weathered granite layer is less than 10 meters, the slope is still stable enough. The angle is recommended as 38°-40°. The results of evaluation and calculation obtained by the neural network are not different from those of the limit equilibrium method and finite element simulation. The neural network can accurately predict slope stability. The conclusions can provide useful reference for similar mines.

An inherent strain based multiscale modeling framework for simulating part-scale residual deformation for direct metal laser sintering

Residual distortion is a major technical challenge for laser powder bed fusion (LPBF) additive manufacturing (AM), since excessive distortion can cause build failure, cracks and loss in structural integrity. However, residual distortion can hardly be avoided due to the rapid heating and cooling inherent in this AM process. Thus, fast and accurate distortion prediction is an effective way to ensure manufacturability and build quality. This paper proposes a multiscale process modeling framework for efficiently and accurately simulating residual distortion and stress at the part-scale for the direct metal laser sintering (DMLS) process. In this framework, inherent strains are extracted from detailed process simulation of micro-scale model based on the recently proposed modified inherent strain model. The micro-scale detailed process simulation employs the actual parameters of the DMLS process such as laser power, velocity, and scanning path. Uniform but anisotropic strains are then applied to the part in a layer-by-layer fashion in a quasi-static equilibrium finite element analysis, in order to predict residual distortion/stress for the entire AM build. Using this approach, the total computational time can be significantly reduced from potentially days or weeks to a few hours for part-scale prediction. Effectiveness of this proposed framework is demonstrated by simulating a double cantilever beam and a canonical part with varying wall thicknesses and comparing with experimental measurements which show very good agreement.

Equilibrium finite elements for plane problems of the elasticity theory

Equilibrium finite elements for plane problems of the elasticity theory

Integrated Digital Design and Manufacturing for 3D Printing Technologies

Abstract A process is proposed and outlined in which optimal structural design, design post-processing, manufacturing process planning, and subsequent manufacturing may be done algorithmically in a digital design and manufacturing platform. Customized algorithms are developed to define the structural design problem, mesh the design domain and solve the finite element equilibrium equations, perform robust structural topology optimization, optimal build orientation determination for additive manufacturing, support structure location requirements, adaptive slicing of the finite element mesh, and control of a custom made Digital Light Processing (DLP), stereolithography-based 3D Printer.

ANALYSIS OF REMEDIAL ACTIONS DESIGNED TO STABILIZE A HIGHWAY CUT IN A LANDSLIDE AREA

The Carpathian flysch is widely recognized as a geological environment prone to slope movements. This fragility in such an environment is due to its complicated geological and hydrogeological conditions. Weakened slip surfaces (developed in clay like material), in combination with present or past tectonic activity and difficult hydrogeological conditions with aquifers under pressure, are the main causes of slope movements. The article proposes to analyze the design of remedial action in a landslide area near Žilina. Slip surfaces and water conditions are assumed regarding present geotechnical monitoring. Deep cut with two rows of pile walls is analyzed by the limit equilibrium method and finite element analysis. Interaction between two walls and the effect of an amount of volume of sliding mass on resultant earth pressures and anchor forces were studied. The results from finite element analysis are compared with analytical calculations and the differences are discussed.