General Finite Element Research Articles

Modeling of the accurate application of the Kernel Efficiency Method in the proportioning process of shield tunnel construction

Abstract The existing control strategies for subway construction struggle to address the challenges posed by the impact of large-diameter shield-driven underpass subway tunnels on soil settlement. In this paper, based on the mechanism of ground settlement of the shield tunnel under the KNX method, the influence of the underpass tunnel on the existing tunnel and its surrounding soil stress-strain characteristics is calculated by the Peck superposition method. The KNX method is optimized by optimizing the ratio of KNX slurry and the grouting pressure to control the existing tunnel and the ground settlement. The geotechnical general finite element analysis software is being introduced to conduct numerical simulation and engineering application experiments to verify its effectiveness. The results show that when the bonding force of the grouting material is 350Pa-s, the maximum value of the variation is 3.91mm, and the mobility is more suitable, which can effectively fill the void of the shield machine and reduce the settlement of the foundation. When the grouting pressure is 280kN/m2, the maximum contraction of the tunnel is 6.25mm, which can ensure the safety of the existing tunnel on the basis of the tunnel so that the actual settlement of the soil in the tunnel is minimized. Comprehensively, the optimization of the ratio of the KNP method in the control of the deformation characteristics of the soil and structures under the shield tunnel has effectiveness and can effectively provide theoretical and technical guidance for the construction of subway tunnels under the large-diameter shield under the subway.

Investigation of bending behavior of foam core sandwich plates with different face and core materials at different layer thicknesses

Sandwich plates consist of a total of three layers with a thick core layer between two thin face layers. While the face layers provide resistance against bending, the core layer provides resistance against shear. General purpose finite element software programs are one of the most convenient and widely used analysis procedures for investigating the behavior of structures. Many design parameters can be easily examined by these analysis programs. In this study, the bending behavior of simply supported sandwich square plates on four sides with a ratio of core layer thickness to face layer thickness between 7 and 9 was investigated by using the general purpose finite element software program. The effect of the thickness change was investigated by changing the face and core layer thicknesses of the sandwich plates with a fixed total thickness. At the same time, the face and core materials were changed and the most suitable design in bending behavior was revealed. For this purpose, 110 analyzes were performed with 2 different face materials, 5 different core materials, 11 different thickness ratios, and the results were presented with graphics.

Out-of-plane punching simulation based on a layered-shell model

A layered-shell model is a potential tool in the numerical simulation of structures. It has been rapidly developed and widely applied in recent years and can simulate the primary stress states of structures. However, the out-of-plane punching effect is the only stress state that traditional layered-shell models cannot simulate. Therefore, this study introduces an out-of-plane nonlinear shear stress–strain constitutive law into the traditional layered-shell model and proposes a new type of layered-shell element that can simulate the punching shear effect. First, based on the layered-shell model element, the out-of-plane nonlinear punching effect was considered in the general finite element program Marc. An efficient and convenient layered-shell element was established for modelling punching in slabs. Then, based on the results of test data, a trilinear model was used to define the constitutive relationship of the out-of-plane punching model. The critical parameters consisted of the punching capacity, cracking load, initial stiffness, and shear stiffness after cracking. Finally, the developed layered-shell element was used in component analysis, and the punching shear in the slab specimens was simulated with different design parameters to verify the accuracy of the model. This study compared and validated the calculation equations for these key parameters using the experimental data of punching in slabs with different design parameters, providing a reliable calculation tool for the nonlinear analysis of punching in slabs.

A neural network finite element method for contact mechanics

Computational biomechanical models of organ systems utilizing the finite element (FE) method have been extensively applied to the study of normal and pathophysiological function. While a robust method and providing for many unique pathophysiological insights, traditional FE methods remain prohibitively slow for real-time many-query clinical applications. To meet these demanding computational requirements, we have developed a general neural network finite element (NNFE) approach for hyperelastic soft tissue organ simulations that can produce equivalent accuracy within clinically relevant time frames. However, many organ systems involve contact between structural elements (e.g. heart valve leaflets), which has not been previously addressed in the NNFE and related approaches. In the present work, we developed a NNFE-based method for contact between elastic deformable bodies. We exploited the fact that stable equilibrium solutions in nonlinear hyperelasticity minimize the potential energy to train the neural network, with contact incorporated through an potential energy penalty. This penalty was discretized and computationally implemented in JAX (Google, Inc.) in a way that could be statically allocated and jit compiled for rapid computation on modern GPU hardware. Following our previous NNFE formulation, we represented the problem domain geometry and enforced the necessary boundary conditions using a Non-Uniform Rational B-Splines (NURBS) based geometry scheme. NURBS were chosen for their ability to smoothly represent body and surface geometries. To demonstrate the method, we developed and verified two basic contact problems using a hyperelastic material model: indentation and flap. Both problems were simulated with a fully connected neural network with a parallel linear layer. Training continued until the gradient of the energy with respect to network parameters dropped below 10−2, taking less than six hours in each case studied. Once trained, the NNFE approach was capable of accurately predicting the equilibrium configurations of representative contact problems. Moreover, the NNFE contact approach required nearly six order of magnitude less time to evaluate than an equivalent FEniCSx implementation that utilized a similar mesh of cubic order Lagrange elements (0.01 s compared to 1715 seconds, respectively). Moreover, the solutions were trained over full ranges of loading and were thus able to faithfully represent families of solutions without requiring retraining. While addressing basic problems in contact, this study serves as crucial stepping stone to generate NNFE organ simulations for rapid prediction of patient specific solutions that involve contact.

A MULTISCALE MULTIPHYSICS FINITE ELEMENT FOR LUNG

The previously formulated finite element for lung mechanics (MSCL) by the author is extended to include airflow and molecular transport by diffusion. The lung mechanics is analyzed in detail providing an insight into the deformation of the microstructural elements. Also, some refinements are introduced with respect to the previous model. Here, the finite element is extended to incorporate airflow and convective-diffusive particulate (molecular) transport. The smeared concept (the Kojic Transport Model – KTM) is implemented with lung small airway generations considered as subdomains within the KTM. The subdomains refer to a selected number of generations according to the airway diameters. Each domain has its own volumetric fraction and transport tensor specified in terms of the airway size. The computational procedure implemented in the PAK-BIO software consists of three passes within each time step: mechanics, airflow, and diffusion. The current geometry is used for the airflow where the alveolar sacs are considered as the source terms for the last domain, according to the rate of volumetric deformation and volumetric fraction of the sacs. The pressure distribution calculated in the pass 2 is used for the convective term in the diffusion. Here, the alveolar sacs are included as the last subdomain. The new element is now termed the General Lung Finite Element (GLFE). Coupling airflow in large airways, governed by the Navier-Stokes equations, to small airways (with the Hagen-Poiseuille equations) is presented; the same coupling is given for diffusion. Numerical examples illustrate the generality of the formulated finite element.

Technological and contact analysis of Hirth joints including manufacturing tolerances

The present work proposes a novel method for determining the influence of the machining tolerances on the effective contact area of Hirth joints. The proposed method is based on a general Finite Element Model (FEM) capable to simulate any meshing condition of Hirth joints including positioning and machining tolerances using the Monte Carlo method. The FEM was developed based on an accurate measurement campaign of several Hirth joints which allowed to determine the geometric parameters affecting the meshing and the related ranges of variation. The machining reference surfaces and the sequence of technological processes which produce the Hirth joint starting from a raw disc were identified through contactless measurement techniques. The related machining tolerances were measured by employing a high-precision Coordinate Measuring Machine (CMM). A mean value and a standard deviation were associated with each geometrical parameter of the joint. The proposed method can be used for the preliminary design and the quality check of the Hirth joint. In particular, the Prussian blue test, which represents the typical test used to verify the joint’s compliance with the technical specification, was simulated. The results highlight the reduction of the effective contact area of the Hirth joint due to the presence of manufacturing tolerances, which can lead to worse mechanical performances and early failure, and could be used to define the machining tolerances limit of Hirth joints.

A dimensionless analytical analysis for buckling and lateral buckling interaction of thin-walled beams with open cross sections

This paper investigates the interaction between buckling and lateral buckling of thin-walled beams with arbitrary open cross-section using nonlinear modeling in large rotation and with warping. First, the equilibrium equations have been transformed into dimensionless ones, and within a nonlinear stability model, various dimensionless parameters are introduced to control the interaction between buckling and lateral buckling. In comparison to a reference of literature, this work focuses on the case of arbitrary sections and includes a greater number of higher-order terms in our analysis. These additions have an impact on the coefficients of the stability formula by expanding its applicability to non- symmetric sections. Then, the effect of the different dimensionless parameters, thus introduced on the stability curve, has been studied. The proposed solutions are validated and compared to numerical solutions obtained by a general finite element package including the warping developed by the authors using Asymptotic Numerical Method (ANM) to solve the initial nonlinear equations.

Pure/combined buckling mode calculation of thin-walled members constraining general shell FE models

This paper proposes a technique for decomposing the buckling solution of thin-walled members into pure deformation modes (global, distortional, local, or other), aiming at providing an insight into the buckling behavior of these members. The calculation of critical loads associated with a specific or combined deformation mode is performed constraining general finite element models. A general constraining procedure is presented, in which the critical load of any mode, combining different section deformation modes and different harmonic shape functions in the longitudinal direction, can be determined. Cases where all possible harmonic terms may be automatically considered are also described. Cross-section deformation modes are defined in the context of the constrained finite strip method (base vectors), and the proposed constraining procedure is implemented by means of relationships between degrees of freedom of the finite element mesh in commercial software. Calculation of combined buckling modes inherently makes it possible to quantify the participation of the considered modes, including along specific longitudinal segments of the member. Results from the analysis of a lipped channel member are presented to demonstrate the concepts and, later, the analysis of a member with a more complex cross-section and intermediate boundary conditions along length is detailed. A discussion on the base vectors chosen for the constraining method is presented. Finally, the potential of the proposed method is discussed.

An equivalent spring model for seam-clip connections of high-vertical standing seam metal cladding systems

The mechanical behavior of the seam-clip connections plays a pivotal role in the effective wind resistance design of the extensively used high vertical standing seam metal cladding system (SSMCS). An equivalent spring model is developed to represent the mechanical behavior of these connections to simplify the contact problems in the general finite element model, which is time-consuming due to the highly nonlinear contact boundary conditions. The developed model is composed of continuous horizontal and rotational springs as well as dispersed vertical rigid connections. A series of tensile experiments are first conducted to investigate the mechanical behavior of seam-clip connections to calibrate the spring parameters in the developed model. Subsequently, the equivalent spring model is validated by the structural response of a double-span sheet module (DSSM) using experimental investigation and finite element analyses. It is found that the shell finite element model incorporating the developed equivalent spring model can achieve an acceptable structural response while remarkably reducing memory requirements and computational time to about 0.3 % and 0.4 ‰, correspondingly, compared to the contact boundary condition analysis. It highlights the advancement in evaluating the structural response of high-vertical SSMCS in practical engineering applications using this developed model. Furthermore, the developed equivalent spring model has proved to be effective in predicting wind-induced seam-clip pullout failures according to the established failure criteria derived from the structural response of the system.

Nonlinear free vibration analysis of internal thickness-tapered multi-layered composite rectangular plates undergoing moderately large deflections

Thickness-tapering in multi-layered composites is achieved by terminating the plies at discrete locations. This allows for effective material utilization and significant weight savings and is adopted in applications involving multi-layered composites that demand variation in thickness such as helicopter yokes, flexbeams and rotor blades, aircraft wing-skin structures and turbine blades. In the present work, the nonlinear free vibration of such tapered composites undergoing moderately large deflections is investigated for the first time. A general nonlinear finite element formulation for tapered multi-layered composite plates based on Reddy's higher-order shear deformation theory and considering Von Karman nonlinearity is developed. Newton–Raphson scheme in conjunction with Newmark time-integration technique is employed to obtain the time response. The developed model is validated against available results in the literature and through experimentally obtained linear natural frequencies of a honeycomb sandwich plate with tapered face sheets. Parametric studies are conducted to deeply understand the nonlinear dynamic behaviour of tapered composite structures. The investigation reveals that tapered multi-layered composite plates exhibit higher nonlinearity compared to uniform plates thus necessitating the consideration of nonlinear effects in the analysis of such structures.

Farklı açılardaki çeşitli çokgen delikli kare plakların burkulma analizi

Buckling of the plates is of great importance in design of structures. If the plate has a hole because of necessity, hole area and shape also affect the critical buckling loads. In this study, buckling analyses of perforated simply supported square plates with various perforation patterns and different loading types were investigated. Three different perforation patterns as circular, hexagonal and square with different orientations were considered. In order to investigate the slenderness ratio effect, samples were calculated with three different ratio values of 100, 20 and 10. The samples were loaded with four different in-plane loads to examine the effect of loading type. Analyses were performed by using a general purpose finite element program and critical buckling loads were determined depending on the orientation angles for square plate models with different hole perforations. The critical buckling load is independent from the orientation angle for circular perforated plates but depends on for hexagonal and square hole perforations. For these plates buckling analyses were performed for different orientation angles of 0 degrees to 90 degrees. The results show that the calculated critical buckling loads did not remain the same although the hole areas were the same.

An adaptive global–local generalized FEM for multiscale advection–diffusion problems

This paper develops an adaptive algorithm for the Generalized Finite Element Method with global–local enrichment (GFEMgl) for transient multiscale PDEs. The adaptive algorithm detects a subset of global nodes with trivial enrichments, which are exactly or close to linearly dependent from the underlying coarse FEM basis, at each time step, and then removes them from the global system. It is based on the calculation of the ratio between the largest and smallest singular values of small sub-matrices extracted from the global system of equations which introduces little overhead over the non-adaptive GFEMgl for transient PDEs. Compared to existing adaptive multiscale approaches, where either an a-posterior error estimate, a change in physical quantities, or a local problem residual is calculated, the proposed approach provides an innovative framework based on singular values. The proposed approach is shown to be robust for solving advection–diffusion problems that require detecting initial conditions with spikes and capturing moving/morphing/merging mass plumes in heterogeneous media and non-uniform flow with sharp fronts. Specific examples are provided for applications in groundwater contaminant and heat dissipation. The accuracy of the proposed adaptive GFEMgl closely matches reference fine-scale FEM solutions in the L∞ norm.

Numerical simulation on seismic pounding damage in a simply-supported steel bridge

Steel bridges are generally considered to perform well during seismic activity. Nevertheless, they still suffered much unexpected seismic damage in the Kumamoto earthquake, especially seismic pounding damage. Previous studies on bridge pounding damage have generally focused on reinforced concrete bridges. However, steel bridges' dynamic characteristics are more complex, the stiffness of each component varies significantly, and relevant research remains limited. Therefore, the numerical simulation method is adopted in this paper to study the pounding damage of simple-supported steel bridges under seismic events in detail. The multiscale, fine three-dimensional finite element model was built using the general finite element calculation platform Abaqus, and dynamic implicit analysis was performed. Numerical results show that large and near-fault seismic activity results in obvious pounding damage to steel beams. Specifically, longitudinal pounding causes damage to the steel beam's ends; however, the damage is typically localized and mild. Lateral pounding further causes direct damage to the steel beams, resulting in extensive and serious damage. Horizontal pounding which combines longitudinal and lateral causes rotation of the bridge deck and aggravates the lateral damage to steel beams. In addition, a pounding identification method based only on displacement data is proposed, and a feasible preventive measure for lateral pounding damage is suggested.

A novel application of recovered stresses in stress intensity factors extraction methods for the generalized/extended finite element method

SummaryAn efficient improvement to compute Stress Intensity Factors (SIFs) in two‐dimensional fracture mechanics problems solved by Generalized/eXtended Finite Element Method and Stable Generalized Finite Element Method is proposed. A stress field obtained by a recovery procedure based on a locally weighted projection of the approximate stresses, is used in the formulation of two energy‐based SIFs extraction methods: the Contour Integral Method (CIM) and the Interaction Integral strategy. The accuracy and the path independence feature of the proposed approach are investigated in three numerical examples, considering crack opening modes I and II, different crack orientations and the presence of holes. The results demonstrate that the recovered stresses significantly improve the accuracy of the CIM and ensure a notable decrease in SIFs variation for different integration paths. On the other hand, an equivalent impact is not observed for the Interaction Integral strategy.

Shear resistance design of semi-supported buckling-restrained steel plate shear walls: Analytical and numerical investigation

Buckling-restrained steel plate shear wall (BRSPSW) rises as an excellent energy-dissipating lateral force-resisting component. Semi-supported BRSPSW is more flexible in structural configuration than the conventional BRSPSW owing to its independent vertical boundary elements (VBEs). In this paper, the shear resistance and the VBEs effect of the semi-supported BRSPSW were studied by the analytical and numerical methods. A simplified model was developed for simulating the semi-supported BRSPSWs. A minimum sectional area of the VBEs, namely, Acr was suggested for the BRSPSW to fully develop its shear field. Meanwhile, the ultimate shear resistance formula of the semi-supported BRSPSW was proposed. Furthermore, a general finite element (FE) model of the BRSPSWs with two-sided, semi-supported, and four-sided connections was established and applied for parametric analyses. It was found that the semi-supported BRSPSW under the shear could be divided into one middle region with the shear field and two vertical edge regions with local stress fields. The edge regions acted as the additional VBEs for the middle region, whose span decreased with the rise in the sectional area of the VBEs, i.e, secondary columns. The hysteretic behavior of the BRSPSW could be improved by increasing the sectional area of the VBEs when the section area of the VBEs was smaller than Acr. The shear field could be utilized more efficiently in the semi-supported BRSPSW with a larger sectional area of the VBEs and a higher span-to-height ratio of the steel plate. Finally, the equations for predicting the ultimate shear resistance and shear field distribution of the BRSPSW were verified by the test and FE results.

Progressive Failure Analysis of Composite Overwrapped Pressure Vessel

Stress and progressive failure analysis (First Ply Failure to Last Ply Failure) of a composite overwrapped pressure vessel (COPV) with an aluminum liner using the finite element method (FEM) in general and commercial finite element analysis (FEA) software ANSYS in particular is presented in this paper. Ply failure prediction is based on failure criteria implemented in ANSYS software. The first-ply failure (FPF) does not necessarily imply the total failure of a laminate. After FPF, the laminate stiffness is reduced consistent with identified ply failure mode. The strength of the composite laminate is evaluated again to see if it could carry additional load. This ply-by-ply analysis progresses, until the ultimate strength is reached. In the present study the methodology is validated using benchmarks and applied to a filament wound fibre reinforced plastic composite pressure vessel with an aluminum liner. Significant results are presented and critically assessed. Directions for further work in this field are identified.

The Composite Grid Method for Singular Problems of Partial Differential Equations

Partial differential equations are crucial in scientific computing, and this paper will consider some of the problems of partial differential equation singularities. The Composite Mesh Method (CGM) is a new and improved numerical method for solving partial differential equations based on existing numerical methods for finite elements. The method has two meshes over the entire domain—a coarse and a fine set. The two sets of meshes generated by Mesh3 are separate in their respective regions and do not nest or interact. This method improves the accuracy of solving the numerical solution of partial differential equations. This paper discusses the CGM method based on the Finite Element Program Generator (FEPG) and uses it to simulate several singular problems. The numerical simulation results show that the proposed method can obtain more satisfactory simulation results for global problems and use a smaller number of computational generations than the general finite element method.

The polygonal finite element method for solving heat conduction problems

In this paper, a general polygonal finite element method (FEM-polygon) based on the Wachspress shape function is used to solve two-dimensional heat conduction problems. The finite element variational form of the heat conduction problem is first established based on the weighted residual method. Then the formulations of the thermal stiffness matrix, thermal damping matrix, and nodal heat vector are derived using the Wachspress coordinates. The global stiffness matrix is further assembled and the well-behaved algebraic equations of the thermal system are established. Finally, intensive numerical tests are conducted to verify the super convergence in temperature and the high precision in equivalent energy and temperature gradient of the present FEM-polygon for 2D heat conduction problems. Besides, the proposed model also performs excellently for traditional triangular and quadrilateral elements.

Numerical analysis of uneven settlement of highway subgrade based on nonlinear algorithm

Abstract In order to accurately and easily calculate the settlement of the foundation, a high-speed roadbed based on a nonlinear algorithm is proposed to broaden the uneven and uniform reduction numerical analysis. The basic loading test results of the foundation loading test results in a series of sand-bearing test results made by gear suppressive elastic Mohr–COMB were verified using general finite element procedure ABAQUS. The results show that for most original slopes of 1:1.5 highways, according to the above research results and relevant specifications, the high-wig ratio of the steps should be controlled in 1:1.2 to 1:1.5. That is, when the width is controlled in a range of about 1.2 m, the height of the step is held at 0.8–1.0 m. The larger the role of filling the top surface, the more obvious is the role of the geogrid to reduce the settlement of the road embankment. Under the conditions of the same subgraduation, the reinforced road embankment of the geotechnical grille, the settling effect that occurs in the load activity is also more obvious. This method offers a better design and construction technique for expanding the project, investigates the control of differential settlements caused by excavation step size and geogrid size, and seeks more complete, scientific programmes. It has the potential to drastically reduce the project’s investigation effort, shorten the survey cycle, and provide incalculable economic and social benefits. Therefore, the research results of this paper have improved the reliability of existing ground settlement analysis.

Evaluation and story drift ratio limits of structures with separated gravity- and lateral-load-resisting systems using pushover analysis

In recent years, China has strongly advocated the development of prefabricated buildings. To meet the growing demand for housing construction, it is necessary to develop high-rise prefabricated structures. To increase the construction efficiency of high-rise prefabricated structures, an innovative composite structural system with separated gravity- and lateral-load-resisting systems (referred to as an ‘innovative structural system’) was developed, and its seismic performance was evaluated. At the component level, efficient numerical models of the composite frames, reinforced-concrete (RC) shear walls, RC coupling beams, and braces in the innovative structural system were developed using the general finite-element software MSC.Marc. The fragility curves of these components were developed through parametric analysis and a literature review of previous research and database documents. At the system level, through finite-element analysis, the seismic mechanism of the innovative structural system under lateral loads, including the lateral displacement pattern, plastic development pattern, and failure mode, was compared with that of the traditional composite frame–shear wall system. A static pushover analysis was performed, and the displacement response results of the innovative structural system under the maximum considered earthquake strength were obtained. The damage to the components was evaluated via fragility analysis, and the seismic performance of the innovative structural system was compared with that of the traditional system according to the safety factor. The results indicated that for high-rise composite structural systems with separated gravity- and lateral-load-resisting systems under frequently occurring earthquakes, the reasonable range of the story drift ratio limit in design is 1/800 to 1/1000, and a limit value of 1/1000 is recommended conservatively.