Traditional Finite Element Analysis Research Articles

Isoparametric B-Spline Elements for Immersed Boundary Explicit Dynamic Simulation

AbstractExplicit dynamic analysis has proven to be advantageous when simulating shock and impact loading, and very small time-scale events. In this article, the feasibility of using a background mesh of B-spline elements for immersed boundary explicit dynamic simulation is studied. In this approach, the geometry is immersed in a background mesh consisting of uniform regular shaped elements to avoid mesh generation difficulties. The boundary conditions are applied using the step boundary method, which uses the equations of the boundaries to construct trial functions that satisfy the essential boundary conditions. An isoparametric formulation is presented for quadratic and cubic B-spline elements and their shape functions are derived from the classical recursive definition of B-splines. The effectiveness of mass diagonalization for B-spline elements is also explored. This approach is validated using several examples by comparing with modal superposition solutions as well as past work using traditional finite element analysis (FEA) and analytical solutions when available.

The study on Reliability Design of Knotter Cam Gear of D-knotter

The outer gear of knotter cam gear of D-knotter and pinion of knotter hook to achieve coordination and cooperation is important guarantee for the movement of “winding rope - biting rope”. This paper analyzes the damage mechanism of the outer gear of knotter cam gear. By application the probability theory for equal effect accuracy synthesis, the outer gear of knotter cam gear and pinion of knotter hook selected from 8 grade precision, and modification of teeth top along the normal direction of the measurement of 50.04 μm for pinion of knotter hook, can control the additional impact dynamic load less than 0.085 times of the calculated load. Two methods of traditional fatigue strength calculation and finite element analysis are used to check the strength of the incomplete outer teeth. And the results obtained by the finite element simulation described in this paper are closer to the real value. This study is of practical value in improving the reliability of the knotter cam gear and promoting the localization of D-knotter.

Survey of Immersed Boundary Approaches for Finite Element Analysis

AbstractMesh generation for traditional finite element analysis has proven to be very difficult to fully automate especially using hexahedral elements for complex 3D geometry. Several modifications to the finite element method (FEM), such as the meshless methods, have been proposed for avoiding mesh generation. An alternative approach has recently gained popularity where the geometry, created as a solid model in cad software, is embedded or immersed in a nonconforming background mesh for analysis. In this approach, referred to here as the immersed boundary approach, a background mesh that is independent of the geometry is used for piecewise interpolation or approximation of the solution. Therefore, a uniform mesh with regular-shaped or undistorted elements can be used, and such a mesh is easy to generate automatically. When the geometry is immersed in the background mesh, the boundary elements are often only partly inside the geometry and the nodes of the mesh may not be on the boundaries. Many new methods have been developed to integrate over partial elements and to apply boundary and interface conditions when the boundaries of the geometries do not conform to the background mesh. These methods are reviewed in this article with particular emphasis on the implicit boundary method and step boundary method for applying boundary conditions. In addition, B-spline elements and several applications of the immersed boundary approach are surveyed including composite microstructures and structural elements for plates and shells.

A new modal theory for wrinkling analysis of stretched membranes

This paper presents a new modal theory for the wrinkling analysis of membranes and discusses the stretch-induced wrinkling behaviour of fixed-ended thin sheets. This modal theory corresponds to an extension of Generalised Beam Theory (GBT) to analyse the wrinkling behaviour of highly stretched sheets. The inherent GBT modal nature adopted in this investigation enables the acquisition of an in-depth knowledge (when compared with the traditional shell finite element analysis) of the behaviour underlying this peculiar buckling phenomena. In order to conduct this study, the work begins by presenting the formulation, describing its main steps and concepts involved in the determination of the “deformation modes” (cross-section analysis), followed by the description of the procedures involved in the development and implementation of the aforementioned formulation that accounts for pre-wrinkling and wrinkling analysis (member analysis). Then, an illustrative example is presented and discussed in detail, which involves the characterisation of the sheet “signature curve” (tensile critical stress vs. length), respective critical wrinkling modes, modal participation diagrams and pre-wrinkling stress distribution patterns. For comparison and validation purposes, refined ABAQUS shell finite element wrinkling results are also reported. Finally, several conclusions are drawn regarding the wrinkling behaviour of stretched sheets, mostly based on the modal nature of this formulation.

Finite Element Analysis of Multi-Position Fatigue Fracture Damage of Nuclear Pipeline Based on X-ray Scattering

The traditional finite element analysis method has poor performance in identification, and there are errors in the selected identification position, resulting in the fact that the accuracy of the results of the finite element analysis is not high. Therefore, based on the characteristics of X-ray scattering, a new finite element analysis method for multi-position fatigue fracture of damage nuclear pipeline is proposed. In this method, a nuclear pipe model is constructed and the three-dimensional scattering identification density of X-ray is established. Based on the creep curve, the material parameters of the nuclear pipeline are analyzed, and the damage index grade is divided according to the yield strength and other parameters; the equivalent stress is calculated, and the constitutive relationship between the material and the damage index is described according to the damage value. The classical scattering formula and Stokes formula are introduced to locate the position of the X-ray cut in node by setting the spatial and temporal distribution function. The parameters of random dynamic change are calculated, and the anchor nodes and position nodes are set to locate the scanning range of damage nuclear pipeline. Experimental results show that compared with the traditional three methods, the proposed method has higher recognition rate and more accurate finite element analysis results. It can be seen that the performance of this method is superior.

Partition of unity finite element for analysis of contact interface stress singularity

Singular mode shapes around the sharp frictional contact interfaces of different materials with linear elastic behavior are derived semi-analytically using the asymptotic eigen-function expansion method. The characteristic equation which is not proposed in a short explicit expression in the literature is extracted in symbolic terms; then solved numerically and the singularity order is derived using Newton's iterative method for the first time in the literature.The extracted eigen-shapes of the high gradient stress fields and the corresponding displacement fields satisfy the compatibility of deformations and tractions on the contact interface with arbitrary frictional interface equations. These asymptotic mode shapes are then implemented into the finite element interpolation using Partition of Unity Finite Element Method (PUFEM). Since the additional enrichment degrees of freedom on the singular contact nodes have the physical meaning of generalized stress intensity factor (GSIF), the direct GSIFs obtained are more accurate and the contour integral manipulations need not be maintained in the post processing phase of the contact analysis.Finally, some engineering problems are solved which demonstrate the capacities of the approach concerning the accuracy of GSIF obtained from the direct-PUFEM proposed compared with that derived by reciprocal work contour integral method used in traditional finite element analyses.

Effect of shear zone on dynamic behaviour of rock tunnel constructed in highly weathered granite

Tunnels have become an indispensable part of metro cities. Blast resistance design of tunnel has attracted the attention of researchers due to numerous implosion event. Present paper deals with the non-linear finite element analysis of rock tunnel having shear zone subjected to internal blast loading. Abaqus Explicit schemes in finite element has been used for the simulation of internal blast event. Structural discontinuity i.e., shear zone has been assumed passing the tunnel cross-section in the vertical direction and consist of Highly Weathered Granite medium surrounding the tunnel. Mohr-Coulomb constitutive material model has been considered for modelling the Highly Weathered Granite and the shear zone material. Concrete Damage Plasticity (CDP), Johnson-Cook (J-C), Jones-Wilkins-Lee (JWL) equation of state models are used for concrete, steel reinforcement and Trinitrotoluene (TNT) simulation respectively. The Coupled-Eulerian-Lagrangian (CEL) method of modelling for TNT explosive and air inside the tunnel has been adopted in this study. The CEL method incorporates the large deformations for which the traditional finite element analysis cannot be used. Shear zone orientations of 0o, 15o, 30o, 45o, 60o, 75o and 90o, with respect to the tunnel axis are considered to see their effect. It has been concluded that 60o orientation of shear zone presents the most critical situation.

Nelder–Mead Optimization of Elastic Metamaterials via Machine-Learning-Aided Surrogate Modeling

One of the fundamental challenges of structural optimization of elastic metamaterials (EMMs) with complex geometry lies within the high consumption of computational power associated with finite element analysis (FEA) simulations, which often render the numerical solution an ineffective and costly attempt. Additionally, due to the inherent mesh dependence of the FEA method, minuscule geometry features, which often arise during optimization, demand very fine elements, resulting in enormously high time consumption, especially when repetitive solutions are needed for objective function validations. In this study, we developed a surrogate modeling algorithm to reduce computational time in structural optimization of EMMs. The surrogate model was constructed based on a multilayer feedforward artificial neural network (ANN) architecture, trained with machine learning techniques and optimized through a genetic algorithm (GA) program to improve its accuracy in predicting the location and width of the primary elastic band gap. With the trained and optimized ANN model at the core, a Nelder–Mead (NM) algorithm was established and its performance inspected in comparison to the traditional FEA method. The ANN-NM model shows remarkable accuracy in predicting the band gap width and impressive reduction in the time consumption.

Prediction of surface variation field in face milling via finite element model updating with considering force-deformation coupling

Effective prediction of surface variation is of great helpf for developing and controlling machining process to maintain surface quality during face milling of large-scale component with discontinuous surface. However, the simulation ranges of machined surface error in traditional finite element analyses are far less than those needed in characterization of large-scale face milling with multi-tooth cutter in order to maintain efficiency. To address this issue, this paper attempts to develop a numerical methodology to estimate the field data of machined surface error based on iterative finite element analysis integrated with cutting trajectory reconfiguration. Finite element model updating (FEMU) method is applied to analysis the cutting deformation in each cutting instant while considering both the cutting force variation in face milling and the locally geometrical differences of component. A flexible model is established to predict the residual cutting material in each cutting instant with considering the coupling effect between instantaneous cutting force and cutting deformation. And then a sub-iteration scheme is proposed to calculate the equilibrium deflection and the real residual material of flexible cutting system with a modified Newton-Raphson method. The proposed simulation methodology can be generally applied for predicting surface variation field in face milling of large-scale component with multi-holed surface, especially for flexible component.

Dynamic analysis of varying speed rotating pretwisted structures using refined beam theories

This paper investigates the dynamic modeling and analysis of rotating pretwisted structures with varying speed, considering complex geometries and setting angles. For thin structures with large curvature and pretwist, a modeling approach with high accuracy and efficiency is needed to capture their highly coupled vibratory behaviors. Therefore, there exists a clear demand for refining beam models with only few additional parameters to describe the shell-like performance. In this paper, we propose a novel three dimensional (3D) pretwisted beam element formulation based on the Carrera unified formulation (CUF) theory. The formulation is implemented to the coupled vibration studies of varying speed rotating pretwisted structures by describing the displacement field in rotating coordinate systems. Using nonlinear strain-displacement relations and Hamilton's principle, a 3D pretwisted beam model is derived on the basis of refined beam theories. Also the inertial, centrifugal and Coriolis effects are taken into account, so that the established model is able to reveal coupled dynamic responses, including in-plane, out-ofplane and torsional deformations. Numerical simulation is performed to study the dynamic characteristics and time responses of a fan blade and a space boom. Results show that this method accurately captures the periodic motions and unstable motions of rotating structures. Compared with traditional theories and finite element analysis (FEA) software, the proposed method significantly reduces the computational cost by using self-adaptive model order and element number. In summary, the proposed method can be used to study dynamics of varying speed rotating pretwisted structures in a precise, flexible and numerically economical fashion.

Triangulation-based isogeometric analysis of the Cahn–Hilliard phase-field model

This paper presents triangulation-based Isogeometric Analysis of the Cahn–Hilliard phase-field model. The Cahn–Hilliard phase-field model is governed by a time-dependent fourth-order partial differential equation. The corresponding primal variational form involves second-order operators, making it difficult to be directly analyzed with traditional C0 finite element analysis. In this paper, we construct C1 Bernstein–Bézier simplicial elements through macro-element techniques, including various triangle-split based macro-elements in both 2D and 3D space. We extend triangulation-based isogeometric analysis to solving the primal variational form of the Cahn–Hilliard equation. We validate our method by convergence analysis, showing the nodal and degree-of-freedom advantages over C0 Finite Element Analysis. We then demonstrate detailed system evolution from randomly perturbed initial conditions in periodic two-dimensional squares and three-dimensional cubes. We incorporate an adaptive time-stepping scheme in these numerical experiments. Our numerical study demonstrates that triangulation-based isogeometric analysis offers optimal convergence and time step stability, is applicable to complex geometry and allows local refinement.

Refined isogeometric analysis for fluid mechanics and electromagnetics

Starting from a highly continuous isogeometric analysis discretization, we introduce hyperplanes that partition the domain into subdomains and reduce the continuity of the discretization spaces at these hyperplanes. As the continuity is reduced, the number of degrees of freedom in the system grows. The resulting discretization spaces are finer than standard maximal continuity IGA spaces. Despite the increase in the number of degrees of freedom, these finer spaces deliver simulation results faster with direct solvers than both traditional finite element and isogeometric analysis for meshes with a fixed number of elements. In this work, we analyze the impact of continuity reduction on the number of Floating Point Operations (FLOPs) and computational times required to solve fluid flow and electromagnetic problems with structured meshes and uniform polynomial orders. Theoretical estimates show that for sufficiently large grids, an optimal continuity reduction decreases the computational cost by a factor of O(p2). Numerical results confirm these theoretical estimates. In a 2D mesh with one million elements and polynomial order equal to five, the discretization including an optimal continuity pattern allows to solve the vector electric field, the scalar magnetic field, and the fluid flow problems an order of magnitude faster than when using a highly continuous IGA discretization. 3D numerical results exhibit more moderate savings due to the limited mesh sizes considered in this work.

Quadrilateral overlapping elements and their use in the AMORE paradigm

We give the formulation of new 4-node overlapping quadrilateral finite elements and demonstrate their performance in several numerical examples. The elements are insensitive to mesh distortions and lead overall to accurate numerical solutions. We show how the quadrilateral elements are utilized in the AMORE scheme of “automatic meshing with overlapping and regular elements”. Since in this paradigm the finite elements interior to the domain of analysis are undistorted regular elements and the distortion-tolerant overlapping elements are used for discretizations near the boundaries, high solution accuracy is achieved. This accuracy is obtained with much less effort for meshing than in traditional finite element analysis and with a reasonable computational expense.

A computationally efficient hybrid model for simulating the additive manufacturing process of metals

Additive manufacturing (AM) suffers from residual stress formation and part distortion. One way to improve AM is to use optimal process parameters that yield residual stress distribution that is less detrimental. A finite element analysis (FEA) based model can be used as a design tool to determine optimal process parameters. Being a design tool, such a model should not only predict the residual stress formation and part distortion accurately but should be capable of performing the simulation in a reasonable time as well. However, the traditional FEA models are either accurate but computationally very expensive as in the case of process-based models that captures the evolution of the temperature and stress/strain field or very fast but often inaccurate as in the case of inherent strain based (IST) based models which comprise a series of quasi-static stress-analyses. In this study, we demonstrate that a model that is both accurate and computationally less expensive can be developed by adopting a hybrid approach in which the spatial and temporal resolution of the field solutions over different regions of the part are selectively controlled depending on the expected levels of stress gradients in these regions. The new model, called Additive FEA Hybrid (AFEA-H) model, uses a previously reported Additive FEA (AFEA) framework [1] to combine a process-based model that has a high spatial and temporal resolution with an IST based model that has a low resolution. Numerical simulations performed for a few example problems demonstrate that the AFEA-H method can enhance the computational efficiency substantially without compromising solution accuracy.

Induction machine model with finite element accuracy for condition monitoring running in real time using hardware in the loop system

Most industrial processes are run by induction machines (IMs). Condition monitoring of IM assures their continuity of service, and it may avoid highly costly breakdowns. Among the methods for condition monitoring, on-line motor current signature analysis is being attracting a rising interest, because it is non-invasive, and it can identify a wide variety of faults at early stage. To favour the development of on-line fault diagnosis techniques, it is necessary to have real-time currents with which test the new techniques and devices. Models running in real time in hardware-in-the-loop (HIL) simulators are a suitable alternative to balance the drawbacks of test benches (costly, limited machines, faults and working conditions). These models must be accurate enough to reflect the effects of a fault and they must be running in real time. A promising technique based on the equivalent circuit parameters calculation of IM by finite element analysis (FEA) is attracting a rising interest due to its reliability, performance and the possibility of being run in a HIL. Nevertheless, prior to running in a HIL, it is necessary to compute the IM parameters using FEA, which requires long simulation times and high computing resources. Consequently, covering a whole range of degrees of a giving fault could be unaffordable. What is proposed in this paper is to apply the sparse subspace learning (SSL) in combination with the hierarchical Lagrangian interpolation (HLI) to obtain the parametric solutions of the faulty IM model that cover the whole range of severity of a given fault, with a reduced number of FEA simulations. By means of this approach it is possible not only to boost the computation speed but also to achieve a significant reduction of memory requirements while retaining reasonable accuracy compared to traditional FEA, so enabling the real-time simulation of predictive models.

Isogeometric Topology Optimization of Continuum Structures using an Evolutionary Algorithm

Topology optimization has been an interesting area of research in recent years. The main focus of this paper is to use an evolutionary swarm intelligence algorithm to perform Isogeometric Topology optimization of continuum structures. A two-dimensional plate is analyzed statically and the nodal displacements are calculated. The nodal displacements using Isogeometric analysis are found to be in good agreement with the nodal displacements acquired by standard finite element analysis. The sizing optimization of the beam is then performed. In order to determine the stress at each point in the beam a formulation is presented. The optimal cross-section dimensions by performing Isogeometric analysis are acquired and verified with the cross-section dimensions achieved by hiring bending stress and shear stress criteria, as well. The topology optimization of a two-dimensional simply supported plate continuum and a problem on three-dimensional continuum are optimized and presented. The results show that the minimum weight which is found by applying Isogeometric topology optimization gives better results compared to the traditional finite element analysis.

Design of manufacturable fiber path for variable-stiffness panels based on lamination parameters

Compared with traditional composite panels, the modeling, analysis and design of variable-stiffness panels with curvilinear fibers are much more complicated. Although the design flexibility is greatly enhanced, the design of variable-stiffness structures must meet manufacturing constraints to ensure that the designed structures can be fabricated finally. In order to design variable-stiffness composite panels that is very challenging due to its nonlinearity and non-convexity, a novel multi-stage design method for variable-stiffness panels is developed based on lamination parameters. First, lamination parameters are taken as design variables, and the stiffness distribution is obtained efficiently by few iterations. Next, the lamination parameters are transformed into actual layups. Finally, the realistic fiber path is regenerated by considering manufacturing constraints. In addition, the isogeometric analysis, which is more suitable for variable-stiffness structure, is used instead of the traditional finite element analysis to improve the analysis accuracy. Illustrative example demonstrates the high computational efficiency and optimization capacity of proposed method, compared to gradient-based algorithm and evolutionary algorithm.

A hypoplastic macroelement model for a caisson foundation in sand under monotonic and cyclic loadings

Nowadays, the numerical analysis of caisson foundations of offshore structures is a big challenge in engineering design. A simple, fast and accurate numerical tool is proposed in this article based on the macroelement concept. The novel macroelement is within the framework of hypoplasticity and can consider static monotonic and cyclic combined (multidirectional) loads for a caisson foundation in sand. The incremental nonlinear constitutive formulas are defined in terms of generalised forces and displacements and an enhanced function of failure surface is introduced. A series of well-documented laboratorial reduced-scale 1g model tests are adopted to validate the novel numerical tool. Results demonstrate a satisfied predictive performance of the proposed macroelement that can be used in caisson foundation design and constitutes an alternative to the traditional finite element analysis.

Prediction and energy contribution analysis of interior noise in a high-speed train based on modified energy finite element analysis

Abstract Compared with traditional finite element analysis and statistical energy analysis, the energy finite element analysis (EFEA) has the advantages of small computations and solving local responses in large-scale complex structures. In this paper, the structural sound insulation effect is introduced to EFEA for predicting and analyzing interior noise responses of extruded structures in a high-speed train. Firstly, the carriage structure and cavity models are established based on EFEA theory, and model parameters are obtained through experiments and effective simulations. Mechanical and acoustic excitation sources of the high-speed train are extracted through multi-body dynamic simulation, acoustic finite element method and nonlinear acoustic solution. The reliability of predicted excitations is validated by verifying the amplitude peak frequency bands. The interior noise responses at several observations are obtained and in good agreement with on-site test results, and the EFEA prediction model of interior noise is verified accurately. Secondly, the energy contribution of exterior excitation sources to interior noise responses is analyzed based on EFEA model. The results indicate that acoustic excitations dominate the acoustic energy in the frequency bands above 800 Hz, and the energy contribution of mechanical excitations and acoustic excitations is relatively close in the frequency bands below 600 Hz. The contribution of aerodynamic noise excitations is predominantly concentrated in the frequency bands below 500 Hz, while that of wheel-rail noise excitations is concentrated in the frequency bands above 800 Hz. In the frequency bands below 1250 Hz, the energy contribution of rail noise excitations is much more important than that of wheel noise excitations, while their contribution gets gradually close in the frequency bands above 1600 Hz. Besides, the acoustic excitations at the bottom of the carriage are quite important sources. Finally, wheel-rail noise excitations are optimized with spoke-shielding damping wheels and dynamic vibration absorbers, and the sound pressure level in the amplitude peak bands is reduced by about 8 dB. The interior noise responses are reduced by about 3–5 dB in the frequency bands above 800 Hz, and total loudness, sharpness and roughness at different locations are decreasing by more than 1 sone, 0.05 acum and 0.03 asper respectively. Therefore, wheel-rail noise optimizations have good reduction effects on interior noise responses in the high frequency bands.

Thermal Buckling Analysis and Optimization of Curvilinearly Stiffened Plates with Variable Angle Tow Laminates

This paper presents results from thermal buckling analysis and optimization of stiffened composite panels with variable angle tow (VAT) laminates and curvilinear stiffeners. Considering the meshing difficulties for curvilinearly stiffened VAT laminates due to both spatially dependent fiber path orientation and arbitrarily shaped stiffeners in the traditional finite element analysis, the present work models the plate and stiffeners separately without the need to place finite element nodes along the stiffener/plate and stiffener/stiffener interfaces. The displacement compatibility conditions are enforced at these interfaces in the finite element analysis. Convergence and verification study results show that the present method can accurately predict the thermal buckling behaviors of VAT laminates and curvilinearly stiffened VAT laminates. Parametric studies show that either VAT laminates or curvilinear stiffeners alone can improve the buckling performance as compared with using straight fiber laminates and straight stiffeners. VAT laminates and curvilinear stiffeners are found to redistribute the in-plane stress resultants and tailor the buckling mode shape, respectively, to improve the total buckling response. Optimization studies using curvilinear stiffeners and VAT laminates together for maximizing buckling temperature for a stiffened plate are conducted.