Finite Element Analysis Solutions Research Articles

A multi-resolution approach for multi-material topology optimization based on isogeometric analysis

A novel multi-resolution scheme to perform the multi-material topology optimization in the framework of isogeometric analysis (IGA) is proposed. To create high resolution optimized designs with a lower computational cost, a new variable parameter space is supplemented to define design density variables and represent the optimal material distribution utilizing the bivariate B-spline basis functions. These functions are simply obtained by k-refinement strategy in the IGA. The non-uniform rational B-spline (NURBS) basis functions are employed to exactly describe geometric domains and approximate unknown solutions in finite element analysis (FEA) as well. An alternating active-phase algorithm associated with the block Gauss–Seidel method is employed to convert a multiphase topology optimization problem under multiple volume fraction constraints into many binary phase topology optimization sub-problems with only one volume fraction constraint. Accordingly, the number of design variables depends only on one active phase in each of those sub-problems regardless of the number of material phases and is significantly decreased in comparison with the original problem. The Optimality Criteria (OC) method is used as an optimizer to update solutions for such sub-problems. The effectiveness and robustness of the proposed method are verified via testing various benchmark examples.

A formulation of tooth deformation and its error compensation for worm gear transmission mechanisms

Milling head and rotary table are the key components in five-axis CNC machine tools. However, tracking and positioning precision of these rotary axes based on worm gear mechanisms are affected by the backlash, friction, elastic deformation, and other nonlinearities. Therefore, finding out a simple and universal principle to predict the tooth deformation in an initial design is quite significant. A novel deformation calculation and compensation method with finite element analysis and circular plate theory is proposed for the worm gear transmissions. When the relationship (form factor) between the solutions of circular plate theory and finite element analysis is derived, deformation calculation with finite element analysis can be replaced by multiplying the solution of circular plate theory and the form factor. Analysis and calculation results show that the presented method can provide a reference for the compensation control of the positioning errors.

Micromechanics Investigation of Wood Cell Walls under Compression Loading

The aim of this study was to detect the determinations of the 3D cell deformations of pine wood (Pinus sylvestris L.) in micro-scale(μm) under mechanical compression loading. The 20×20×50mm sized wood specimens were tested under compressive pressure load through 35–40 MPa parallel to the grain orientations. The pressure applied samples were divided into three parts, then processed to form smaller cubic pieces and this pieces stained with gold liquid in order to get scanning electron microscopy images (12 × 12 × 12 mm parts). The deformed cells were photographed in 3D-plane with magnification of (100×), (1500×) and in the range of 3.0–5.0 kV light voltage under the scanning electron microscope. Unloaded and loaded pine wood specimens were visualized and photographed to observe and examine the contraction or expansion of the cell walls comparatively. Based on the experimentally obtained microstructural permanent deformations of the cell structures, a numerical model had been proposed to explain the complex behaviour of cell structures under compression loading. Using the finite element method and ANSYS code, the permanent deformation ratios of three different pinewood cell models were simulated for 35–40 MPa loading to explain the overall stiffness and strength of the pinewood cells. In this way, by considering the results obtained from scanning electron microscopy measurements and related finite element analysis solutions, permanent deformation of honeycomb type pinewood cells was examined in detail.

A multiscale and multiphysics model of strain development in a 1.5 T MRI magnet designed with 36 filament composite MgB2 superconducting wire

High temperature superconductors such as MgB2 focus on conduction cooling of electromagnets that eliminates the use of liquid helium. With the recent advances in the strain sustainability of MgB2, a full body 1.5 T conduction cooled magnetic resonance imaging (MRI) magnet shows promise. In this article, a 36 filament MgB2 superconducting wire is considered for a 1.5 T full-body MRI system and is analyzed in terms of strain development. In order to facilitate analysis, this composite wire is homogenized and the orthotropic wire material properties are employed to solve for strain development using a 2D-axisymmetric finite element analysis (FEA) model of the entire set of MRI magnet. The entire multiscale multiphysics analysis is considered from the wire to the magnet bundles addressing winding, cooling and electromagnetic excitation. The FEA solution is verified with proven analytical equations and acceptable agreement is reported. The results show a maximum mechanical strain development of 0.06% that is within the failure criteria of −0.6% to 0.4% (−0.3% to 0.2% for design) for the 36 filament MgB2 wire. Therefore, the study indicates the safe operation of the conduction cooled MgB2 based MRI magnet as far as strain development is concerned.

Lateral Load Analysis of Stand-off Anchor Bolt Connections Using the Load-Distribution Method

AbstractA comprehensive method was derived for the analysis of stand-off anchor bolt connections with various stand-off distances that are subjected to lateral loading. The procedure applied the load-distribution method that is commonly used for shear wall analysis in buildings, and the base plate was treated as a rigid diaphragm. The lateral load resistance provided by each anchor bolt within the anchor bolt group was calculated on the basis of its lateral stiffness, which was defined as a function of the stand-off distance. Close agreement with finite-element analysis solutions for various stand-off distance conditions was found. An irregular distribution of lateral resistive forces within the anchor bolt group was found for connections with uneven stand-off distances compared to the uniform distribution found for connections with even stand-off distances. The intensity of lateral resistive forces provided by the anchor bolts was found to be impacted by the proximity of the individual anchor bolt to the...

Life and damage mode modeling applied to plastic gears

There is a need to correctly dimension gears for an application with an understanding of how the gear will deteriorate until final failure. However, this task has been difficult because engineers must consider the complexity of gear meshing phenomena combined with the gear material-specific properties and application particularities to determine the critical failure and maintenance points. This article provides a review of the multiple damage modes of plastic gears, including both general and plastic gear-exclusive modes.This article reviews the different branches of the damage problem, performs a combined solution of finite element analysis (FEA) and validated analytical equations for plastic gears. With this knowledge, a unique system of analysis of gear utilization perspectives that evaluates all possible damaging processes is built.By applying a range of normal loads on a plastic gear, it was verified that the damage mode depends highly on the applied load. The identification of the proper damage mode allows preventive actions to be taken because the limits of plastic gears and the optimal usage are identified. With this damage modeling strategy, the designer can skip several steps in reaching a decision regarding plastic gear applicability. This synthesis represents significant progress for plastic gear damage modeling because the major factors of plastic gear functioning and the damage factors are observed.

Interfacial stresses in sandwich structures subjected to temperature and mechanical loads

Through sequential coupling of the differential equations for interfacial shearing and peeling stresses, concise closed-form strength-of-material solutions for these stresses in symmetric and non-symmetric sandwich structures subjected to the combined loadings of temperature, stretching, and bending have been developed. The free-edge effects of the interfacial shearing stress, the maximum magnitude of the interfacial shear stress, and the location of its occurrence are accurately modelled using a single high-frequency hyperbolic function. The analytical solutions have been validated against finite element analysis (FEA) solutions using four sandwich structures: one symmetric, two mildly asymmetric, and another severely asymmetric; and for three load cases: differential thermal expansion, differential mechanical stretching, and mechanical bending. The maximum deviation between the analytical and the FEA solutions for the interfacial shearing and peeling stresses for all the structures and load cases, including that for the severely asymmetric sandwich structure, was less than 15%.

Analytical-Solution Based Corner Correction for Transient Thermal Measurement

The one-dimensional (1D) conduction analytical approaches for a semi-infinite domain, widely adopted in the data processing of transient thermal experiments, can lead to large errors, especially near a corner of solid domain. The problems could be addressed by adopting 2D/3D numerical solutions (finite element analysis (FEA) or computational fluid dynamics (CFD)) of the solid field. In addition to needing the access to a conduction solver and extra computing effort, the numerical field solution based processing methods often require extra experimental efforts to obtain full thermal boundary conditions around corners. On a more fundamental note, it would be highly preferable that the experimental data processing is completely free of any numerical solutions and associated discretization errors, not least because it is often the case that the main purposes of many experimental measurements are exactly to validate the numerical solution methods themselves. In the present work, an analytical-solution based method is developed to enable the correction of the 2D conduction errors in a corner region without using any conduction solvers. The new approach is based on the recognition that a temperature time trace in a 2D corner situation is the result of the accumulated heat conductions in both the normal and lateral directions. An equivalent semi-infinite 1D conduction temperature trace for a correct heat transfer coefficient (HTC) can then be generated by reconstructing and removing the lateral conduction component at each time step. It is demonstrated that this simple correction technique enables the use of the standard 1D conduction analysis to get the correct HTC completely analytically without any aid of CFD or FEA solutions. In addition to a transient infrared (IR) thermal measurement case, two numerical test cases of practical interest with turbine blade tip heat transfer and film cooling are used for validation and demonstration. It has been consistently shown that the errors of the conventional 1D conduction analysis in the near corner regions can be greatly reduced by the new corner correction method.

Rotor eddy loss in high‐speed permanent magnet synchronous generators

Analytical and transient finite element analysis (FEA) methods are used to calculate on-load rotor eddy current power loss in permanent magnet machines taking into account the effect of the reaction of eddy currents. The effect of the phase advance angle between the back electromotive force, and the phase current on rotor eddy current power loss is investigated. Both magnet flux tooth ripple and magnetomotive force harmonics are considered in the analytical calculation of rotor loss; the harmonics of the magnet tooth ripple flux and armature reaction flux are added vectorially. Good agreement between analytical and FEA results is observed when the stator laminations are assumed to have a linear BH curve. However, a significant discrepancy is observed between the analytical and FEA solutions when a non-linear BH curve is used.

Parametric modeling, higher order FEA and experimental investigation of hat-stiffened composite panels

Sizing of hat-stiffened composite panels presents challenges because of the broad design hyperspace of geometric and material parameters available to designers. Fortunately, design tasks can be simplified by performing parameter sensitivity analysis a priori and by making design data available in terms of a few select parameters. In the present study, we describe parametric modeling and design sensitivity analyses performed on hat stiffener elements for both single and multiple-hat-stiffened panels using parametrically defined scripting finite element analysis (FEA) models and an idealized analytical solution. We fabricated a composite skin panel and 4 hat stiffeners using out of autoclave (OoA) and vacuum bag only (VBO) techniques. The stiffeners were subsequently bonded to the skin to form a multi-hat-stiffened panel. To validate the FEA and analytical solutions, multi-point deflections were measured using different loading conditions. The analytical solution provided upper and lower bounds for the center-point deflections of the panels, values potentially useful for hat-stiffened composite panels. The detailed FEA results accurately revealed the design sensitivities of relevant geometric parameters of hat-stiffened composite panels. The findings constitute a first step towards a structural and scripted FEA framework to speed the development and qualification of composite aircraft structures. The framework has the potential to reduce design cost, increase the possibility of content reuse, and improve time-to-market.

Study on sliding layer of cross-tensioned concrete pavement

In order to reduce the number of transverse joints and improve the cracking resistance of Portland cement concrete pavement, a series of diagonally arranged prestressed tendons are applied in the pavement slab, defined as cross-tensioned concrete pavement (CTCP). However, the reduction in the number of transverse joints causes additional stresses and deformations within the CTCP slab which cannot be addressed by only increasing the level of prestress applied to the slab. It is necessary to lay a well-designed sliding layer between the base and the CTCP slab to reduce the stresses and deformations. The influence of coefficient of friction (COF) of a sliding layer on the CTCP structure was studied using both finite element analysis and analytical solutions. Results show that the sliding layer with a smaller initial (before final post-tensioning) COF can reduce the stresses caused by wheel and thermal load while maintaining the prestress in the CTCP slab. Larger long-term (after final post-tensioning) COF of the sliding layer can minimise the CTCP slab end movements. However, the long-term COF should not be larger than 1.04. In addition, a coefficient of friction tester for the CTCP sliding layer was designed and developed based on the Amonton law. Optimum structure parameters and type of the CTCP sliding layer were obtained using “Sand + Polyethylene-plastic Sheeting” as a sliding layer. The optimum cement content of the “Sand + Cement + Polyethylene-plastic Sheeting” sliding layer was also determined from the experimental results.

Real-Time Visualization of Finite Element Models Using Surrogate Modeling Methods

Parametric finite element analysis (FEA) models are commonly used in iterative design processes to obtain an optimum model given a set of loads, constraints, objectives, and design parameters to vary. In some instances, it is desirable for a designer to obtain some intuition about how changes in design parameters can affect the FEA solution of interest, before simply sending the model through the optimization loop. For example, designers who wish to explore the design space and understand how each variable changes the output in a visual way, looking at the whole model and not just numbers or a response surface of a single FEA node. This could be accomplished by running the FEA on the parametric model for a set of part family members, but this can be very time consuming and only gives snapshots of the model's real behavior. This paper presents a method of visualizing the FEA solution of the parametric model as design parameters are changed in real-time by approximating the FEA solution using parametric FEA modeling, surrogate modeling methods, and visualization methods. The implementation develops a parametric FEA mode that includes mesh morphing algorithms that allow the mesh to change parametrically along with the model geometry. This allows the surrogate models assigned to each individual node to use the nodal solution of multiple finite element analyses as regression points to approximate the FEA solution. The surrogate models can then be mapped to their respective geometric locations in real-time. The results of the FEA calculations are updated in real-time as the parameters of the design model change allowing real-time visualization.

Effect of Adhesive Behavior on Normal Stress Distributions in the Single-Lap Adhesive Joints

The effect of adhesives behavior on the normal stress distributions of single-lap adhesive joints is investigated using the three-dimensional finite element technique. Numerical examples are provided to show the influence on the normal stresses of the joints using adhesives of different characteristics which encompass the entire spectrum of elastic stiffness behaviour. finite element analysis solutions of the normal stress distributions in the adhesive layer have been obtained for four typical characteristics of adhesives. The results indicate that Young’s modulus and Poisson’s ratios of adhesives strongly affect the normal stress distributions of the joints.

FEA Solutions for Simulating Multi-workpiece and Multi-process in Manufacturing Process of Submarine Welded Pressure Hull

To realize the numerical simulation of multi-workpiece and multi-process, two difficulties encountered in continuous finite element analysis (FEA) were brought forward firstly. Then the theoretical basis of merging measured initial residual stresses into FEA models was discussed. Based on which the mapping method of multi-model in continuous FEA was put forward. This method can be potentially used to realize such continuous FEA as manufacturing of welded submarine pressure hull by transferring the finite element analysis results between different processes and workpieces. No commercial FEA codes can give perfect solutions to these transfer processes at present. The commercial FEA code MSC.Marc was used as the FEA platform to realize simplifying analysis. Because of all the welding processes are multi-process, so the mapping method of multi-model in continuous FEA can be potential used in the welding simulation to make the calculating results be accurate.

Effects of Mechanical Resonance on Vibrations of Mechanical Systems With Permanent Magnet Machines

In this paper, we describe the effects of mechanical resonance on the vibrations of mechanical systems with permanent magnet (PM) machines. Electromagnetic vibration sources produced by a PM machine were calculated using finite element analysis (FEA) solutions. Subsequently, the harmonic orders related to the mechanical vibrations of the PM machine itself were investigated experimentally by driving the machine at various rotor speeds. To investigate the effects of mechanical resonance, a cantilever beam whose mechanical resonance frequency can be changed by adjusting its length was employed. Finally, the resonance condition was achieved by matching the natural frequency of the cantilever beam with the vibration frequencies produced by the PM machine. The natural frequency mode shapes were validated using 3-D FEA solutions, and the results were confirmed through modal analyses of the frequency response function results from impact tests. Comparisons of the measured vibration data of the PM machine with and without the cantilever demonstrated that mechanical resonance significantly influenced the vibrations of mechanical systems using PM machines.

Coupling analysis of transcutaneous energy transfer coils with planar sandwich structure for a novel artificial anal sphincter

This paper presents a set of analytical expressions used to determine the coupling coefficient between primary and secondary Litz-wire planar coils used in a transcutaneous energy transfer (TET) system. A TET system has been designed to power a novel elastic scaling artificial anal sphincter system (ES-AASS) for treating severe fecal incontinence (FI), a condition that would benefit from an optimized TET. Expressions that describe the geometrical dimension dependence of self- and mutual inductances of planar coils on a ferrite substrate are provided. The effects of ferrite substrate conductivity, relative permeability, and geometrical dimensions are also considered. To verify these expressions, mutual coupling between planar coils is computed by 3D finite element analysis (FEA), and the proposed expressions show good agreement with numerical results. Different types of planar coils are fabricated with or without ferrite substrate. Measured results for each of the cases are compared with theoretical predictions and FEA solutions. The theoretical results and FEA results are in good agreement with the experimental data.

Rigid-Plastic Finite Element Simulation of Cold Forging and Sheet Metal Forming by Eulerian Meshing Method

A computational technique of rigid-plastic finite element method by using the Eulerian meshing method was developed to deal with large deformation problem in metal forming by replacing the conventional way of applying complicated remeshing schemes when using the Lagrange’s elements. During metal forming process, a workpiece normally undergoes large deformation and causes severe distortion of elements in finite element analysis. The distorted element may lead to instability in numerical calculation and divergence of non-linear solution in finite element analysis. With Eulerian elements, the initial elements are generated to fix into a specified analytical region with particles implanted as markers to form the body of a workpiece. The particles are allowed to flow between the elements after each deformation step to show the deforming pattern of material. Four types of cold forging and sheet metal clinching were conducted to investigate the effectiveness of the presented method. The proposed method is found to be effective by comparing the results on dimension of the final product, material flow behaviour and punch load versus stroke obtained from simulation and experiment.

Experiment, Finite Element Analysis and EPRI Solution for J-integral of Commercially Pure Titanium

Abstract In this paper, the J -integral of commercially pure titanium (CP Ti) for standard compact tensile (CT) specimen was obtained by four methods containing fracture experiment, two-dimensional (2-D) finite element analysis (FEA), three-dimensional (3-D) FEA, and the calculation formula in electric power research institute (EPRI). Although the J -integral obtained by EPRI solution is consistent with that by 2-D FEA, they are lower than the result of the experiment. Moreover, the J -integral obtained by 3-D FEA is more close to that of the experiment. In order to improve the prediction accuracy of J -integral by EPRI solution, the improved EPRI solution was developed based on 3-D FEA and verified by the experiment. In addition, two failure assessment curves (FACs) of CP Ti corresponding to traditional EPRI solution and the improved one were compared with the experimental results, which indicates that the improved EPRI solution not only improve the prediction accuracy of J -integral, but also increases the reliability of FAC.

Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response

In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions.

表面粘贴式光纤布拉格光栅传感器层状结构对测量应变的影响

When a surface-bonded Fiber Bragg Grating(FBG)sensor is used to measure the strain of a host material,it will effect the strain distribution of the host material.Therefore,this paper explores the relationship between optical fiber strain and host material strain.A theoretical model of strain transfer of the host material to the optical fiber was presented to modify the measured strain,and the interaction between FBG sensor and host material was considered.Finally,the theoretical predictions proposed in this paper were verified by Finite Element Analysis(FEA)and practical experiments.The results show that the error between FEA and theoretical solution is controlled within 5%,and thatbetween theoretical solution and experimental data is controlled within 8%.These mean that the strain transfer mode satisfies the accuracy requirement of surface-bonded FBG sensors.Moreover,the effects of geometrical and material parameters on the average strain transfer rate and the strain transfer rate were analyzed.The obtained results indicate that the average strain transfer rate and the strain transfer rate increase with the Young's modulus of the host material.However,they decrease with increasing the top thickness and bottom thickness of an adhesive layer.