Two-dimensional Finite Element Research Articles

Two-dimensional biomechanical finite element modeling of the pelvic floor and prolapse.

We developed the pelvic floor model in physiological and pathological states to understand the changes of biomechanical axis and support that may occur from the normal physiological state to the prolapse pathological state of the pelvic floor. Based on the physiological state model of the pelvic floor, we model the uterus to the pathological state position by balancing intra-abdominal pressure (IAP) and uterine pathological position load. Under combined impairments, we compared the patterns of changes in pelvic floor biomechanics that may be induced by different uterine morphological characteristic positions under different IAP. The orientation of the uterine orifice gradually changes from the sacrococcygeal direction to the vertical downward of vaginal orifice, and a large downward prolapse displacement occurs, and the posterior vaginal wall shows "kneeling" profile with posterior wall bulging prolapse. When the abdominal pressure value was 148.1cmH2O, the descent displacement of the cervix in the normal and pathological pelvic floor system was 11.94, 20, 21.83 and 19.06mm in the healthy state, and 13.63, 21.67, 22.94 and 19.38mm in the combined impairment, respectively. The above suggests a maximum cervical descent displacement of the uterus in the anomalous 90° position, with possible cervical-uterine prolapse as well as prolapse of the posterior vaginal wall. The combined forces of the pelvic floor point in the direction of vertical downward prolapse of the vaginal orifice, and the biomechanical support of the bladder and sacrococcygeal bone gradually diminishes, which may exacerbate the soft tissue impairments and biomechanical imbalances of the pelvic floor to occur of POP disease.

Theoretical and numerical investigations of acoustic field characteristics of shear-horizontal feature guided waves in a welded joint

This paper investigates acoustic field characteristics of shear-horizontal feature guided waves (SH-FGWs) propagating through topographic waveguides like welds and stiffeners in plate-like structures. It establishes mathematical models of second harmonic and quasi-static component (QSC) generated by SH-FGWs in a welded joint and analyzes their theoretical characteristics. Using two-dimensional semi-analytical finite element and three-dimensional finite element methods, it studies the dispersion characteristics of FGWs and acoustic field distribution at specific frequencies of SH-FGWs, as well as their nonlinear response. This study provides new physical insights into the acoustic field distribution and nonlinear response of SH-FGWs in topographic waveguides.

On the seismic performance of block type quay walls: Numerical analyses against 1g shaking tank tests

Up to date national and international codes and standards recommends the performance-based design to better estimate the seismic response of the gravity type quay walls. Advances in computer-based solutions paved the way for numerical studies and important developments have been achieved in several commercial computer programs some of which are used for the seismic analysis of gravity type quay walls. Experimental and/or numerical research have been conducted to provide an understanding of the vulnerability of these structures, however, only a few are devoted to the seismic performance of block type quay walls. In this study, a two-dimensional (2D) finite element analysis was performed to simulate the seismic response of three different block type quay walls. A vertical wall and two recently invented hunchbacked walls, namely: first type hunchbacked wall (FHW) with a larger hunch and second type hunchbacked wall (SHW) with a smaller hunch were used in analyses. The calibrated numerical models were used to predict the seismic behaviour of the walls, and the computed horizontal displacements were compared against measured data. In general, the computed response was found to be in satisfactory agreement with the experimental produced one. It was found that the first type hunchbacked wall exhibited the most satisfactory performance compared to the performance of the other studied wall types. The main reason for this is the lower centre of gravity (compared to that of the other walls), resulting in smaller inertia-driven overturning moments at the wall base and therefore smaller rotation-induced horizontal displacements. The worst performance was observed in the vertical wall due to the mobilization of smaller shaft and base shear resistances. The observations were supported by both the numerical and the experimental results.

Evaluation of the Size of a Defect in Reinforcing Steel Using Magnetic Flux Leakage (MFL) Measurements.

This study aimed to evaluate 2D magnetic flux leakage (MFL) signals (Bx, By) in D19-size reinforcing steel with several defect conditions. The magnetic flux leakage data were collected from the defected and new specimens using an economically designed test setup incorporating permanent magnets. A two-dimensional finite element model was numerically simulated using COMSOL Multiphysics to validate the experimental tests. Based on the MFL signals (Bx, By), this study also intended to improve the ability to analyze defect features such as width, depth, and area. Both the numerical and experimental results indicated a high cross-correlation with a median coefficient of 0.920 and a mean coefficient of 0.860. Using signal information to evaluate defect width, the x-component (Bx) bandwidth was found to increase with increasing defect width and the y-component (By) amplitude rise with increasing depth. In this two-dimensional MFL signal study, both parameters of the two-dimensional defects (width and depth) affected each other and could not be evaluated individually. The defect area was estimated from the overall variation in the signal amplitude of the magnetic flux leakage signals with the x-component (Bx). The defect areas showed a higher regression coefficient (R2 = 0.9079) for the x-component (Bx) amplitude from the 3-axis sensor signal. It was determined that defect features are positively correlated with sensor signals.

Analysis of Sealing Characteristics of Lip Seal Rings for Deep-Sea Separable Pressure Vessels

Deep-sea pressure vessels are specialized pressure vessels designed for automatic deployment from underwater to the surface. These vessels find extensive applications in underwater life-saving and transportation. Their interiors are furnished with a pair of sealing rings, one of which is lip-shaped, and the other is a convex shape, to ensure a dependable seal. With increasing water depth, the sealing rings experience augmented pressure, resulting in a gradual pressing of the rings into the sealing groove. Using ANSYS workbench finite element software, a two-dimensional axisymmetric lip seal finite element model using forces for overall constraint was established, the complete process of progressive pressing into the sealing groove was simulated, and the deformation, contact stress, maximum shear stress, and von Mises stress distribution was also simulated. We also conducted a comparative analysis of lip seals under low and high-water pressure sealing conditions. The findings of the study indicate that when subjected to a combined effect of the installation pre-tightening force and the working water pressure, the lip seal experiences complete compression into the sealing groove at a specific water depth. When subjected to the simultaneous influence of water pressure on the sealing ring material and friction force on the contact surface, two extremes of contact stress manifest in the primary sealing zone of the lip seal. These extremes have the capacity to elevate the contact stress and the effective sealing width, ultimately leading to an improvement in the sealing performance. Concurrently, as the water pressure gradually increases, the inner concave circle of the sealing ring experiences stretching, leading to a reduction in stress concentration, equivalent stress, and shear stress to a considerable extent. This mechanism ensures that the lip-shaped sealing ring retains sufficient strength. This study offers a viable solution for conducting sealing studies on deep-sea separable pressure vessels.

The Method of Optical Paths for the Numerical Solution of Integrated Photonics Problems

A number of topical problems of integrated photonics are reduced to oblique incidence of radiation on a plane-parallel scatterer. For such problems, a method for integrating Maxwell’s equations along the direction of beam propagation is proposed. As a result, the original two-dimensional problem is reduced to a one-dimensional problem, and it is solved using recently proposed one-dimensional bicompact schemes. This significantly reduces the computational cost compared with the conventional two-dimensional finite difference and finite element methods. The proposed method is verified by solving test problems for which exact solutions are known.

Optimal design and performance analysis of Rotating Power Flow Controller

In this paper, a scheme of rotating power flow controller (RPFC) is proposed, which can flexibly and effectively reduce the voltage deviation under the disturbance of distributed generation and load side. Firstly, based on the prototype of a new rotating power flow controller (RPFC) with a rated capacity of 40 kVA, a two-dimensional finite element model based on the core component RPST is established. Then the optimal parameter combination in RPST is determined by the Taguchi experiment method and weight calculation. Finally, Matlab, Maxwell, and Simplorer are used to realize the joint simulation of field-circuit coupling. The results show that the voltage regulation efficiency and power factors of RPFC are increased by 1.4% and 2.7% respectively under the optimal parameter combination, which provides a reference for the design and engineering application of large-capacity RPFC.

Numerical investigation on the coupled vibrations of piezoelectric energy harvester with a liquid-filled proof mass

Replacing the solid tip mass of a piezoelectric cantilever beam with a liquid-filled mass can increase its frequency bandwidth due to the effect of nonlinear liquid sloshing. To investigate the coupled vibrations of the piezoelectric beam and the sloshing liquid, as well as their contributions to the output power, a coupled two-dimensional finite element method-smoothed particle hydrodynamics model has been developed in this study. Using this model, the dynamic behavior of a piezoelectric beam with a liquid-filled rectangular container as the tip mass, subjected to vertical harmonic excitation, has been investigated. The effects of parametric sloshing, excitation level, and geometric nonlinearity on the output voltages have been studied in detail. The simulation results indicate that: (a) the parametric sloshing in the liquid container exhibits subharmonic characteristics, which can be triggered by matching the excitation frequency to twice the natural frequency of the sloshing mode; (b) the piezoelectric beam exhibits subharmonic or harmonic oscillations at parametric resonance; (c) due to the effect of coupled vibrations, the energy harvester with a liquid-filled proof mass has a broader bandwidth compared to the traditional harvester; (d) the frequency response diagram of the output voltage shows multiple peaks at high excitation amplitudes, and the bifurcations are caused by parametric sloshing.

A modified sonic black hole structure for improving and broadening sound absorption

In order to improve and broaden the absorption performance of Sonic Black Hole (SBH), we propose a modified SBH structure with micro-perforated panels which is embedded the multiple resonator cavities, and investigate the sound absorption effect of the structure. Characteristics of acoustic streaming effects are embodied in sound pressure and flow velocity distribution. Further, proposed SBH structure can achieve high sound absorption under 6.0 kHz. Based on the symmetry of the structure, the Two-dimensional axisymmetric Finite Element Method (FEM) model is proposed to study the sound absorption mechanism, which shows that the change of flow velocity gradient of acoustic medium leads to the loss of acoustic energy inside the structure. By discussion on acoustic streaming effects of different frequencies, the resonator cavity and micro-perforated panels contributes more to the sound absorption performance at low frequencies, and SBH produces a sound absorption advantage at high frequencies.The theoretical calculation and simulation result match and prove the correctness of the sound streaming effect. Sound absorption tests by acoustic impedance tube confirm that the proposed structure can maintain a sound absorption coefficient of over 0.5 in the range of 0.05–6.0 kHz. The combination of micro-perforated panels and SBH structure is widely applicable to muffler design and has good application prospects.

Reduction of Train-Induced Vibrations—Calculations of Different Railway Lines and Mitigation Measures in the Transmission Path

The reduction of train-induced ground vibrations by different railway lines and by mitigation measures in the propagation path is analysed in a unified approach by two-dimensional finite element calculations where the reduction is expressed as the amplitude ratio between a specific and the reference situation (the surface track without a mitigation measure). In general, there is no reduction at low frequencies, and the reduction becomes stronger with increasing frequency. A maximum reduction ratio of 0.1 at high frequencies is established with an open trench. Reduction ratios between 0.7 and 0.2 have been found for the other situations, filled trenches, walls, plates, and blocks, as well as for railway lines on embankment, in cuts and in a tunnel. Bridges can produce amplifications due to their resonance frequencies, but also strong reductions due to the massive bridge piers. The influence of some parameters has been analysed, the length of the bridge span, the inclination of the embankment and the cut, and the stiffness of the soil and of the tunnel structure. The dynamic track stiffnesses of a surface, bridge and tunnel track have been calculated by the 3D finite-element boundary-element method for comparison with corresponding measurements.

Experimental study, numerical simulation and GRNN model for predicting the flexural loading capacity of corroded reinforced concrete beams

The present article is an effort to quantify the flexural strength of corroded reinforced concrete (RC) beams. Eight RC beams with dimensions of 150 × 200 × 2200 mm were tested in four-point bending, including six beams corroded in a chloride environment with average corrosion of longitudinal reinforcement in the range of 5% to 15%. The remaining two beams were used as control beams. The ultimate strength, failure mode and particularly the relationship between crack width and corrosion level are analyzed and discussed. A two-dimensional non-linear finite element model has been presented to simulate the steel bar corrosion considering the deterioration of concrete strength and steel-concrete bond stress. The generalised regression neural network (GRNN)-based model for the ultimate flexural strength of corroded RC beams has been established based on 123 experimental data collected from previous studies. The experimental results were used to separately validate the non-linear finite element model and novel GRNN model. Experimental results indicate that if the overall corrosion rate is used, the corrosion crack width can be a function of the percentage of section loss. The GRNN model provides superior predictive results compared to previous empirical methods with the highest correlation coefficient (r), and the smallest normalised root mean square error.

Seismic performance of U-shaped spillway retaining wall from shake table tests

A series of large-scale shake table tests were performed to evaluate the seismic behavior of a U-shaped spillway retaining wall. Three test model configurations were employed using different backfill conditions in terms of in-place soil density. Two earthquake records were employed as input motion and scaled in terms of time duration and acceleration amplitude to assess various aspects of seismic response. The test results showed that dynamic wall deflection and wall bending moment generally increased with Peak Ground Acceleration (PGA) amplitude. At peak wall deflection, the seismic earth pressure increment coefficient (ΔKAE) was back-calculated from the measured bending moment along each wall. In addition, the location of ΔKAE along the wall height and the resulting base moment were evaluated and discussed. The results suggested that seismic demands were generally lower up to a PGA of about 0.8 g, compared to the classic Seed and Whitman recommendation for seismic lateral earth pressure and seismic bending moment of retaining walls. Beyond PGA of 0.8 g, test results were in general agreement with the Seed and Whitman solution. Finally, two-dimensional finite element analyses were performed, and the computational results showed overall reasonable agreement with the experimental data.

Seismic response and instability analysis of the liquefiable soil-piles-superstructure interaction system

Based on the shaking table test of the liquefiable soil-piles-superstructure system, the liquefaction process and seismic failure mode of the liquefiable site with an overlying non-liquefiable soil layer, as well as the instability or damage mechanism of a low pile cap-pile group-superstructure system are analyzed by a two-dimensional finite element model. The model considers the post-liquefaction shear deformation of sand, the interface models for the pile and cap with the liquefiable and non-liquefiable soil, and the interface model between the liquefiable and non-liquefiable soil to account for the discontinuity of interface deformation. The typical calculation results, including the excess pore pressures, accelerations, displacements of soil, and bending moments of the piles, are compared with the experimental results to verify the developed models and reveal the effects of site liquefaction and the soil-structure dynamic interaction on the seismic responses and instability mechanisms of the piles-superstructure system.

Free Shrinkage Strains of Box Girders with Concrete Overlays

The aging of reinforced concrete structures is one of the biggest concerns in civil engineering today since billions of dollars are spent annually on deck repairs and replacements. This study focuses on the rehabilitation of reinforced concrete box girders used in bridge construction. Bridge rehabilitation with a new concrete overlay possesses many challenges that involve cracking and debonding of the overlay caused by the restraining effect of the substrate. This effect leads to the development of tension stresses in the overlay, compression stresses in the substrate, and shear stresses at the interface. In order to mitigate this type of cracking and to ensure a desirable monolithic structural behavior of the rehabilitated bridge, a long-term assessment of the free shrinkage strains acting in the overlay is necessary. This study conducts a two-dimension finite element analysis of a reinforced concrete box girder bridge to evaluate humidity and free shrinkage strain profiles at different times. The humidity gradient between the overlay and the substrate generates differential volume changes between substrate and overlay. The substrate deformations are negligible, while the overlay is subjected to high shrinkage; 78% of the ultimate shrinkage strain is reached after 3 years, indicating a high susceptibility to cracking.

Mesoscale modelling of concrete damage in FRP-concrete debonding failure

It is challenging to simulate fibre-reinforced polymer (FRP)-concrete debonding failure in detail because concrete damage usually occurs with a thin layer of mortar debonding attached to the FRP. This study applied a single-lap shear test with a digital image correlation technique to externally bonded FRP–strengthened concrete elements. An improved random walk algorithm method generated a realistic mesostructure of concrete. The two-dimensional mesoscale finite element model for FRP–strengthened concrete was established. The cohesive interface elements were inserted along all mortar–aggregate interfaces. Concrete damaged plasticity and cohesive zone model were applied to simulate the nonlinear properties of mortar and mortar–aggerate interface, respectively. The experimental and numerical load–displacement curves, strain/stress distribution, and local bond–slip curves were obtained and compared. A numerical parametric study investigated the effects of the aggregate, mortar, and adhesive on debonding failure. The main conclusions are: (1) the initiation and propagation of mortar damage and mortar–aggregate interface cracking in the FRP debonding process were directly conducted by the mesoscale model; (2) the numerical curves showed considerable oscillation, possibly due to the stress concentration near the aggregate boundary when the crack transmitted the aggregate, and the stiffness decreased after cracking was initiated at the mortar–aggregate interface; (3) concrete damage may extend to a depth of 25 mm, indicating that the concrete damage is greater than a thin layer of mortar debonding observed in the test; (4) applying polygonal aggregates, increasing aggregate size and surface mortar thickness, and reducing the adhesive layer thickness improves bond performance.

Analysis and Experimental Verification of the Sealing Performance of PEM Fuel Cell Based on Fractal Theory

Aiming to accurately predict the leakage rate of the sealing interface, this work proposes a two-dimensional finite element model of a proton exchange membrane fuel cell, which includes the microscopic surface morphology and the asperity contact process of the components. First of all, we constructed the surface morphology of the seal by the two-dimensional W-M (Weierstrass–Mandelbrot) fractal function and explored the influence of fractal dimension (D) and scale parameter (G) on the surface profile. Furthermore, the finite element method and Poiseuille fluid theory were adopted to obtain the deformation variables of the asperity under different clamping pressures and leakage rates. Moreover, we quantitatively analyzed the impact of surface roughness on the clamping pressure and leakage rate. It was found that both the surface amplitude and surface roughness are positively correlated with G and negatively correlated with D. Surface morphology is proportional to D but has no relationship with G. Additionally, the deformation asperity decreases exponentially with growing clamping pressure, and the leakage rate is consistent with the experimental values at a clamping pressure of 0.54 MPa. With the same leakage rate, when the seal surface roughness value is less than 1 μm, a doubled roughness value leads to an increase of 31% in the clamping pressure. In contrast, when the surface roughness of the seal is greater than 1 μm, a doubled roughness value induces an increase of 50% in the corresponding clamping pressure.

Transient heat transfer and temperatures in closed compressor rotors

During transient gas turbine operating cycles, the radial clearance between the rotating blades and the stationary casing is governed by the thermal stresses and radial growth of the compressor discs. Robust and accurate prediction of the temperature and heat transfer inside compressor cavities is critical to controlling these clearances and the design of reliable and efficient engines. This paper presents a fully predictive model to determine disc temperatures and shroud heat fluxes for a closed disc cavity (rotating cylindrical annulus), simulating an engine compressor. This is the first published reduced-order modelling of compressor cavities during engine transients in literature and the most detailed publication of transient experimental data in this context. Due to the conjugate nature of the heat transfer, a conduction model of the compressor disc and a model of the flow and heat transfer in the cavity between the co-rotating discs are included. The conduction was computed using a two-dimensional finite element solver, and the disc heat transfer was calculated assuming conductive laminar Ekman layers on the disc surfaces. Correlations for free convection on flat plates are used to model the heat transfer on the inner and outer radii of the rotating cavity. The transient core temperatures were calculated in a quasi-steady manner, with the heat transfer at every time step predicted assuming zero net heat flow. The model was validated using new transient data collected from the Compressor Cavity Rig at the University of Bath. The model shows consistent agreement with all experimental cases, providing insight into the conjugate relationship between the disc and shroud heat transfer, revealing that disc heat transfer is sustained long after there is no convective heat transfer from the shroud. This approach has direct application to practical thermo-mechanical codes, contributing to the design of next-generation, net-zero aerospace architectures.

Local wavenumber estimation for small damages based on artificial neural network

The local wavenumber feature of ultrasonic guided waves can be used to detect wall-thinning because the thickness at each spatial location determines the wavenumber at that point. However, this paper shows that the accuracy of the local wavenumber estimation results is closely related to the size of the damage. When the size is small to a certain extent, the estimated local wavenumber can be significantly lower than the true value. In order to obtain the local wavenumber accurately, an artificial neural network (ANN) method is introduced in this paper to relate the estimated local wavenumber to the true wavenumber. A two-dimensional finite element guided wave model is developed to generate the rich inputs (estimated local wavenumber), while the outputs (true local wavenumber) are obtained by a semi-analytical finite element (SAFE) method. The ANN method is experimentally validated with a laser-generated ultrasonic system, and the error between the predicted local wavenumber and the true wavenumber is within 5% for a wide range of damage sizes, thus ensuring the accuracy of assessing wall-thinning.

A macro-modeling approach for non-linear analysis of multi-story perforated masonry walls with grout and reinforcement concentrated at their pier ends

A current topic of interest in structural engineering is the assessment of the non-linear response of masonry buildings subject to seismic loading. Researchers have proposed several macro-modeling approaches to date, which have been mainly focused on unreinforced masonry. However, there has been little progress on reinforced masonry, particularly partially grouted masonry (PGM), despite its wide use, especially in North America. This is because the numerical simulation of the inelastic behavior of PGM walls is a complex issue, given the interaction between the grouted/reinforced masonry and the ungrouted portions of the system. These two parts have differences in stiffness and the partial grouting also causes non-uniformity of the cross-section. In the study described herein, a relatively simple and practical macro-modeling approach is evaluated for non-linear analysis of PGM walls with reinforcement concentrated at the side ends of piers. For this, previous results of experimental tests and robust two-dimensional finite element models were used as references. Aspects related to the horizontal force‒displacement response, lateral displacement profiles along the height, and damage mechanisms were assessed. A sensitivity analysis of the numerical model was also performed. The results indicate that the macro-model could simulate the global behavior of the experimental walls with low computational cost and good accuracy.

Modeling continuous laser ablation of glass fiber-reinforced epoxy resin plate with two-dimensional finite element

Modeling continuous laser ablation of glass fiber-reinforced epoxy resin plate with two-dimensional finite element