Equivalent Finite Element Model Research Articles

Efficient homogenization of honeycomb sandwich panels using orthotropic core simplification and Finite Element-based method: A comparative study

Composite materials, particularly honeycomb composites, are widely utilized in various industries, including aerospace, due to their high energy absorption against the impact and exceptional strength-to-weight ratio. This study aims to leverage the plastic and elastic properties of these materials to develop a simplified numerical model that incorporates orthotropic properties for core modeling. By doing so, the need for detailed honeycomb structure modeling is eliminated, resulting in reduced computational costs and time. A comprehensive three-dimensional finite element model, accounting for structural intricacies, is presented based on experimental data from a reputable source (isotropic model) and its equivalent finite element model (orthotropic model). The model is validated by the experimental results, demonstrating good agreement. The study also investigates parameters such as energy absorption, the internal energy of the core and faces, maximum displacement, and maximum contact force under low-velocity impact scenarios with spherical and cylindrical projectiles. These findings highlight the effectiveness of the orthotropic model, particularly in showcasing greater energy absorption in the core of the sandwich panel when subjected to a cylindrical impactor.

Approximate global mode method for flutter analysis of folding wings

The aircraft with folding wings benefits from the ability to transform its folding wings to adapt to various flight missions but suffers from the change of the wings’ aeroelastic characteristics as a result. To clarify the change, it is necessary to study the dynamical modeling of the folding wing and also its aeroelastic response. This paper proposes a novel approximate global mode method (AGMM) for dealing with complex boundary conditions and models a folding wing consisting of separate rectangular plates for nonlinear flutter analysis. A high-precision low-dimensional dynamical model of the folding wing is developed, which is first validated by comparing the modal results obtained from the AGMM model with those obtained from an equivalent finite element model and is also experimentally validated by a comparison of forced vibration responses. On this basis, an AGMM model of the folding wing in supersonic aerodynamic loads based on the piston theory is further developed. The critical flutter velocity at different folding angles and the aeroelastic response are comprehensively studied by simulations based on the model. The result shows that the first 7th-order modes are sufficient for obtaining a converged critical flutter velocity, which varies with geometric parameters and potentially increases by 714 %. In addition, the low-order torsional modes of the wing contribute more to the vibration than the other modes during flutter. This work provides a new way of developing advanced dynamical modeling methods of folding and combinational structures for their dynamics design, optimization, and system control.

Two-Step Identification Method and Experimental Verification of Weld Damage at Joints in Spatial Grid Structures

Welded joints in grid structures are susceptible to damage and destruction when exposed to random excitation. The complexity of the grid structure poses challenges for realizing the damage recognition of welded joints. In this study, a two-step method is proposed specifically for damage identification of welded joints in grid structures, combining wavelet analysis and fuzzy pattern recognition to accurately identify the location and extent of damage in welded joints. Firstly, the structure is divided based on the analysis of the influence range of joint damage. Key joints are selected within the sub-regions where sensors are installed, and the acceleration response of these key joints is measured. Wavelet analysis is then applied to identify the sub-regions where weld damage occurs. Secondly, an equivalent finite element model is established for joints with varying degrees of damage. The damage index, calculated as the ratio of the absolute value of the difference in the first-order element strain mode of the members, increases with the degree of damage during joint weld damage. By monitoring the changes in the damage index of sensitive members, which exhibit significant changes with varying weld damage degrees, a damage pattern database is constructed for each sub-region. The membership degree between joint damage and the patterns in the pattern database is then calculated to determine the location and degree of weld damage. To validate the effectiveness of the proposed method, an experiment was conducted using a grid structure model with replaceable members. Highly sensitive FBG sensors were designed to measure the acceleration response of the joints, resulting in accurate identification of damaged sub-regions solely through the measurement of key joint acceleration responses. Furthermore, within the damaged sub-regions, the fuzzy pattern recognition method precisely determined the location and degree of weld damage in the joints. The experimental results demonstrate that the proposed method effectively reduces the complexity of the structure by dividing the grid structure into sub-regions, and enables the two-step identification method to achieve successful damage identification for the joints in the grid structure with high efficiency and accuracy.

Ground Vibration Test Based Flutter Prediction for a Combat Aircraft

This paper compares the flutter characteristics of a combat aircraft predicted using experimental modal parameters from ground vibration tests with the results obtained by flight flutter tests. An equivalent finite element model representing the test points in ground vibration tests has been developed and further refined to obtain a finite element model with fine mesh encompassing the entire lifting surface areas. Infinite plate interpolation scheme has been used to extrapolate the eigenvectors for the refined model. A Direct Matrix Abstraction Program (DMAP) written in NASTRAN replaces the generated mass normalized eigenvalues and vectors of the refined model from a dynamic analysis in NASTRAN, with the experimentally obtained eigenvalues and extrapolated eigenvectors. Flutter analysis has been carried out with the replaced experimental modal parameters in subsonic, transonic and supersonic regimes using flutter modules in NASTRAN and ZAERO software. The results obtained using this procedure have been compared with the flight flutter test results. The dispersion in the damping and frequency results obtained from computations and the flight flutter tests were within acceptable limits showing a good correlation.

Mechanical properties of rigid and flexible polyurethane foam in-situ foamed Nomex honeycomb

To enhance the mechanical properties of Nomex honeycomb, the honeycomb was foamed in-situ using rigid polyurethane (PU) foam and flexible polyurethane foam (NHRPU, NHFPU, collectively NHPU). Mechanical properties were studied based on tests, theoretical and finite element (FE) methods, respectively. The results showed that NHRPU and NHFPU improve the energy absorption by 85.25% and 47.27% compared to the sum of PU and honeycomb alone. The specific energy absorption (SEA) of NHRPU is improved by 21.76%, while the SEA of NHFPU decreases, NHRPU significantly improves in terms of the honeycomb energy absorption performance, while NHFPU enhances the resilience of the honeycomb. The mesoscale FE model and equivalent FE model were constructed to achieve better prediction of NHPU. 75.6% energy absorption and 19.8% SEA can be improved by NHPU as a core-filled thin-walled tube compared with empty tube, and the passive safety protection capability is significantly improved by applying NHPU-filled structures in railway vehicles.

Research on Electromagnetic Vibration Characteristics of a Permanent Magnet Synchronous Motor Based on Multi-Physical Field Coupling

Background and Purpose: The stator vibration characteristics are comprehensively mastered by considering the influence of winding and the housing structure on the stator modes. This effect is neglected in the research field of electromagnetic vibration of permanent magnet synchronous motors (PMSMs). Methods: The radial air-gap flux density equations and PMSM’s electromagnetic force density are derived, and then the harmonic characteristics of electromagnetic force density are studied. An equivalent finite element model of the stator is proposed that investigates the impacts of the winding and stator housing rules on the stator modal frequency. Finally, the harmonic response and acoustic analyses of electromagnetic vibration are carried out based on multi-physics field coupling. Results: The equivalent radiated power distribution laws and acoustic field of motor electromagnetic vibration under transient operating conditions are obtained. The theoretical analysis results are consistent with the experimental results. Conclusion: The obtained results show that the spatial order of the radial electromagnetic force is not equal to the order of the radial mode of the motor stator. The reason for this is that structural resonance is induced when the frequency components of the spatial radial electromagnetic force are coupled with the intrinsic frequency of the stator.

Seismic performance of RC frame structure across the earth fissure based on pushover analysis

This study aims to investigate the seismic performance and failure mechanism of reinforced concrete frame structures across the earth fissure. A five-story reinforced concrete frame structure across the earth fissure was tested by shaking table and the test equivalent finite element model was established by simulation software, the seismic performance of the reinforced concrete frame structure across the earth fissure was carried out and analyzed by these two methods. The results showed that the earth fissure has an amplification effect on the structure displacement response, the damage indexes and internal forces of the structure across the earth fissure were always larger than the structure on the ordinary site. The maximum damage index deviation increases from 6.1% to 11.4% under 0.2 g and 0.4 g seismic waves, and the maximum axial and shear forces deviation of column increases from 29% to 50% and 11.7% to 15.2% during 0.2 g to 0.6 g Cape Mendocino waves, respectively. With the increase of seismic intensity, the deviation of damage indexes and internal forces increased. The damage to the structure of the hanging wall were earlier and more seriously, and the first floor was the most vulnerable floor. The research in this paper has practical significance for seismic performance evaluation and provides reference for reinforced concrete frame structure across the earth fissure seismic design.

Finite Element Model for Vibration Serviceability Evaluation of a Suspended Floor with and without Tuned Mass Dampers

This study aims to provide an accurate finite element (FE) modeling method for structural vibration serviceability evaluation of the suspended floor under human-induced excitation. The fundamental dynamic characteristics and human-induced vibration responses of a typical suspended floor were first measured via a series of field tests. Subsequently, the overall and local equivalent FE models of the suspended floor were respectively established, and their applicability was then verified by comparing the predicted dynamic characteristics and responses of the suspended floor with the corresponding field test results. Finally, passive tuned mass dampers (TMDs) were designed for vibration control of the suspended floor using the local equivalent FE model, and the applicability of the local FE model in assessing the vibration serviceability of the suspended floor with TMDs was further confirmed via pedestrian-induced vibration tests. Results demonstrate that the simplified local equivalent FE model proposed in this study can well replace the complicated overall FE model to evaluate the vibration serviceability of the suspended floor with and without TMDs.

Study on the Cell Magnification Equivalent Method in Out-of-Plane Compression Simulations of Aluminum Honeycomb

The large scale and long calculation times are unavoidable problems in modeling honeycomb structures with large sizes and dense cells. The cell magnification equivalent is the main method to solve those problems. This study finds that honeycomb structures with the same thickness-to-length ratios have the same mechanical properties and energy absorption characteristics. The improved equivalent finite element models of honeycomb structures with the same thickness-to-length ratios were established and validated by experiments. Based on the validated finite element model of the equivalent honeycomb structures, the out-of-plane compression behaviors of honeycomb structures were analyzed by LS-DYNA software. The results show that the performance of honeycomb structures is not equivalent before and after cell magnification. Thus, the cell magnification results were further subjected to CORA (correlation analysis) to determine the magnification time and prove the accuracy of the cell magnification time through drop-weight impact tests. In addition, a first-order decay exponential function (ExpDec1) for predicting cell magnification time was obtained by analyzing the relationship between the cell wall length and the cell magnification time.

Extending the Incidence Angle of Shear Vertical Wave Electromagnetic Acoustic Transducer with Horizontal Magnetization.

Angled shear vertical (SV) waves have been successfully employed in the non-destructive testing of welds, pipes, and railways. Non-contact meander-line coil electromagnetic acoustic transducers (EMAT) have many benefits in generating angled SV waves. The most important benefit is that the incidence angle of an SV wave can be controlled by the excitation frequency. However, the incidence angle of a traditional SV-wave EMAT is reported to be under 45 degrees in many cases. In this work, such cases are tested, and the problems of the received signal at large incidence angles are found to be due to wave interference and small signal amplitudes. An equivalent finite element (FE) model is established to analyze the problem, and the main reason is found to be the head wave. An alternative configuration of angled SV-wave EMAT with horizontal magnetization is proposed to reduce the influence of the head wave. Finally, the results from simulations and experiments show that the proposed EMAT has a larger signal amplitude and significantly reduced interference in large-incidence angle scenarios. Moreover, an incidence angle of an SV wave of up to 60 degrees can be achieved, which will help improve the performance and capability of nondestructive testing.

A universal elastoplastic equivalent method for sandwich panels and its application in plastic forming

Based on Hill’48 yield criterion, a simple and universal elastoplastic equivalent method for sandwich panels was proposed. In this method, the core of sandwich panel was equivalent to an orthotropic homogeneous panel, and the elastoplastic parameters of equivalent sandwich model were quickly obtained by uniaxial tensile and pure shear numerical simulations of the mesoscopic sandwich model utilizing user-defined material subroutine (UMAT). The equivalent elastoplastic parameters of brazed aluminum honeycomb panels (BAHPs) with core heights of 9 mm (BAHP-H9) and 12 mm (BAHP-H12) were obtained, which were proved to be effective by comparison with analytical solutions and analysis of numerical simulation results. Then, the effectiveness of elastoplastic equivalent method was further demonstrated by comparing the numerical simulation results of multi-point forming (MPF) for the mesoscopic and equivalent finite element (FE) model of BAHPs. Finally, MPF experiments of cylindrical BAHPs under different target forming radii were carried out. The results showed that the elastoplastic equivalent method could be effectively applied to the plastic forming of sandwich panels.

Parallel Evaluation of Chebyshev Approximations: Applications in Astrodynamics

Approximations based on Chebyshev polynomials have several astrodynamic applications. The performance of these approximations can be improved by parallel implementations exploiting parallel architectures, such as OpenMP and CUDA. In this paper, we introduce the parallel implementation to two astrodynamic applications. The first is the gravitational finite element model (FEM): a piecewise Chebyshev approximation that replaces high degree and order gravitational spherical harmonic models (SHMs). Thus, much lower degree, locally valid functions can efficiently model and compute local gravity perturbations in parallel structure for efficient performance. For this model, the total gravity acceleration is split into a reference and disturbance term. The reference includes two-body plus J_2, which are relatively cheap to compute. The FEM approximates the higher-order gravity terms. It is developed from a 2D mesh grid covering a sphere of a specified radius, and a family of spherical shells is sampled using a cosine distribution in the radial direction. To reduce the required memory when seeking a specific accuracy, an adaptive version of the gravitational FEM is introduced. In addition, a parallel implementation of the FEM using OpenMP is preseneted. We show the runtime comparison for the 200 degree × 200 order EGM2008 SHM and the serial and parallel equivalent FEM algorithms. The other application is the Chebyshev-Picard method (CPM): a numerical integrator that solves an ordinary differential equation by approximating the integrand using a Chebyshev approximant and iterates over the trajectory via Picard iteration. A parallel CUDA implementation of the CPM method in conjunction with the EGM2008 SHM and the FEM is introduced. We present numerical examples for propagating four Earth-orbiting satellites considering both the 200times 200 EGM2008 SHM and the equivalent FEM representation to test the algorithm’s performance via parallel and serial computation (i.e., a single CPU thread).

A subject-specific FEM to predict deep tissue mechanical stresses when supine: Development of efficient contact interfaces using Shared Topology

Prior studies have demonstrated Finite Element (FE) analysis is a useful tool when analysing the complex interplay of tissue and body loads which act through the human pelvis in a subject lying supine. The computational accuracy and efficiency of FE models that contain complex non-linear geometric interfaces between different anatomical and tissue regions can be compromised by superfluous node interactions and contact penetrations. This study proposes a method for the development of efficient contact definitions using shared topology. The Shared Topology Finite Element Model (FEM) resulted in a 37% reduction in solution time compared to an equivalent FEM defined with Bonded contact. At all tissue interfaces, contact penetration occurred in the Bonded FEM, with subsequent under-prediction of peak compressive strains and stresses by 1–7% compared to the Shared Topology FEM. Simulating supine lying of a 19-year-old male, the Shared Topology FEM predicted peak compressive stress in the muscle interfacing the sacrum of 29.4 kPa, and peak compressive strain of 50%. The proposed methodology can be applied for any medical imaging derived FEM where there are multiple congruent 3D geometries with negligible sliding across interfaces.

Dynamic Behavior of a Suspended Steel Space Frame-Glass Composite Floor

This study investigates the dynamic performance of a large-span suspended steel space frame-glass composite floor (SSSF-GCF). Both the ambient vibration and the human-induced vibration of the floor were experimentally measured to identify vertical dynamic characteristics and evaluate vibration serviceability of the floor. Although vertical dynamic characteristics of the floor based on the global simplified finite element (FE) model of the structure agree well with those identified via experimental modal analysis, the global simplified FE model significantly underestimates vertical vibration amplitudes of the floor due to the coupled effect between two layers. Accordingly, an equivalent local FE model of the floor system was proposed and updated via adjusting the vertical stiffness of the interstory hanging pillars. It is shown that the equivalent local FE model can well predict both the dynamic characteristics and human-induced vibration response of the floor. Finally, the effect of the damping ratio on the acceleration response of the floor was numerically demonstrated with the verified local FE model.

Design by analysis of a multi-layer fabric reinforcement of jet engine containment for fragments mitigation

In current investigation, the preliminary design by analysis of a multilayer fabric reinforcement of a jet engine containment is studied. In particular, the development of a continuum equivalent finite element model for the simulation of fabric material response to high-velocity impact is presented. The main goal is to minimize the computational cost keeping the level of accuracy close to that of mesoscale modelling. The proposed methodology will aid in the design of large protection systems made of fabric materials. For the target attainment, representative volume element (RVE) models of plain-woven Kevlar 29 fabric are created and virtually tested to tensile and shear loading for the calculation of equivalent macroscopic mechanical properties. Afterwards, a continuum equivalent model at coupon level is built for the validation of proposed method. The numerical results in terms of absorption energy and damage extension were compared with those of mesoscale model and of experimental ones. In conclusion, the continuum equivalent FE model reduces the computational cost by over 400 times with less than 6% accuracy loss. Finally, using the validated modeling approach, the simulation of a conventional metallic engine containment unit and a fabric-reinforced one to fan blade-out loading is carried-out.

A Novel, Improved Equivalent Circuit Model for Double-Sided Linear Induction Motor

A novel, improved equivalent circuit model of double-sided linear induction motors (DLIMs) is proposed, which takes the skin effect and the nonzero leakage reactance of the secondary, longitudinal, and transverse end effects into consideration. Firstly, the traditional equivalent circuit with longitudinal and transverse end effects are briefly reviewed. Additionally, the correction coefficients for longitudinal and transverse end effects derived by one-dimensional analysis models are given. Secondly, correction factors for skin effect, which reflects the inhomogeneous air gap magnetic field vertically, and the secondary leakage reactance are derived by the quasi-two-dimensional analysis model. Then, the proposed equivalent circuit is presented, and the excitation reactance and secondary resistance are modified by the correction coefficients derived from the three analytical models. Finally, a three-dimensional (3D) finite element model is used to verify the proposed equivalent circuit model under varying air gap width and frequency, and the results are also compared with that of the traditional equivalent circuit models. The calculated thrust characteristics by the proposed equivalent circuit and 3D finite element model are experimentally validated under a constant voltage–frequency drive.

Critical coupling span number in high-speed railway simply supported beam bridge

In long-distance railways, some particular spans of high-speed railway simply supported beam bridges (HSRSBs) are commonly selected as the target structure. The target structure is the part of interest for the study and intended to be analyzed. Due to longitudinal constraints of the track system, the target structure is tightly coupled with other spans within certain range, and is affected by the coupled spans under longitudinal earthquake condition. A massive amount of time-consuming computation is required to determine the coupling span number using current finite element models. In an effort to overcome this challenge, an equivalent method for the longitudinal constraints of the track system is proposed, which greatly reduces the complexity of finite element model while retaining calculation precision. The coupling span number was determined by seismic analyses of a large number of cases using equivalent finite element models. Moreover, the influence of pier height and bottom pier stiffness on coupling span number was studied. Based on the relationship between the equivalent boundary sensitivity critical point and coupling span number, a method to quickly obtain coupling span number of the target structure in arbitrary HSRSB was constructed.

WraptMor: Confirmation of an Approach to Estimate Ligament Fiber Length and Reactions With Knee-Specific Morphology.

Knee ligament length can be used to infer ligament recruitment during functional activities and subject-specific morphology affects the interplay between ligament recruitment and joint motion. This study presents an approach that estimated ligament fiber insertion-to-insertion lengths with wrapping around subject-specific osseous morphology (WraptMor). This represents an advancement over previous work that utilized surrogate geometry to approximate ligament interaction with bone surfaces. Additionally, the reactions each ligament imparted onto bones were calculated by assigning a force-length relationship (kinetic WraptMor model), which assumed that the insertion-to-insertion lengths were independent of the assigned properties. Confirmation of the approach included comparing WraptMor predicted insertion-to-insertion length and reactions with an equivalent displacement-controlled explicit finite element model. Both models evaluated 10 ligament bundles at 16 different joint positions, which were repeated for five different ligament prestrain values for a total of 80 simulations per bundle. The WraptMor and kinetic WraptMor models yielded length and reaction predictions that were similar to the equivalent finite element model. With a few exceptions, predicted ligament lengths and reactions agreed to within 0.1 mm and 2.0 N, respectively, across all tested joint positions and prestrain values. The primary source of discrepancy between the models appeared to be caused by artifacts in the finite element model. The result is a relatively efficient approach to estimate ligament lengths and reactions that include wrapping around knee-specific bone surfaces.

Finite element model updating of a satellite honeycomb sandwich plate in structural dynamics

The honeycomb sandwich structures have a crucial participation in aerospace industry, especially in the design of satellite structures due to their exceptional mechanical properties. The equivalent finite element modeling of such structures is initially presented through the implementation of modal analysis via the three-layered sandwich theory. Subsequently, the computational results are validated by carrying out an experimental modal testing. In addition, sensitivity analysis based upon design of experiments and parameters correlation, is executed for the sake of selecting the most appropriate design parameters for the optimization problem. Finally, finite element model updating of a honeycomb sandwich plate is thoroughly introduced using three optimization algorithms including genetic algorithms, adaptive-multiple optimization, and response surface method. A good agreement between the previously-mentioned optimization algorithms is obtained. Meanwhile, response surface method and its related design of experiments tool succeed in avoiding such time-consuming process and reduce the involved computational expense with an acceptable accuracy.

Experimental modal testing of a honeycomb sandwich plate

Honeycomb structures have been widely used in several applications and industries in the past decades. Such structures have a significant role in aerospace engineering especially in building up the satellite structures. Honeycomb structures provide key benefits represented in high specific strength, high specific stiffness, and superior dimensional stability. Detailed finite element modelling of such structures is a great challenge as it involves high computational expense. Thus, equivalent modelling is mandatory. The detailed and equivalent finite element models of a honeycomb plate are introduced intensively throughout analyzing its dynamic behaviour using the modal analysis module in ANSYS workbench software. The equivalent modelling is carried out via the three-layered sandwich theory and leads to the calculation of the first four natural frequencies and the related mode shapes. An experimental modal testing of the honeycomb sandwich plate is implemented for the sake of validating the computational results. A good agreement is obtained when comparing both experimental and computational results with mean error not exceeding 5%. Finally, a parametric study is performed to relate the modal analysis results with different boundary conditions cases. The results show that the model can be a reliable basis for satellite honeycomb sandwich structures design.