Large Finite Element Models Research Articles

ANALYSIS OF REINFORCED BOLTED JOINTS IN HIGH-CAPACITY SILOS

ABSTRACT: This paper presents an analysis of the mechanical performance of bolted joints used in silos for storing bulk materials. In particular, we investigated the effectiveness of three types of bolted joints: one without reinforcement, one with angular reinforcement, and one with squared reinforcement. Our analysis involved the use of the finite element analysis sub-modeling technique, which allowed us to construct a large finite element model with shell elements and a sub-model with solid elements. By analyzing the stress state of each joint, we were able to determine the contact state and contact pressure of the bolted joint. Our findings showed that bolted joints reinforced with triangular and square plates were effective in maintaining contact pressure, even under high-pressure conditions. This study provides valuable insights into the design of bolted joints used in silos, which can help ensure their reliable and safe operation. Keywords: bolted joints, high-capacity silo, FEA sub-modeling.

Optimization of spudcan penetration and influence on caisson foundation

The penetration of spudcans have adverse effects on pre-existing bucket foundations during the blade lifting process of offshore wind power systems, which brings uncertainties for the design and construction of bucket foundations. This study employs the Euler-Lagrange method to explore the influence of spudcan penetration on the adjacent caissons in homogeneous clay within a large deformation finite element (LDFE) model. The LDFE model is validated against centrifuge tests data, with good agreement obtained. Parametric study is then conducted to explore, (i) the influence of the angle between vessel and caissons on the movements of the caisson, and (ii) potential influence factors on the movements of the caisson with an optimal angle between the vessel and caissons, including soil properties, dimensions of caisson and spudcan, and the distance between spudcan and caissons. The results show that 60° is the optimal angle between the vessel and caissons that results in the smallest movement of the caisson, and the caisson foundation inclination angle ranges between 0° and 0.025°, when the pile shoe penetration progress ranges between 0.1 and 1.0. An empirical formula is proposed to predict the rotational angle of caisson with the optimal angle. The study establishes a quantitative approach to assess the influence of the spudcan penetration on existing three-caisson jacket foundations, which provides guidance for the design and construction of offshore wind turbine bucket foundations.

A computationally efficient procedure for calibrating model parameters of multiple specimens

Model calibration can be a very intensive and time-consuming task, especially when dealing with non-linear and large finite element models. The computational effort further increases when multiple specimens have to be calibrated. This is typical of laboratory experiments where several specimens made with the same and/or different constituent materials are tested. This paper proposes a calibration procedure aimed at reducing the computational effort of multiple specimen model calibration. The calibration procedure combines the robustness of a surrogate-assisted evolutionary algorithm with the exploitation of a database collecting the results of the previously calibrated specimens. In this research, the proposed procedure is applied to the calibration of the parameters of a cohesive crack model for fiber-reinforced concrete specimens. The benefit of the proposed procedure is shown by comparing the results with those obtained from the same calibration method but without accounting for the previous results in the calibration of a new specimen.

A two-stage Bayesian model updating framework based on an iterative model reduction technique using modal responses

A two-stage Bayesian model updating framework based on an affine-invariance sampling in Transitional Markov Chain Monte Carlo (TMCMC) algorithm is proposed. In the first stage, unknown modal coordinates are identified with an improved iterative model reduction technique. Subsequently, a modified TMCMC algorithm is proposed where obtaining the statistical estimators in the usual TMCMC algorithm is not necessary. In detail, an affine-invariance sampling approach is proposed to estimate a multi-dimensional scaling (MDS) factor in the affine-transformed space that accounts for the frequencies and mode shapes which are of different natures and dimensions at the levels of likelihood, prior and posterior distributions. The TMCMC sampling adaptively utilizes the plausibility value from the proposed MDS-based tuning algorithm to improve its transition levels. The proposed algorithm in the affine-invariance sampling space accounting for the observables of different dimensions is expected to facilitate the estimation of the posterior distribution of model parameters. The effectiveness of the proposed algorithm is demonstrated by considering a simply-supported steel beam, a ten-storied reinforced concrete building model and an eight-degree-of-freedom spring–mass model for which experimental data is available. The second example demonstrates the applicability of the approach for updating large finite element models involving substructuring.

Deformation and Strength Characteristics of Marine Soft Soil Treated by Prefabricated Vertical Drain-Assisted Staged Riprap under Seawall Construction

Prefabricated vertical drains (PVDs) with staged riprap preloading have been widely used in soft soil ground improvement and embankment construction. However, ground treatment effectiveness evaluation is still a difficult problem due to multiple factors. Considering this, in situ monitoring and numerical simulation were conducted to study the deformation and strength characteristics of marine soft soil ground treated by PVD-assisted staged riprap under the Lingni Seawall construction in China. Monitoring and analysis of results showed that use of PVD-assisted staged riprap resulted in a good improvement effect. In particular, in the PVD-treated zone within 10 m in depth, corresponding to a half-length of the PVD, the average radial degree of consolidation reached up to 75–100%, and the soil strength increased significantly by 200–700%. Moreover, numerical simulation showed that the linear 1-dimensional drain element of PVD closely met the engineering accuracy requirements with good consistency with the monitoring data. Compared with a totally solid element model, the numbers of elements and nodes were reduced and the calculating efficiency and model accuracy were increased by using a PVD linear element, which provides a basis for building large complex finite element models.

Bayesian structural parameter identification from ambient vibration in cultural heritage buildings: The case of the San Jerónimo monastery in Granada, Spain

The deterioration of Cultural Heritage assets caused by the natural hazards is a pressing issue in many countries. Therefore, reliable models based on the large-scale structural response of the assets is key to assess their resilience. However, reliable models such as large and detailed Finite Element (FE) models, require a large number of data and input parameters. This paper proposes a Bayesian learning approach to identify the main parameters of a FE model with quantified uncertainty based on ambient vibration data. As a novelty when compared with other Bayesian structural parameter identification methods from ambient vibration data, here the likelihood function is formulated in a principled way considering information from both frequencies and modes using a probabilistic version of the Modal Assurance Criterion for the modes. This method is embedded into a parameterised computational model to automate the simulation process, and a real case study for a sixteenth century heritage building in Granada (Spain) is presented. The results show the suitability and effectiveness of the proposed Bayesian approach in identifying the most plausible values of the uncertain model parameters in a rigorous probabilistic way, but also in obtaining the modelled frequencies and the modal assurance criterion values with quantified uncertainty.

Reduced Order Modeling of Nonlinear Vibrating Multiphysics Microstructures with Deep Learning-Based Approaches

Micro-electro-mechanical-systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications. Starting from full-order representations, we apply deep learning techniques to generate accurate, efficient, and real-time reduced order models to be used for the simulation and optimization of higher-level complex systems. We extensively test the reliability of the proposed procedures on micromirrors, arches, and gyroscopes, as well as displaying intricate dynamical evolutions such as internal resonances. In particular, we discuss the accuracy of the deep learning technique and its ability to replicate and converge to the invariant manifolds predicted using the recently developed direct parametrization approach that allows the extraction of the nonlinear normal modes of large finite element models. Finally, by addressing an electromechanical gyroscope, we show that the non-intrusive deep learning approach generalizes easily to complex multiphysics problems.

Evaluating numerical techniques with HPC systems in predicting vibratory responses of large finite element models

Finite element (FE) analyses have been widely used to support design optimizations in various disciplines to improve performance and possibly save material, cost, and schedule. As computational resources (i.e., CPU, memory, storage, and accelerator) are getting more powerful and cost effective, the complexity and model sizes of numerical models are greatly increasing to capture geometry details and features of the design. Correspondingly, the computational time for complex and large FE models are significantly growing. Traditional brute-force approach is not quickly enough to support design iterations. In this presentation, various numerical techniques are investigated and exercised in the DoD High Performance Computing systems to identify their advantages and limitations in conducting large FE analyses. Those techniques include utilization of GPGPU, direct versus iterative solvers, approximation of frequency sweep, etc. As a benchmark case, frequency response functions of a flat plate with viscoelastic material is exercised at the DoD HPC systems to examine the numerical techniques' impacts.

Methods of Model Order Reduction for Coupled Systems Applied to a Brake Disc‐Wheel Composite

AbstractIn this contribution, investigations on model order reduction for coupled systems composed from components of a passenger car are shown. In today's development processes, the simulation of mechanical components is indispensable and large Finite Element models are often used for this purpose. For the calculation of time‐domain or frequency‐domain analyses, for example, a lot of computing power is required. However, with the application of model order reduction methods, this effort can be reduced, but this results in a trade‐off between the reduction error and the computational time. Since the computation of reduction bases for complete systems can be computationally expensive, it is of interest to be able to reduce components individually and then assemble them into a reduced overall model. This can result in both, a saving of computational effort when creating the bases, as well as a saving of the required memory space. Furthermore, there are many possible combinations of components in the modular systems of today's automotive industry, which emphasizes the model order reduction by parts and not by assemblies. In this work, methods of model order reduction for coupled systems are presented and will be tested on components in the chassis of a sports car. Therefore, an assembly consisting of a brake disc and wheel rim together with the wheel hub are investigated. For this purpose, the eigenmodes and transfer functions of the overall model, the reduced overall model and the assembly built from individual reduced bodies are compared.

High actuation capability and smooth-deformation piezo morphing wing based on multi-layer parallel pre-compressed MFC bimorph

A single macro-fiber composite (MFC) unimorph or bimorph wing can only be applied to micro aerial vehicles (MAV) at speeds lower than 20 m/s owing to its relatively small output work. In this study, a high-actuation MFC pre-compressed bimorph actuator (MFC-PBA) multilayer parallel morphing wing is proposed for application in high-speed miniature unmanned aerial vehicles (mini-UAVs). The morphing wing adopts the proposed ribs with an arc groove and three parallel layers of MFC-PBAs to improve the output work and guarantee smooth morphing wing surface. The large deformation finite element (FE) models of a single MFC-PBA and its multilayer parallel morphing wing are established to evaluate the output deformation and output force. Subsequently, a prototype of the morphing wing is fabricated, and the actuation capabilities of the single MFC-PBAs and morphing wing are tested. The experimental and FE simulation results satisfactorily agree. The results show that at the peak driving voltage, with axial compression forces of 18 and 27 N applied to the side and middle MFC-PBAs, respectively, the deflection angle of the morphing wing reaches ±12°, which is twice that of the morphing wing without compression; and its blocking force is maintained at 1.682 N; thus, its output work has doubled. The multiphysics model of the proposed morphing wing under airflow is established to evaluate the deformation capability. The results show that the present morphing wing achieves a deflection of 5.04° on the side of the incoming flow direction, and a unit lift of 249.1 N/m at an air speed of 40 m/s and angle of attack of 15°. Consequently, the proposed morphing wing exhibits a high deformation capability. We expect the proposed morphing wing will be used for the flight control of mini-UAVs at higher speeds and larger sizes.

A Reduction Technique for the Calculation of the Forced Response of Bladed Disks in the Presence of Contact Mistuning at Blade Root Joints

Abstract The effect of differences in nominally equal sectors of a bladed disk (mistuning) is a well-known problem for designers since the forced response may show localized amplification of the blade response with respect to a cyclically symmetric (tuned) configuration. In order to perform a large number of simulations in a reasonable amount of time to characterize the highest blade response, corresponding to the worst mistuning pattern, reduction techniques have been developed, where the mistuning is introduced directly in a compact, reduced order model (ROM) obtained from very large finite element (FE) models. Typically, mistuning is introduced in the ROM in terms of natural frequency perturbations of the blade; nevertheless, a better insight is specifically required in order to correlate mistuning to a specific source (geometrical, material, contact mistuning). In this paper, a reduction technique is presented to take into account mistuning due to the contact uncertainties at the blade root joint, which can be caused by design tolerances, manufacturing process, assembly procedures, wear, etc. The technique takes its basis from the Craig–Bampton component mode synthesis (CB-CMS) applied to the uncoupled blade and disk sector, which is typically included in most of the FE software for easy implementation in standard industrial practice. The full set of master degrees-of-freedom (DOFs) at the random contacts are purposely reduced using an optimal local modal basis based on the Gram–Schmidt interface (GSI) technique developed by the authors. Experimental evidence of actual uncertain contact obtained during joint preloading is used to find an appropriate base to represent typical contact patterns.

Multi-level curvature-based parametrization and model updating using a 3D full-field response

Model updating improves the correlation between the response of the real structure and the response of the finite-element (FE) model; however, the selection of the updating parameters (parametrization) is crucial for its success. Using full-field modal shapes, a large number of parameters can be updated, e.g., the Young’s moduli of all the finite elements; however, the structural response is not necessarily sensitive to an arbitrary parameter, making the optimization problem ill-conditioned. Additionally, the computation of the full sensitivity matrix is not feasible for relatively large FE models. Not all locations are equally important for model updating; at locations of the highest mechanical loads, more focus is required. In this research, the updating parameters are based on the curvature of the 3D full-field experimental shape, where locations with high curvature are associated with high sensitivity. The assumption is initially researched with the Euler–Bernoulli beam elements and second-order tetrahedrons. The proposed method is investigated on numerical and real experiments, where successful updating was confirmed. With the proposed parametrization and updating approach, a geometrically complex structure is parametrized and the parameters updated without significant user input, generalizing the model-updating procedure.

Numerical analyses of energy balance and installation mechanisms of large-diameter tapered monopiles by impact driving

Large-diameter monopiles are widely used as the foundation to support offshore wind turbines (OWTs) in shallow coastal waters. The benefits of small-to-medium diameter tapered piles have been reported in the past. The potential use of large-diameter tapered monopiles installed by impact driving to support OWTs is thus presented, and then comparatively assessed by numerical analyses in terms of energy balance and installation mechanisms. A three-dimensional large deformation finite element (3D-LDFE) model of monopiles driven in clay was developed using a Coupled Eulerian-Lagrangian (CEL) approach. An advanced user-defined hypoplasticity clay (HC) model was employed to model undrained kaolin clay, featuring nonlinear behavior from small strain to large strain. The force-time curve defined by the operating data of a state-of-the-art hammer in the offshore industry was inputted to explicitly model impact driving. Better agreement between the measured and the simulated results was observed to validate the accuracy of the numerical model. The numerical results obtained give greater confidence to the future use of large diameter tapered monopiles for OWTs.

Modelling and characterisation ultrasonic phased array transducers for pipe inspections

Nuclear pipes require regular inspection to prevent critical damage and extend their safe working lifetime. Ultrasonic inspection using phased array transducers is a Non-Destructive Testing (NDT) method used to monitor the condition of pipes, providing internal integrity information using multiple small transducer elements. This grants a controllable ultrasonic beam that provides more detail than a conventional single element transducer. This paper presents a hybrid simulation model to characterise phased array ultrasonic transducers for pressure pipe inspections. The paper focuses on identifying defects on pipe surfaces, which have total propagation path lengths in the order of 170 ultrasound wavelengths. Simulating inspections with such large path lengths is challenging due to unreliable results from numerical dispersion errors in large finite element models. The model presented here combines the benefits of finite element modelling with analytical extrapolation to overcome the issue of large propagation distances. A practical experiment demonstrates and verifies that the hybrid simulation model matches real world inspections. Inspection accuracy was quantified using the hybrid simulation model over frequency (5, 7.5 and 10 MHz) and number of elements (8, 16 and 32) to inspect two defect shapes (rectangular and V-shape). The 10 MHz transducer showed the highest resolution for the depth measurement, while the 5 MHz transducer presented the strongest penetration to inspect the defects on the pipe's outer surface. The largest aperture transducer, 32 elements, brought about the most accurate defect size measurement. This work serves to inexpensively guide the selection and later deployment of phased array inspection tools in nuclear pipe defect detection and monitoring.

Multidimensional Modeling of Ablation Heat Transfer

This paper describes multidimensional modeling of ablation heat transfer with a focus on ablative insulation materials used in rocket motor nozzles. Phenomenology is discussed, and detailed three-dimensional math models are presented along with a finite element solution strategy. Implementation into a computer program named Hero is described, including a description of the parallel processing capability that enables computational support for large finite element models. A validation case is presented using measurement data from booster motors of the space shuttle program. The validation results are quantified in terms of the probabilistic propensity for misprediction of the char depth at varying levels. The validation results show a trend toward the overprediction of char depth by around 4%. The standard deviation of percent misprediction is shown to be between 6 and 16%, depending on boundary condition fidelity. This suggests that accuracy to three standard deviations can be expected to fall in the range of 18–48% for ablation modeling in rocket nozzles. This paper provides an important reference for multidimensional ablation heat transfer analysis and quantification of related modeling uncertainty.

Optimal sensor placement of triaxial accelerometers for modal expansion

Sensor placement is a vital factor affecting the quality and accuracy of virtual sensing. Modal expansion techniques are well-known methods to expand the measured displacements or accelerations to all unmeasured degrees of freedom. For this purpose, a two-phase sensor placement optimisation method is proposed for commonly used triaxial accelerometers. The method uses minimum variance criterion of an estimation error of structural responses. A measure of redundancy of information is introduced as an additional criterion for the placement of the triaxial sensors to minimise the redundancy between the sensors. This was addressed to avoid spatial correlation and clustering of the sensor locations. In addition, a proposal for modal displacement-based weighting is introduced to avoid potential selection of sensor locations with low vibration energy, which can be critical in noisy environments. The efficiency of the proposed method is verified with numerical models of different types of structures and finally with the laboratory scale experiments. The mean error of the reconstructed response in this particular experimental case study was 1.4% of the maximum measured response amplitude. This method is especially applicable to large finite element models of industrial-scale structures with fine meshes.

An improved iterative model reduction technique to estimate the unknown responses using limited available responses

A major challenge in structural health monitoring (SHM) is the availability of responses at limited degrees of freedom (DOFs). This requires the determination of the transformation parameter to expand the available DOFs to the full size of a model. The present study proposes an improved iterative model reduction algorithm by eliminating the stiffness terms from the transformation equation. The modified equation is a function of measured modal responses and mass matrices. This enables obtaining the unknown responses without repeated evaluations in case of stiffness reductions typically involved in SHM problems. The transformation parameter is solved using an improved Levenberg-Marquardt (LM) based iterative least-squares optimization technique. Specifically, the LM algorithm is enhanced by introducing an adaptive damping term in the least-squares problem. The proposed approach is further integrated into the substructuring scheme so that it can be readily applied for large finite element models. The algorithm is numerically demonstrated by considering a beam and a ten-storey building model using modal data with Gaussian noise. The effectiveness of the proposed reduced-order model is studied for a gradually decreasing number of modes and available responses for various measurement configurations by comparing with the results of the existing model reduction techniques.

Energy harvesting from the gust response of membrane wing using piezoelectrics

Micro-air vehicles face challenges in aerodynamic and endurance. This paper presents a novel gust response-based membrane wing energy harvester to solve these issues. An aero-electro-mechanical model based on CFD/CSD coupling method is established to investigate the dynamic response and the energy harvesting performance of this energy harvester under harmonic gust loads. The geometric nonlinearity of structure and aerodynamic nonlinearity are considered in this paper. The harmonic gust loads were obtained from a Navier–Stokes CFD solver based on unstructured meshes. The large deformation electro-mechanical finite element model was built based on the updated Lagrangian formulation and the principle of virtual work. The mean power density is defined to evaluate the energy harvesting performance. The effects of the external load resistance, the PVDF patch location, the gust amplitude and frequency, and Reynold number are studied, respectively. The results show that the optimal resistance of this energy harvester is 1.6kΩ, and the flexibility of the membrane wing improves the aerodynamic and energy harvesting performance greatly through increases the amplitude of odd super harmonics. The PVDF location has a relatively small impact on the energy harvesting performance except near end surfaces. The PVDF patch located at 0.1c–0.9c all can get better energy harvesting performance. When the equivalent angle of attack of gust amplitude exceeds 4 deg, the energy harvesting performance decreases slightly due to the formation and convection of leading-edge vortex. A sustained output power density of 5.31mW/cm3 is harvested at Re=25,000. The present work provides an effective theoretical basis for further studying energy harvesting of Micro air vehicles.

Numerical investigation of caisson with pad-eye stiffener installation into nonhomogeneous clay

Caisson foundations are widely used in offshore engineering. During installation, the soil flow mechanism of stiffened caissons with local thickening at the pad-eye is still not well understood. In this study, large deformation finite element (LDFE) model is established to investigate the penetration behavior of caisson with pad-eye stiffener, where the soil flow mechanism is studied considering soil strain softening effect. The numerical model is validated by comparing with available testing data. Parametric study is then conducted to examine potential influencing factors, including the penetration depth, the geometry of stiffener, the clay shear strength, and strain softening parameters. It is found that the soil failure mechanisms and the corresponding penetration resistances of locally stiffened caisson at the pad-eye are significantly different from that of unstiffened caisson or stiffened caisson with interval rings. Two parameters, i.e. the critical rotational soil flow depth (Hr) and the limiting cavity depth (Hc) are introduced to quantitatively describe the behavior of the observed soil flow mechanisms. Based on the modeling results, a simplified flow mechanism is proposed, and approximating expressions are derived to predict the penetration resistance of the caisson for engineering design application.

Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

In biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R2 ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).Graphical Cancellous Bone with Fabric Tensor Ellipsoid representing anisotropy and principal axis (colored coordinate system) of given trabecular structure