Parametric Finite Element Model Research Articles

Parametric finite element modelling of deformed state of steam turbine blade assemblies

The paper presents a methodology for construction of computational finite element models of steam turbines blade assemblies. A parameterized description of the driven wheel blade structure is presented. The set of geometric parameters and the system of association between them is defined. The algorithms of the automated construction of geometric three-dimensional models is developed, which al-lows you to apply automated computational mesh, boundary conditions and load. As an example the construction of a model of the rotor blade of the third stage of the low pressure steam turbine cylinder is made. The analysis of static deformed state of the blade have been carried out in the cyclic symmetry formulation. The influence of the technological gap in the inter-blade shroud connection on the de-formed state of the blade under centrifugal forces has been analyzed

Theory and Implementation of Finite Element Model Updating of the Structures Based on Time Domain Data

In this paper, the updating approach of the finite element model based on time domain response data is proposed. The model of response surface based on time domain is obtained by comparing the characteristics of time domain response of the test and the finite element model, and the functional relationship between the time domain response and structural parameters is established. Based on the response surface model, the parameters of the structural finite element model are modified by optimization calculation. In order to investigate the feasibility and accuracy of the approach, the general realization of the theory is explained by choosing the simply supported beam. The initial finite element model of the simply supported beam is modified, and the update results show that the finite element model updating based on time domain response can reduce the number of the finite element calculation, and improve the efficiency of the model optimization. The updated finite element model can more accurately reflect the mechanical properties of the actual structure, and can be used as the reference finite element model.

Design and sizing of a parametric structural model for a UCAV configuration for loads and aeroelastic analysis

The authors present the setup of a parametric structural finite element model for the loads and aeroelastic analysis of an unmanned combat air vehicle (UCAV). The DLR-F19 is a “flying wing” configuration with a geometry based on previous research conducted in the scope of the “Mephisto” project and its predecessors “FaUSST” and “UCAV2010”. While a considerable body of knowledge exists regarding conventional configurations, unconventional configurations lack that same level of experience, and data for comparison is rarely available. Using an adequate structural model, the conceptual design stage becomes more sophisticated and already allows for the investigation of physical effects at an early stage of the design process. Strategies for structural modeling and proper condensation, aero-structural coupling, loads integration, control surface attachment, and the use of composite materials are addressed in this paper. The resulting model is sized for minimum structural weight, taking into account 216 load cases. In addition, a comprehensive loads analysis campaign is conducted and the resulting loads are evaluated at defined monitoring stations. In addition to maneuver loads, quasi-static gust loads are calculated using the Pratt formula and compared to results obtained from a dynamic 1-cosine gust simulation. The reasons for higher loads of the Pratt formula based method are discussed. The conclusion is that the Pratt formula is suitable for the preliminary sizing of “flying wing” configurations.

Thermal stress analysis on the thick tubesheet with square layout of tubes

In this paper, finite element analyses were carried out on thermal stresses at the tubesheet of floating-head or U-tube heat exchangers with square layout of tubes based on parametric finite element models of the tubesheet established with ANSYS parametric design language (APDL). It is found that for thick tubesheet with large temperature difference between two the sides, the maximum thermal stress can be comparable with the mechanical stress induced by pressures and should not be neglected in some circumstances. When hot fluid flows on the tube-side, both the shell-side and tube-side surfaces of the tubesheet are in tensile stress state while the region in the middle of the tubesheet is in compressive. Conversely, if the cold fluid flows on the tube-side, compressive thermal stresses are produced at the two tubesheet surfaces, which is helpful to prevent the tubesheet from cracking. By changing design parameters in APDL commands, parametric analysis was completed and the results show that the thermal stresses at the surface center of the tubesheet are sensitive to the thickness and the perforated region size of the tubesheet. Based on sufficient numerical results, a regressed formula for evaluating the thermal stress at the surface center of the tubesheet with squarely arranged tubes was obtained, this can facilitate the strength design of the tubesheet in floating-head or U-tube heat exchangers when considering the thermal stress.

A PARAMETRIC INVESTIGATION OF THE EFFECTS OF CERVICAL DISC PROSTHESES WITH UPWARD AND DOWNWARD NUCLEI ON SPINE BIOMECHANICS

This work aimed at investigating the influence of Baguera and Discocerv cervical disc prostheses, with mobile downward center of rotation (COR) and fixed upward COR, respectively, on the biomechanical behavior of C4–C6 cervical spine. For this purpose, using computed tomography (CT) data, a parametric nonlinear finite element (FE) model of intact C4–C6 spinal segments was developed, and an artificial disc was implanted at C5–C6 level. To assess the influence of implants on the biomechanics of cervical spine, the FE models were analyzed in flexion, extension, lateral bending, and axial rotation, and the results were presented in the range of motion (ROM) curves, and torsional stiffness. Results of this study, in agreement with the literature, suggested that both Baguera and Discocerv implants might be able to preserve the motion, and limit the alteration of the biomechanics of adjacent levels. Except for the possible confliction of adjacent vertebrae at the implanted level with Baguera implant in lateral bending, results of this study also indicated that the movability and downward COR of Baguera disc prosthesis caused ROMs of the implanted segment to be more similar to the intact model than Discocerv implant. Moreover, the upward COR of Discocerv implant may result in over-distraction on facets in the maximal flexion, with the ratio of 1.22 versus 1.36, and consequently facet syndrome during extension for Bageura and Discocerv disc prostheses, respectively.

Thermal buckling and post-buckling behaviour of continuous welded rail track

ABSTRACTBecause thermal expansions are constrained within continuous welded rail track, the track can buckle, and does so mainly in the horizontal plane. In this paper, a parametric finite element model of railway track is presented, and its sensitivity to the variations of the main parameters that characterise the scenario has been investigated and discussed. Comparison with existing literature shows good agreement. It is found that curved tracks suffer from thermal buckling more than tangent tracks do. To simulate a track misalignment defect, a new methodology has been utilised that does not introduce, as is usual, geometrical discontinuities near the same defect, because it takes into account – in a natural way – the bending stiffness of the whole railway track in the horizontal plane. To contribute to a better understanding of the safe utilisation of raw experimental data obtained from in situ tests, a deep analysis of the effects on the thermal track buckling response produced by each parameter characterising the sleeper–ballast lateral resistance curve is presented and discussed. It is found that for current ballasted railway tracks, the minimum buckling temperature depends only on the limit lateral resistance, whereas a high value of the initial stiffness can lead to overestimation of the maximum buckling temperature, also taking into account the ‘natural’ decrease in the maximum buckling temperature due to an increase in the railway-traffic-induced defect amplitude.

Uncertainty analysis of the effect of grout injection on the deformation of multi-wythe stone masonry walls

The eighteenth century Prince of Wales Fort in Manitoba Canada has experienced extensive freeze-thaw damage and mortar washout within the escarp walls resulting in distress and failures at multiple locations. Injection of grout could counteract this degradation of structural stability. However existing literature provides little guidance as to the improvement level that could be expected, especially with respect to out-of-plane performance. As such, the proposed treatment was modelled to include a high level of uncertainty in the system through the application of a Random Field Finite Element Micro-modelling technique. A Latin Hyper cube simulation method was used in conjunction with a parametric finite element model to randomize the material properties of each stone and relevant grouting layers. The numerical results predicted that the stone-grout bond was the most critical parameter in the proposed intervention, and that in the grouted wall sections, collapse would be avoided and lateral displacements stabilized with the proposed treatment.

Influence of measurement data metrics on the identification of Interval Fields for the representation of spatial variability in finite element models

AbstractDue to the exponential growth in computing power, numerical modelling techniques method have gained an increasing amount of interest for engineering and design applications. Nowadays, the deterministic finite element (FE) method, an efficient tool to accurately solve the Partial Differential Equations (PDE) that govern most real‐world problems, has become an indispensable tool for an engineer in various design stages. A more recent trend herein is to use the ever increasing computing power incorporate uncertainty and variability, which is omnipresent is all real‐live applications, into these FE models. Several advanced techniques for incorporating either variability between nominally identical parts or spatial variability within one part into the FE models, have been introduced in this context. For the representation of spatial variability on the parameters of an FE model in a possibilistic context, the theory of Interval Fields (IF) was proven to show promising results. Following this approach, variability in the input FE model is introduced as the superposition of base vectors, depicting the spatial ‘patterns’, which are scaled by interval factors, which represent the actual variability. Application of this concept, however, requires identification of the governing parameters of these interval fields, i. e. the base vectors and interval scalars. Recent work of the authors therefore was focussed on finding a solution to the inverse problem, where the spatial uncertainty on the output side of the model is known from measurement data, but the spatial variability on the input parameters is unknown. Based on an a priori knowledge on the constituting base vectors of the interval field, the simulated output of the IFFEM computation is compared to measured data, and the input parameters are iteratively adjusted in order to minimize the discrepancy between the variability in simulation and measurement data. This discrepancy is defined based on geometric properties of the convex sets of both measurement and simulation data. However, the robustness of this methodology with respect to the size of the measurement data set that is used for the identification, as yet remains unclear. This paper therefore is focussed on the investigation of this robustness, by performing the identification on different measurement sets, depicting the same variability in the dynamic response of a simple FE model, which contain a decreasing amount of measurement replica. It was found that accurate identification remains feasible, even under a limited amount of measurement replica, which is highly relevant in the context of a non‐probabilistic representation of variability in the FE model parameters. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Determination of the in situ mechanical behavior of ankle ligaments

The mechanical behavior of ankle ligaments at the structural level can be characterized by force–displacement curves in the physiologic phase up to the initiation of failure. However, these properties are difficult to characterize in vitro due to the experimental difficulties in replicating the complex geometry and non-uniformity of the loading state in situ. This study used a finite element parametric modeling approach to determine the in situ mechanical behavior of ankle ligaments at neutral foot position for a mid-sized adult foot from experimental derived bony kinematics. Nine major ankle ligaments were represented as a group of fibers, with the force–elongation behavior of each fiber element characterized by a zero-force region and a region of constant stiffness. The zero-force region, representing the initial tension or slackness of the whole ligament and the progressive fiber uncrimping, was identified against a series of quasi-static experiments of single foot motion using simultaneous optimization. A range of 0.33–3.84mm of the zero-force region was obtained, accounting for a relative length of 6.7±3.9%. The posterior ligaments generally exhibit high-stiffness in the loading region. Following this, the ankle model implemented with in situ ligament behavior was evaluated in response to multiple loading conditions and proved capable of predicting the bony kinematics accurately in comparison to the cadaveric response. Overall, the parametric ligament modeling demonstrated the feasibility of linking the gross structural behavior and the underlying bone and ligament mechanics that generate them. Determination of the in situ mechanical properties of ankle ligaments provides a better understanding of the nonlinear nature of the ankle joint. Applications of this knowledge include functional ankle joint mechanics and injury biomechanics.

Micro-leveled modeling of structural stitched FRP joints as energy absorbing rupture points

Compared to their capability for compression loads, continuous fiber reinforced polymers show poor energy absorption capability for tensile or bending loads. An appropriate structural design must compensate this disadvantage. Following an integrated lightweight strategy, connecting elements can be addressed as energy absorbing points. Consequently, textile seams between FRP components can be used. Adapting the stitching layout allows the failure process to be adjusted. However, appropriate design principles have to be identified in order to optimize the energy absorption. For this purpose, a parametrized finite element model of a single lockstitch was developed based on real stitching geometries and validated with experimental data. The validated numerical analysis helps in evaluating the influence of the thread properties and the stitching design. The parameter study reveals a strong influence of the thread material. In a loaded seam, polyamide yarns with a distinctive plasticity offer much better energy absorption capacity than high tenacity UHMWPE (Dyneema) threads. Furthermore, friction between the yarn and the surrounding material as well as wide stitch lengths are beneficial for energy absorption.

Non-uniform Solar Temperature Field on Large Aperture, Fully-Steerable Telescope Structure

In this study, a 110-m fully steerable radio telescope was used as an analysis platform and the integral parametric finite element model of the antenna structure was built in the ANSYS thermal analysis module. The boundary conditions of periodic air temperature, solar radiation, long-wave radiation shadows of the surrounding environment, etc. were computed at 30 min intervals under a cloudless sky on a summer day, i.e., worstcase climate conditions. The transient structural temperatures were then analyzed under a period of several days of sunshine with a rational initial structural temperature distribution until the whole set of structural temperatures converged to the results obtained the day before. The non-uniform temperature field distribution of the entire structure and the main reflector surface RMS were acquired according to changes in pitch and azimuth angle over the observation period. Variations in the solar cooker effect over time and spatial distributions in the secondary reflector were observed to elucidate the mechanism of the effect. The results presented here not only provide valuable realtime data for the design, construction, sensor arrangement and thermal deformation control of actuators but also provide a troubleshooting reference for existing actuators.

Parametric modeling and updating for bolted joints of aeroengine casings

To establish accurate finite element (FE) model of bolted joint structures of aeroengine stator system (casings), this work implements the parametric FE modeling and updating of bolted joints of aeroengine stator system with multi-characteristic responses (multi-object). Firstly, the parametric FE modeling approach of bolted joint structure was developed based on the thin layer element method. And then the FE model updating thought of aeroengine stator system was developed based on the probabilistic analysis method. Finally, the parametric modeling and updating of the bolted joints of aeroengine stator system with multi-characteristic responses was completed by the optimization iteration calculation of objective function based on the proposed methods and the static stiffness testing data. Through the parametric modeling of bolted joint structures based on the thin layer method, the complexity of FE model of aeroengine casings with many bolted joint structures is reduced. As shown in the FE model updating of casings with multi-characteristic responses analysis, the static stiffness from the updated model are very close to the test data, in which the maximum relative error decreases to 3.9% from 30.52% and the others are less than 3%, so that the design precision of aeroengine stator system with the many and wide variety of bolted joints gets a great improvement. Moreover, the proposed methods of parametric modeling and model updating for multi-characteristic responses are validated to be effective in the simulation and equivalent of the mechanical characteristics of bolted joints in complex systems like aeroengine stator system.

The sensitivity of the burst performance of impact damaged pressure vessels to material strength properties

This numerical study is carried out to improve the understanding of short-term residual strength of impacted composite pressure vessels. The relationship between the impact, created damage and residual strength is predicted by finite element (FE) analysis. The burst predictions depend largely on the strength properties used in the material models. However, it is typically not possible to measure all laminate properties on filament wound structures. Reasonable testing efforts are concentrated on critical properties, while obtaining other less sensitive parameters from e.g. literature. A parametric FE model is hereby employed to identify the critical strength properties, focusing on the cylindrical section of the pressure vessel. The model simulates an impactor strike on an empty vessel, which is subsequently pressurized until burst. Monte Carlo Simulations (MCS) are employed to investigate the correlations between strength related material parameters and the burst pressure. The simulations indicate the fracture toughness of the composite, hoop layer tensile strength and the yield stress of the PE liner as the most influential parameters for current vessel and impact configurations. In addition, the conservative variation in strength parameters is shown to have a rather moderate effect (COV ca. 7%) on residual burst pressures.

A high-performance parametrized mixed finite element model for bending and vibration analyses of thick plates

Based on the parametrized mixed variational principle, a high-performance finite element model has been developed for bending and vibration analysis of thick plates. The proposed mixed variational formulation combines the concept of Reissner’s mixed variational theorem and Rong’s generalized mixed variational theorem. In addition to unknown parameters of the displacement fields, the transverse normal component of the stress tensor is also assumed as the independent field variable in the present variational formulation. The latter allows the fulfillment of the boundary conditions of the transverse normal stress at the top and bottom surfaces of the plate in a natural way. The variational constraint of the transverse normal strain–displacement relations is relaxed via the parametrized Lagrange multipliers method. The functional of the proposed variational formulation contains an arbitrary free parameter, called the splitting factor. Simple formulations have been proposed for selecting the splitting factor which leads to the results of higher precision. The numerical results obtained from the proposed mixed formulation have been compared with the results of three-dimensional (3D) theory of elasticity and other plate theories available in the literature. The comparison study shows that the proposed parametrized mixed plate theory is capable of achieving the accuracy of nearly exact 3D solutions.

Model updating of a full-scale FE model with nonlinear constraint equations and sensitivity-based cluster analysis for updating parameters

The objective of structural model updating is to reduce inherent modeling errors in Finite Element (FE) models due to simplifications, idealized connections, and uncertainties of material properties. Updated FE models, which have less discrepancies with real structures, give more precise predictions of dynamic behaviors for future analyses. However, model updating becomes more difficult when applied to civil structures with a large number of structural components and complicated connections. In this paper, a full-scale FE model of a major long-span bridge has been updated for improved consistency with real measured data. Two methods are applied to improve the model updating process. The first method focuses on improving the agreement of the updated mode shapes with the measured data. A nonlinear inequality constraint equation is used to an optimization procedure, providing the capability to regulate updated mode shapes to remain within reasonable agreements with those observed. An interior point algorithm deals with nonlinearity in the objective function and constraints. The second method finds very efficient updating parameters in a more systematic way. The selection of updating parameters in FE models is essential to have a successful updating result because the parameters are directly related to the modal properties of dynamic systems. An in-depth sensitivity analysis is carried out in an effort to precisely understand the effects of physical parameters in the FE model on natural frequencies. Based on the sensitivity analysis, cluster analysis is conducted to find a very efficient set of updating parameters.

Evaluation of solar temperature field under different wind speeds for Shanghai 65 m radio telescope

The Shanghai 65 m radio telescope is currently the largest full range rotatable radio telescope in Asia. Gravity, wind and temperature are the three main factors which may have a bad effect on the reflector’s surface precision. To study the effect of the thermal deformation caused by daily non-uniform temperature fields on the surface precision of the main reflector, both the temperature field and its effect were studied in detail for two typical days (January 15th and July 15th). The method to simulate temperature fields was studied initially, considering heat conduction, solar radiation, shadowing, air convection, sky radiation and ground radiation. Then, an integral parametric thermal finite element model (FEM) of the telescope was established using the ANSYS thermal analysis module. Finally, the effect of non-uniform temperature fields on the surface precision of the main reflector was estimated in terms of the Root Mean Square (RMS) deformation based on temperature transient analysis. The proposed methods and conclusions drawn can provide valuable information for thermal design, thermal monitoring and thermal control of the Shanghai 65 m radio telescope and other similar giant antenna structures.

Structural optimisation of composite wind turbine blade structures with variations of internal geometry configuration

Structural optimisation techniques are frequently used as part of the design process for composite wind turbine blades. Most commonly this is achieved by modifying material placement within a standard structural design; less attention has been paid to the possibility of varying internal geometry to create novel structural configurations. In this work, a series of wind turbine blade designs with differing structural configurations have been created and compared to investigate the effect of allowing various aspects of the internal structural geometry to be varied. The geometry of the structural spar is thoroughly investigated by modifying the width of the spar caps, and the number and location of shear webs including the spanwise starting and ending locations. The location and extent of a trailing edge reinforcement are also considered, along with the material thickness distribution of the spar and trailing edge reinforcement. A series of five parametric 2D finite element models with geometry and materials placement variables were created and incorporated into a genetic optimisation algorithm. This method allows the optimisation process sufficient freedom to generate designs without being constrained by preconceived ideas of how the internal geometry should be configured. The optimum designs had mass reduced relative to the baseline by 3.5–7.4%. Structural analysis of the optimum designs revealed that the active constraint varied greatly between the different designs, and it is therefore recommended that a wider range of loading cases and constraints needs to be accounted for in optimisations that allow the structural geometry to vary compared to those that use a standard geometry.

Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer–Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic structural FE models of a bridge pier and a moment resisting steel frame, are performed to validate the performance and accuracy of the presented nonlinear FE model updating approach and demonstrate its application to SHM. These validation studies show the excellent performance of the proposed framework for SHM and damage identification even in the presence of high measurement noise and/or way-out initial estimates of the model parameters. Furthermore, the detrimental effects of the input measurement noise on the performance of the proposed framework are illustrated and quantified through one of the validation studies.

Design Methodology of a Dual-Halbach Array Linear Actuator with Thermal-Electromagnetic Coupling.

This paper proposes a design methodology for linear actuators, considering thermal and electromagnetic coupling with geometrical and temperature constraints, that maximizes force density and minimizes force ripple. The method allows defining an actuator for given specifications in a step-by-step way so that requirements are met and the temperature within the device is maintained under or equal to its maximum allowed for continuous operation. According to the proposed method, the electromagnetic and thermal models are built with quasi-static parametric finite element models. The methodology was successfully applied to the design of a linear cylindrical actuator with a dual quasi-Halbach array of permanent magnets and a moving-coil. The actuator can produce an axial force of 120 N and a stroke of 80 mm. The paper also presents a comparative analysis between results obtained considering only an electromagnetic model and the thermal-electromagnetic coupled model. This comparison shows that the final designs for both cases differ significantly, especially regarding its active volume and its electrical and magnetic loading. Although in this paper the methodology was employed to design a specific actuator, its structure can be used to design a wide range of linear devices if the parametric models are adjusted for each particular actuator.

On the Relationship Between Tooth Shape and Masticatory Efficiency: A Finite Element Study.

Dental topography has successfully linked disparate tooth shapes to distinct dietary categories, but not to masticatory efficiency. Here, the relationship between four dental topographic metrics and brittle food item breakdown efficiency during compressive biting was investigated using a parametric finite element model of a bunodont molar. Food item breakdown efficiency was chosen to represent masticatory efficiency as it isolated tooth-food item interactions, where most other categories of masticatory efficiency include several aspects of the masticatory process. As relative food item size may affect the presence/absence of any relationship, four isometrically scaled, hemispherical, proxy food items were considered. Topographic metrics were uncorrelated to food item breakdown efficiency irrespective of relative food item size, and dental topographic metrics were largely uncorrelated to one another. The lack of a correlation between topographic metrics and food item breakdown efficiency is not unexpected as not all food items break down in the same manner (e.g., nuts are crushed, leaves are sheared), and only one food item shape was considered. In addition, food item breakdown efficiency describes tooth-food item interactions and requires location and shape specific information, which are absent from dental topographic metrics. This makes it unlikely any one efficiency metric will be correlated to all topographic metrics. These results emphasize the need to take into account how food items break down during biting, ingestion, and mastication when investigating the mechanical relationship between food item shape, size, mechanical properties, and breakdown, and tooth shape.