Reduced-order Finite Element Model Research Articles

Modeling error assessment of reduced-order finite element models for SHM: A case study of Milad Tower

Modeling error assessment of reduced-order finite element models for SHM: A case study of Milad Tower

Transient topology optimization for efficient design of actively cooled microvascular materials

Microvascular materials containing internal microchannels are able to achieve multi-functionality by flowing different fluids through vasculature. Active cooling is one application to protect structural components and devices from thermal overload, which is critical to modern technology including electric vehicle battery packaging and solar panels on space probes. Creating thermally efficient vascular network designs requires state-of-the-art computational tools. Prior optimization schemes have only considered steady-state cooling, rendering a knowledge gap for time-varying heat transfer behavior. In this study, a transient topology optimization framework is presented to maximize the active-cooling performance and mitigate computational cost. Here, we optimize the channel layout so that coolant flowing within the vascular network can remove heat quickly and also provide a lower steady-state temperature. An objective function for this new transient formulation is proposed that minimizes the area beneath the average temperature versus time curve to simultaneously reduce the temperature and cooling time. The thermal response of the system is obtained through a transient Geometric Reduced Order Finite Element Model (GRO-FEM). The model is verified via a conjugate heat transfer simulation in commercial software and validated by an active-cooling experiment conducted on a 3D-printed microvascular metal. A transient sensitivity analysis is derived to provide the optimizer with analytical gradients of the objective function for further computational efficiency. Example problems are solved demonstrating the method’s ability to enhance cooling performance along with a comparison of transient versus steady-state optimization results. In this comparison, both the steady-state and transient frameworks delivered different designs with similar performance characteristics for the problems considered in this study. This latest computational framework provides a new thermal regulation toolbox for microvascular material designers.

Standard versus natural fire resistance for partially restrained composite floor beams: 2-Analysis

A thermo-structural reduced-order finite element modeling approach is used to evaluate the results of two fire tests (presented in Part 1 of this study) on identically designed, highly composite floor beam specimens with SFRM protection, shear tab connections at each end, a lightweight concrete slab on a corrugated metal deck, and partial restraint of both axial thermal expansion and connection rotation. Model validation is performed for both an ASTM E119 standard fire and a parametric natural fire, with a constant load applied to the specimens via four-point bending to a maximum service condition. Predictions of temperature increase in the protected steel beam and the composite slab show good agreement with experimental measurements by implementing a series of weighted averaging strategies on thermal FE results for 2D cross-sections at the thick and thin portions of the composite slab. Predictions of temperature-induced deflections, which used the results of thermal FE analysis as input, also show good agreement with experimental results when little-to-no rotational stiffness is applied to the connections. The numerical models are then re-analyzed at a reduced loading level (representing a middling service condition) and with varying rotational stiffness in the shear tab connections. The results of parametric analysis are used to draw correlations between standard fire resistance and natural fire robustness as a function of applied loading and temperature increase in the steel beam. Simplified modeling strategies and recommendations for performance-based structural-fire design are discussed, and opportunities for future research are highlighted.

Gibbs Sampler-Based Probabilistic Damage Detection of Structures Using Reduced Order Model

Vibration-based global damage detection based on updating of finite element (FE) model by targeting the modal measurements is a significant area of interest in structural health monitoring (SHM). In a typical modal testing setup, the measured mode shapes have missing components against various degrees of freedom (DOFs) due to the limitation in the number of sensors available. In this context, a novel Gibbs sampling approach is proposed for updating of FE model incorporating model reduction (MR) to facilitate the global-level detection of structural damages from incomplete modal measurements. In addition to the ease with similar sizes of analytical and experimental mode shapes, the proposed Gibbs sampling approach (for updating the reduced order FE model in the Bayesian framework) has some important advantages like: (A) no need for consideration of system mode shapes as parameters (unlike needed in the typical Gibbs sampling approach) thereby having a significant reduction in the number of parameters, (B) non-requirement of mode matching with consequent reduction in computation time to a significant extent. A generalized formulation is presented in this work providing the scope for incorporating measurements from multiple sensor setups. Moreover, formulations are adapted to incorporate multiple sets of data/measurements from each setup targeting the epistemic uncertainty. Finally, validation is carried out with both numerical (truss structure and building structure) and experimental (laboratory building structure) exercises in comparison with the typical Gibbs sampling approach having a full-sized model. The proposed approach is observed to be evolved as a computationally efficient technique with satisfactory performance in FE model updating and global damage detection.

Two hybrid model-based control strategies for a flexible parallel planar manipulator

Designers can reduce the inertia of moving parts of a robotic manipulator aiming for energy efficiency. Nevertheless, this design option could yield undesired vibrations due to its lighter components, requiring control strategies for their mitigation. In addition, other challenges arise when designing parallel manipulators since the control strategies cannot use a direct measurement of the manipulator end-effector’s pose and their coupling dynamics. This work proposes two hybrid model-based control design strategies for a 3RRR parallel manipulator with flexible links in this work. Both strategies have two feedback loops, one of which exploits the encoder’s measurements and the inverse kinematic model of the manipulator considering rigid links. The difference between the strategies is related to the feedback signal used in the second feedback loop that exploits an LQR/LQG strategy. The first strategy uses the end-effector’s pose measured by a limited frame camera, while the second uses the end-effector’s pose derived from a reduced-order finite element model. These strategies are experimentally compared with a PID strategy for assessing their assets and limitations. The steady-state error was lower when using the model-based control strategies. Moreover, the second strategy responds faster than the first for the evaluated tasks.

Dynamic Reduction-Based Virtual Models for Digital Twins—A Comparative Study

Digital models are the foundation of digital twins, which form the basis of autonomous off-road vehicles. Developing virtual models of off-road vehicles using dynamic reduction techniques is one of several approaches. The article commences with a comprehensive overview of the most widely used dynamic reduction methods and then introduces performance metrics for assessing their efficacies in the context of digital twins. The paper additionally includes a detailed mathematical derivation of the state-space representation for reduced-order finite element models. The state-space representation of the reduced finite element models facilitates their export to problem-solving environments for dynamic analysis. The state-space models are eventually solved utilizing the built-in libraries of numerical solvers in textual and graphical programming platforms. In addition, the article identifies the set of solvers that best suit the simulation of virtual models for off-road vehicles. This article also includes an evaluation of the simulation results for digital models with modes ranging from 0 to 30 Hz. In addition, the article demonstrates the lower bound of the frequency range necessary and sufficient to be retained in off-road vehicle virtual models. Finally, the paper presents the simulation outcomes for digital models of commercial off-road vehicles with custom-built virtual modules of powertrain, electrical, and control systems in a problem-solving environment.

Physics-based sound radiation estimation from multiple speakers by combined lumped parameter and reduced-order finite element modeling

In this paper a virtual sensor is derived that can perform full field estimation of the sound field radiating from a number of loudspeakers in the time domain. The virtual sensor scheme contains two parts: Firstly, a time-domain physics-based numerical system level model that includes both the electro-mechanical behavior of the loudspeaker and the resulting wave propagation. Secondly, a Kalman filter in which the numerical model and a limited set of microphone measurements are combined to perform full field estimation. The loudspeaker dynamics are captured in a lumped parameter model and the resulting wave propagation is captured in a finite element model. To reduce the calculational complexity of the system level model, Krylov subspace based reduced order modeling is applied on the finite element model, leading to a significant reduction of the number of states. The system level model is brought to a discrete time state–space format, which allows for efficient implementation in the Kalman filter. The method is validated using two setups that use both vented and closed box loudspeakers, leading to improved estimation results as compared to pure simulation results, thus showing the merits of the virtual sensor. Furthermore, the importance of including the lumped parameter speaker model in the system level model is shown by comparing the estimation results with and without the inclusion of the lumped parameter model.

Artificial intelligence data-driven 3D model for AIS.

Scoliosis is a 3D deformation of the spinal column, characterized by a lateral deviation of the spine, accompanied by axial rotation of the vertebrae. Adolescent Idiopathic Scoliosis (AIS), is the most common type, affecting children between ages 8 to 18 when bone growth is at its maximum rate. The selection of the most appropriate treatment options is based on the surgeon's experience. So, developing a clinically validated patient-specific model of the spine would aid surgeons in understanding AIS in early stages and propose an efficient method of treatment for the individual patient. This project steps include: Developing a clinically validated patient-specific Reduced Order Finite Element Model (ROFEM) of the spine, predicting AIS progression using data mining and proposing a method of treatment. First we implement FE synergistically with bio-mechanical information, image processing and data science techniques to improve predictive ability. Initial geometry of the spine will be extracted from the x-ray images from different planes and imported to FEM software to generate the spine model and perform analysis. A RO model is developed based on the detailed spinal FEM. Next, a neural network is used to predict the spinal curvature. The ability to predict the severity of AIS will have an immense impact on the treatment of AIS-affected children. Access to a predictive and patient-specific model will enable the physicians to have a better understanding of spinal curvature progression. Consequently, the physicians will be able to educate families, choose the most appropriate treatment option and asses for surgical intervention.

An enhanced reduced-order model based optimization method for buckling and postbuckling performances of variable stiffness composite plates

The great potential of variable stiffness laminates in maximizing buckling load is obvious over straight fiber laminates, however the optimum design of such VAT laminates which has much more design variables and larger computational efforts, is still a challenge even for the modern computational method and capability. In addition, the postbuckling performance and the correlations with buckling resistance still need to be further studied for VAT laminates. This work proposes an enhanced reduced-order model based on the improved Koiter perturbation theory for buckling and postbuckling analysis of variable stiffness composite plates. The VAT laminas composed by “two-segment” fibers and “four-segment” fibers are considered, respectively, in construction of the reduced-order finite element model. The nonlinear prediction for initial postbuckling response of VAT laminate can be achieved, by solving the small-scaled reduced-order model. The nonlinear buckling load, postbuckling stiffness and postbuckling stiffness residual factor, are accurately and efficiently extracted from the initial postbuckling predictor, and then subsequently to be selected as inputs to the GA based optimization process for the design of VAT laminates. Extensive numerical investigations validate that the proposed method can find a combination of several varied angle fiber layers with constant thicknesses such that the combination results in an optimal stiffness distribution and provides a more favorable structural performance in both buckling and postbuckling regime for different demands of structure design.

Sagittal curvature of the spine as a predictor of the pediatric spinal deformity development.

The sagittal curvature of the spine is hypothesized to play an important role in induction of spinal deformities in adolescent idiopathic scoliosis. We previously showed an S shaped flexible rod, with the same curvature as the pediatric sagittal spinal curve, produces scoliotic-like deformities under physiologic loading. Yet, detailed characteristics of the pediatric sagittal spinal curves associated with higher risk of scoliosis are not well defined. A total of 32 patients in a population with a high prevalence of idiopathic-like scoliosis, 22q11.2 deletion syndrome (22q), were included and followed up for at least two-years. We developed a reduced order finite element model (FEM) of the sagittal profile of these 32 patients where the spine was modeled as an S shaped elastic rod. We related the geometrical parameters of the sagittal curves and the deformed FEM of the corresponding S shaped rods to the risk of scoliosis development at two-year follow-up in this cohort. Variations in the sagittal curvature in the cohort of 22q patients resulted in five different deformity patterns shown by finite element analyses. Two sagittal plane deformity pattern groups had high rate of scoliosis development (86% and 100%) whereas the other 3 groups had less than 50% rate of scoliosis development (40%, 33%, and 0%). The pre-scoliotic position of the inflection point (where lordosis turns into kyphosis), the ratio of the spinal curvatures above and below the inflection point, and the length of the spinal curve above and below the inflection point were significantly different between the five deformity patterns groups, p < 0.05. Combination of geometrical parameters of the sagittal profile prior to onset of scoliosis can relate to the development of spinal deformity in pediatric population.

Model updating of a scaled piping system and vibration attenuation via locally resonant bandgap formation

This study presents a Finite Element (FE) model updating methodology of a piping system and demonstrates vibration attenuation at its resonant frequencies using tuned local resonators distributed along its length. An experimental laboratory scaled version of a prototype piping system inspired from existing piping structures in the oil and gas industry is assembled to study its dynamic behavior under laboratory conditions. A dynamic structural similitude analysis is carried out to derive scaling factors for frequencies and mode shapes between the prototype and scaled piping systems. These scaling factors are verified with the aid of both detailed and reduced-order FE models. Experimental natural frequencies and mode shapes are obtained based on the impact hammer modal test and the forced vibration sine sweep test and then compared with numerical results. Discrepancies between measured and computed results due to uncertainties in the FE model necessitate the use of an FE model updating technique to minimize the error between the predicted and the measured response. This updating strategy is carried out by iteratively adjusting parameters associated with the assumed boundary conditions until a relatively faithful computational model that can replicate the actual behavior of the structure is obtained. The updated reduced order model is then used to investigate the creation of locally resonant bandgaps centered at the first three resonant frequencies of the structure by embedding tuned resonant cantilever beams with tip masses along the length of the piping system. Using a harmonic response analysis, it is shown that an attenuation is obtained at all considered target frequencies with distinct edge frequencies appearing in the frequency response for the third mode of vibration.

Abnormal stiffness behaviour in artificial cactus-inspired reinforcement materials

Cactus fibres have previously shown unusual mechanical properties in terms of bending and axial stiffness due to their hierarchical structural morphology. Bioinspiration from those cactus fibres could potentially generate architected materials with exciting properties. To that end we have built bioinspired artificial analogues of cactus fibres to evaluate their mechanical properties. We have generated 3D printed specimens from rendered models of the cactus structure using two different printing techniques to assess the reproducibility of the structural topology. Bioinspired additive manufactured materials with unusual mechanical properties constitute an ever-evolving field for applications ranging from novel wing designs to lightweight plant-inspired analogues. The cactus-inspired 3D printed specimens developed here demonstrate an unusually high bending to axial stiffness ratios regardless of the manufacturing method used. Moreover, when compared to their equivalent beam analogues the cactus specimens demonstrate a significant potential in terms of specific (weight averaged) flexural modulus. Imaging of the artificial cactus reinforcements has enabled the generation of a one-dimensional reduced order finite element model of the cactus structure, with a distribution of cross sections along the length that simulate the inertia and mechanical behaviour of the cactus topology. The novel bioinspired material structure shows an excellent reproducibility across different manufacturing methods and suggest that the tree-like topology of the cactus fibre could be very suited to applications where high bending to axial stiffness ratios are critical.

Finite element analysis of mechanical behavior of electrical wire harnesses: High fidelity and reduced-order models

High-fidelity and reduced-order finite element (FE) models are introduced to simulate and characterize the bending behavior of flexible electrical wire harnesses undergoing large deflections. A composite wire harness consists of a bundle of wires, put together using layers of tape and/or a protective tube, which could be subdivided into smaller branches. In this work, elastoplastic constitutive models are adopted for wire harness components (wires, tape, and tube) and calibrated by matching their simulated and experimental force-displacement responses. Customized three-point bending tests are carried out on composite wire bundles (CWBs) and resulting data are utilized to calibrate friction coefficients between different components, as well as cohesive contact and damage parameters along taped surfaces in the high-fidelity FE model. After the validation of this model, we show that it can be used as a reliable surrogate to laborious mechanical testing for characterizing the bending response of CWBs. Resulting effective properties are then incorporated in a reduced-order FE model relying on beam elements, which can achieve a similar level of accuracy while reducing the computational cost > 99.5%. Both FE models are also employed to study the behavior of branching wire harnesses, showing that a viscoelastic material model is needed to properly characterize the stiffness of the branch break-out joint.

On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models

This paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.

Vibration reduction of the blisk by damping hard coating and its intentional mistuning design

This paper presents a vibration reduction approach of the blisk by using of the damping hard coating and its intentional mistuning design. Firstly the amplified forced vibration responses of mistuned blisk were studied based on the reduced order finite element model (FEM) established by component mode synthesis (CMS) method, by using the actual mistuning value of a blisk specimen. Then the effects of damping hard coating on forced vibration responses of the tuned and mistuned blisk were investigated. Further, intentional mistuning design by depositing hard coating with different thickness on blades was researched, after comparing several mistuning patterns. At last, experiment research was conducted by using a blisk specimen with random mistuning. NiCrAlY coating was deposited on blades with designed thickness, in accordance with the simulation results. It reveals to be an effective approach for reducing the vibration level of mistuned blisk, judging from the observed lower vibration response level after the intentional mistuning design by hard coating. The results of this paper can help to decrease the fatigue failure induced by mistuned vibration and improve the structure integrity and security of the blisk in aero-engine.

Effect of material parameter variability on vibroacoustic response in wood floors

The use of wood as construction material in multi-story buildings increased in Europe during the last decades. Wood buildings are more sensitive to dynamic loading compared to conventional concrete buildings, especially in terms of vibroacoustic comfort. Furthermore, it is more difficult to predict the accurate response due to dynamic loading for wood buildings. This is due to factors such as a complex structure involving many connections which vary in their mechanical behavior and the variability in the material parameters of wood. In the study, a reduced-order finite element model correlated to measurement data is used to examine the effect of experimentally obtained variability in material parameters on the vibroacoustic response of a wooden floor. The floor is subjected to surface loading. Monte Carlo simulations are conducted and in order to execute the probabilistic analysis in an efficient manner, the use of various sampling techniques is investigated. It was concluded that the variability in material parameters of wood significantly affects the predicted low-frequency vibrations, and thereby also affects the transmission of structure-borne sound.

A Schur-complement model-order-reduction technique for the finite element solution of transient elastohydrodynamic lubrication problems

The current work presents a reduced order finite element modeling framework for the solution of transient elastohydrodynamic lubrication (EHL) problems. The model order reduction technique is based on a Schur-complement method, applied to the elastic part within EHL problems. As such, it is exact and introduces no additional errors to the solution, with respect to the standard non-reduced finite element model. The technique reduces by one, the dimension of the linear elasticity part within the EHL problem. The use of the Schur-complement method however leads to a semi-dense Jacobian matrix. This is why the technique is complemented with a splitting procedure, allowing it to retrieve a standard finite-element-like sparsity pattern. In terms of computational performance, it is shown through a set of numerical experiments that the proposed reduced model offers a speed-up in computational times of the order of 15:1, compared to the equivalent full model, without any compromise on the accuracy of the solution.

Thermal modeling and efficiency of a dual-stage sodium heat engine

A thermal design of an axisymmetric dual-stage sodium thermal electrochemical converter (Na-TEC) is presented, where a reduced-order finite-element model is used in conjunction with a Na-TEC thermodynamic model to determine the total parasitic heat loss of this dual-stage design. A number of simplifications are applied in the reduced-order model to decrease the computational time while maintaining acceptable accuracy. These include the use of effective thermal conductivities to account for complex corrugated geometries and apparent surface emissivities to accommodate the effect of radiation shields. Furthermore, a simplified analytical model is developed to account for conduction bypass through the Na-TEC liquid-return path. An iterative procedure between the finite-element and thermodynamic models is described in detail, and the thermal performance of the design proposed herein is analyzed. According to this analysis, a maximum efficiency of 29% and a maximum power output of 125 W can be achieved.

Cross-linked fiberglass packs: Microstructure reconstruction and finite element analysis of the micromechanical behavior

An automated computational framework is introduced for simulating the micromechanical behavior of a fiberglass insulation pack with cross-linked fibers under compression. A new microstructure reconstruction algorithm is proposed that utilizes the NURBS representation of fiber geometries, together with statistical descriptors extracted from imaging data, to synthesize realistic microstructures by virtually packing fibers with the desired volume fraction, diameter distribution, and spatial orientations. Given the highly nonlinear micromechanical behavior of this nonwoven entangled material due to large deformations and contact-friction between fibers, a reduced-order finite element model is utilized to simulate its deformation response. In this approach, beam elements are used for modeling fibers, while a truss-shaped set of bushing-like connector elements are utilized to model binder particles that provide cross-linking between fibers. The accuracy of this model is verified through comparison with high-fidelity 3D simulations. Appropriate boundary conditions for simulating the mechanical behavior of microstructural models are then studied and the size of representative volume element (RVE) of the fiberglass pack is identified. The model is then employed to analyze the impacts of cross-linking and presence of fiber bundles in the microstructure on the deformation response of this materials system subject to a compressive load.

Geometric element parameterization and parametric model order reduction in finite element based shape optimization

This contribution proposes a new approach to derive geometrically parameterized, reduced order finite element models. An element formulation for geometrically parameterized finite elements is suggested. The parameterized elements are used to derive models with a parameterized geometry where the parameterized system matrices are expressed in an affine representation. Parametric model order reduction can then be efficiently used to reduce the full order parameterized model to a reduced order parameterized model. The approach shows two beneficial features. First, design studies and shape optimizations can be conducted with parameterized reduced order model of much lower dimension compared to the parameterized, full order model. Second, it is possible to compute sensitivities analytically, and therefore, to avoid the computation of finite differences gradients. The approach is illustrated with two numerical examples. The first example includes a detailed error analysis. The second example is a shape optimization example of an adaptive structure.