Fast Finite Element Model Research Articles

Finite Element Model Updating for Improved Box Girder Bridges with Corrugated Steel Webs Using the Response Surface Method and Fmincon Algorithm

We propose a practical and fast finite element (FE) model updating method in which the response surface method and fmincon algorithm (FA) are used to modify the FE model of a new, improved box girder bridge with corrugated steel webs. Two three-dimensional FE bridge design models were compared to develop a reasonable initial FE model for updating this bridge. The response surface method (RSM) was used in our method for the optimal experimental design of the updated parameters, which were used as the basis of the numerical analyses performed to obtain the explicit relationships between the structural responses from the FE results and the parameters themselves. A comparison of the two optimisation methods — genetic algorithm and FA — revealed that FA provides more stable optimised results with higher efficiency. Using FA, parameters can be updated by minimising an objective function, which is constructed from residuals between measured and predicted structural responses using the expressed relationships. A numerical example of a simply supported composite girder was discussed to illustrate the effectiveness of our procedure. The method was applied to the FE model updating of the Jingzhong Bridge using in situ static and dynamic results; satisfactory agreement was observed between measured and predicted bridge responses.

A machine learning approach for magnetic resonance image-based mouse brain modeling and fast computation in controlled cortical impact.

Computational modeling of the brain is crucial for the study of traumatic brain injury. An anatomically accurate model with refined details could provide the most accurate computational results. However, computational models with fine mesh details could take prolonged computation time that impedes the clinical translation of the models. Therefore, a way to construct a model with low computational cost while maintaining a computational accuracy comparable with that of the high-fidelity model is desired. In this study, we constructed magnetic resonance (MR) image-based finite element (FE) models of a mouse brain for simulations of controlled cortical impact. The anatomical details were kept by mapping each image voxel to a corresponding FE mesh element. We constructed a super-resolution neural network that could produce computational results of a refined FE model with a mesh size of 70μm from a coarse FE model with a mesh size of 280μm. The peak signal-to-noise ratio of the reconstructed results was 33.26dB, while the computational speed was increased by 50-fold. This proof-of-concept study showed that using machine learning techniques, MR image-based computational modeling could be applied and evaluated in a timely fashion. This paved ways for fast FE modeling and computation based on MR images. Results also support the potential clinical applications of MR image-based computational modeling of the human brain in a variety of scenarios such as brain impact and intervention.Graphical abstract MR image-based FE models with different mesh sizes were generated for CCI. The training and testing data sets were computed with 5 different impact locations and 3 different impact velocities. High-resolution strain maps were estimated using a SR neural network with greatly reduced computational cost.

Computationally Efficient Strand Eddy Current Loss Calculation in Electric Machines

A fast finite element (FE) based method for the calculation of eddy current losses in the stator windings of randomly wound electric machines is presented in this paper. The method is particularly suitable for implementation in large-scale design optimization algorithms where a qualitative characterization of such losses at higher speeds is most beneficial for identification of the design solutions that exhibit the lowest overall losses including the ac losses in the stator windings. Unlike the common practice of assuming a constant slot fill factor s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> for all the design variations, the maximum s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> in the developed method is determined based on the individual slot structure/dimensions and strand wire specifications. Furthermore, in lieu of detailed modeling of the conductor strands in the initial FE model, which significantly adds to the complexity of the problem, an alternative rectangular coil modeling subject to a subsequent flux mapping technique for determination of the impinging flux on each individual strand is pursued. Rather than pursuing the precise estimation of ac conductor losses, the research focus of this paper is placed on the development of a computationally efficient technique for the derivation of strand eddy current losses applicable in design optimization, especially where both the electromagnetic and thermal machine behavior are accounted for. A fractional-slot concentrated winding permanent magnet synchronous machine is used for the purpose of this study due to the higher slot leakage flux and slot opening fringing flux of such machines, which are the major contributors to strand eddy current losses in the windings. The analysis is supplemented with an investigation on the influence of the electrical loading on ac winding loss effects for this machine design, a subject that has received less attention in the literature. Experimental ac loss measurements on a 12-slot 10-pole stator assembly will be discussed to verify the existing trends in the simulation results.

Fast Finite Element Analysis Method Using Multiple GPUs for Crustal Deformation and its Application to Stochastic Inversion Analysis with Geometry Uncertainty

Crustal deformation computation using 3-D high-fidelity models has been in heavy demand due to accumulation of observational data. This approach is computationally expensive and more than 105 repetitive computations are required for various application including Monte Carlo simulation, stochastic inverse analysis, and optimization. To handle the massive computation cost, we develop a fast Finite Element (FE) analysis method using multi-GPUs for crustal deformation. We use algorithms appropriate for GPUs and accelerate calculations such as sparse matrix-vector product. By reducing the computation time, we are able to conduct multiple crustal deformation computations in a feasible timeframe. As an application example, we conduct stochastic inverse analysis considering uncertainties in geometry and estimate coseismic slip distribution in the 2011 Tohoku Earthquake, by performing 360,000 crustal deformation computations for different 8 × 107 DOF FE models using the proposed method.

Fast and robust Matlab-based finite element model used in the layup optimization of composite laminates

The layup optimization of the laminated composites is a very complex topic which involves a convoluted solution space usually explored using heuristic computational techniques. Due to the solution space complexity a lot of layup configurations are evaluated during the optimization process. This fact leads to the mandatory requirement that the configuration evaluation should be fast enough to ensure the convergence of the optimization procedure without sacrificing the accuracy. In this work, we propose a robust, accurate and very fast finite element model based on the first-order shear deformation theory (FSDT). The model is structured in three main parts: preprocessing, processing and post processing. The main strategy is to transfer as much as possible operations in the preprocessing phase which is executed only once and to subsequently reuse the results in the processing and post processing phases which are executed for each layup configuration. Using this strategy, the execution time of the processing and post processing phases is drastically reduced and almost consists of regenerating and solving the global linear system - more that 95%. The proposed procedure is relatively easy to implement in Matlab which holds a very powerful linear system solver for sparse matrices. Also, the accuracy of the model was demonstrated by comparison with Ansys and with some closed form solutions.

A finite element parametric modeling technique of aircraft wing structures

A finite element parametric modeling method of aircraft wing structures is proposed in this paper because of time-consuming characteristics of finite element analysis pre-processing. The main research is positioned during the preliminary design phase of aircraft structures. A knowledge-driven system of fast finite element modeling is built. Based on this method, employing a template parametric technique, knowledge including design methods, rules, and expert experience in the process of modeling is encapsulated and a finite element model is established automatically, which greatly improves the speed, accuracy, and standardization degree of modeling. Skeleton model, geometric mesh model, and finite element model including finite element mesh and property data are established on parametric description and automatic update. The outcomes of research show that the method settles a series of problems of parameter association and model update in the process of finite element modeling which establishes a key technical basis for finite element parametric analysis and optimization design.

Accurate and Fast Finite-Element Modeling of Attenuation in Slow-Wave Structures for Traveling-Wave Tubes

This paper presents a novel 3-D finite-element modeling technique for the arbitrary lossy slow-wave structure (SWS) of a traveling-wave tube (TWT). By using this technique, we can accurately and quickly calculate not only dielectric losses but also conductivity losses of the SWS. In this modeling technique, a new frequency-specified eigenmode analysis (FSEA) for SWSs is proposed and utilized. Unlike the traditional phase-advance-specified eigenmode analysis for SWSs, which has to solve a nonlinear generalized eigenvalue problem (GEP), the new FSEA approach only needs to solve a linear GEP and is capable of obtaining the attenuation constant more accurately and directly without any postprocessing when simulating the lossy SWSs. Moreover, to further significantly improve the efficiency of modeling lossy SWSs, three advanced techniques are introduced in the standard implicit restarted Arnoldi method (IRAM) and an improved inexact IRAM is proposed. By simulating many practical SWSs, the accuracy and highly efficient performance of this modeling technique have been validated. It is shown that this modeling technique would be very useful to design a low-loss SWS for high-efficiency TWTs.

Finite element analysis of linear boundary value problems with geometrical parameters

PurposeThe purpose of this paper is to enable fast finite element (FE) analysis of electromagnetic structures with multiple geometric design variables.Design/methodology/approachThe proposed methodology combines multi‐variable model‐order reduction with mesh perturbation techniques and polynomial interpolation of parameter‐dependent FE matrices.FindingsThe resulting reduced‐order models are of comparable accuracy as but much smaller size than the original FE systems and preserve important system properties such as reciprocity.Research limitations/implicationsThe method is limited to mesh variations that are obtained from a nominal discretization by continuous deformation. Topological changes in the mesh are not permissible.Practical implicationsIn contrast to the underlying FE models, the resulting reduced‐order systems are very cheap to analyze. Possible applications include parametric libraries, design optimization, and real‐time control.Originality/valueThe paper extends the scope of moment‐matching order‐reduction techniques to a class of non‐polynomial systems arising from FE models with geometric parameters.

A methodology for fast finite element modeling of electrostatically actuated MEMS

AbstractIn this paper, a methodology is proposed for expediting the coupled electro‐mechanical finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by using an approximation of the charge density on the movable electrode in the deformed geometry in terms of the charge density in the non‐deformed geometry and displacements of the movable electrode. The electrostatic problem has to be solved only once and thus this method speeds up the coupled electro‐mechanical simulation process. The proposed methodology is demonstrated through its application to the modeling of four MEMS devices with varying length‐to‐gap ratios, multiple dielectrics and complicated geometries. Its accuracy is assessed through comparisons of its results with results obtained using both analytical solutions and finite element solutions obtained using ANSYS. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Deformable modelling of the cervical spine for neurosurgical navigation

Surgical intervention at the cervical spine is one of the most difficult interventions in surgery. Special care must be taken to the sensitive anatomy around, e.g., the trachea, oesophagus, arteries and spinal nerves. This paper presents a novel approach in neurosurgical navigation which takes into account these structures in the cervical region by calculating continuously the soft tissue's deformation during the neurological intervention. We use a fast finite element model (FFEM) for the functional modelling of the cervical spine and a graphical deformation algorithm for the surrounding.

Robust multigrid preconditioner for fast finite element modeling of microwave devices

A robust preconditioning technique is presented for the fast finite element modeling of microwave devices. The proposed preconditioner is based on a multigrid scheme for the vector-scalar potential finite element formulation of electromagnetic problems. Numerical experiments from the application of the new preconditioner to the finite element analysis of microwave devices are used to demonstrate its superior numerical convergence and efficient memory usage.

Virtual reality for dermatologic surgery: Virtually a reality in the 21st century

In the 20th century, virtual reality has predominantly played a role in training pilots and in the entertainment industry. Despite much publicity, virtual reality did not live up to its perceived potential. During the past decade, it has also been applied for medical uses, particularly as training simulators, for minimally invasive surgery. Because of advances in computer technology, virtual reality is on the cusp of becoming an effective medical educational tool. At the University of Washington, we are developing a virtual reality soft tissue surgery simulator. Based on fast finite element modeling and using a personal computer, this device can simulate three-dimensional human skin deformations with real-time tactile feedback. Although there are many cutaneous biomechanical challenges to solve, it will eventually provide more realistic dermatologic surgery training for medical students and residents than the currently used models. (J Am Acad Dermatol 2000;42:106-12.)

Creating fast finite element models from medical images.

The procedure for creating a patient-specific virtual tissue model with finite element (FE) based haptic (force) feedback varies substantially from that which is required for generating a typical volumetric model. In addition to extracting geometrical and texture map data to provide visual realism, it is necessary to obtain information for supporting a FE model. Among many differences, FE-based VR environments require a FE model with appropriate material properties assigned. The FE equation must also be processed in a manner specific to the surgical task in order to maximize deformation and haptic computation speed. We are currently developing methodologies and support software for creating patient-specific models from medical images. The steps for creating such a model are as follows: 1) obtain medical images and texture maps of tissue structures; 2) extract tissue structure contours; 3) generate a 3D mesh from the tissue structure contours; 4) alter mesh based on simulation objectives; 5) assign material properties, boundary nodes and texture maps; 6) generate a fast (or real-time) FE model; and 7) support the tissue models with task-specific tools and training aids. This paper will elaborate on the above steps with particular reference to the creation of suturing simulation software, which will also be described.

Fast finite element modeling for surgical simulation.

Given the geometric complexity of anatomical structures, realistic real-time deformation of graphical reconstructions is prohibitively computationally intensive. Instead, real-time deformation of virtual anatomy is roughly approximated through simpler methodologies. Since the graphical interpolations and simple spring models commonly used in these simulations are not based on the biomechanical properties of tissue structures, these "quick and dirty" methods typically do not accurately represent the complex deformations and force-feedback interactions that can take place during surgery. Finite element (FE) analysis is widely regarded as the most appropriate alternative to these methods. Extensive research has been directed toward applying the method to modeling a wide range of biological structures, and a few simple FE models have been incorporated into surgical simulations. However, because of the highly computational nature of the FE method, its direct application to real-time force-feedback and visualization of tissue deformation has not been practical for most simulations. This limitation is primarily due to the overabundance of information provided by the standard FE approaches. If the mathematics is optimized to yield only the information essential for the surgical task, computation time can be drastically reduced. Parallel computation and preprocessing of the model before the simulation begins can also reduce the size of the problem and greatly increase computation speed. Such methodologies are being developed in a combined effort between the Human Interface Technology Laboratory (HIT Lab) and the Mechanical Engineering Department of the University of Washington. We have created computer demonstrations which support real-time interaction with simple finite element soft tissue models. In collaboration with the Division of Dermatology, a real-time skin surgery simulator is being developed using these fast FE methods.

Finite element modeling in surgery simulation

Modeling the deformation of human organs for surgery simulation systems has turned out to be quite a challenge. Not only is very little known about the physical properties of general human tissue but in addition, most conventional modeling techniques are not applicable because of the timing requirements of simulation systems. To produce a video-like visualization of a deforming organ, the deformation must be determined at rates of 10-20 times/s. In the fields of elasticity and related modeling paradigms, the main interest has been the development of accurate mathematical models. The speed of these models has been a secondary interest. But for surgery simulation systems, the priorities are reversed. The main interest is the speed and robustness of the models, and accuracy is of less concern. Recent years have seen the development of different practical modeling techniques that take into account the reversed priorities and can be used in practice for real-time modeling of deformable organs. The paper discusses some of these new techniques in the reference frame of finite element models. In particular, it builds on the recent work by the author on fast finite element models and discusses the advantages and disadvantages of these models in comparison to previous models.