Academic literature on the topic 'Generalized Essential Matrix'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Generalized Essential Matrix.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Journal articles on the topic "Generalized Essential Matrix"
1
Birkenmeier, Gary F., and Donald D. Davis. "FI-extending generalized matrix rings." Journal of Algebra and Its Applications 19, no. 01 (February 27, 2019): 2050018. http://dx.doi.org/10.1142/s0219498820500188.
Full textAbstract:
Recall that a module [Formula: see text] is FI-extending if every fully invariant submodule is essential in a direct summand of [Formula: see text]. Let [Formula: see text] be a generalized matrix ring, where [Formula: see text] and [Formula: see text] are rings and [Formula: see text] and [Formula: see text] are bimodules. In this paper, we investigate necessary and/or sufficient conditions on [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for [Formula: see text] to be FI-extending.
2
Miraldo, Pedro, and Helder Araujo. "Generalized essential matrix: Properties of the singular value decomposition." Image and Vision Computing 34 (February 2015): 45–50. http://dx.doi.org/10.1016/j.imavis.2014.11.003.
Full text
3
Kim, Jun-Sik, and Takeo Kanade. "Degeneracy of the Linear Seventeen-Point Algorithm for Generalized Essential Matrix." Journal of Mathematical Imaging and Vision 37, no. 1 (February 12, 2010): 40–48. http://dx.doi.org/10.1007/s10851-010-0191-9.
Full text
4
Kumar, Ashim, Dijana Mosić, Predrag S. Stanimirović, Gurjinder Singh, and Lev A. Kazakovtsev. "Commuting Outer Inverse-Based Solutions to the Yang–Baxter-like Matrix Equation." Mathematics 10, no. 15 (August 2, 2022): 2738. http://dx.doi.org/10.3390/math10152738.
Full textAbstract:
This paper investigates new solution sets for the Yang–Baxter-like (YB-like) matrix equation involving constant entries or rational functional entries over complex numbers. Towards this aim, first, we introduce and characterize an essential class of generalized outer inverses (termed as {2,5}-inverses) of a matrix M, which commute with M. Towards this aim, first, we introduce and characterize an essential class of generalized outer inverses (termed as {2,5}-inverses) of a matrix, which commute with it. This class of {2,5}-inverses is defined based on resolving appropriate matrix equations and inner inverses. In general, solutions to such matrix equations represent optimization problems and require the minimization of corresponding matrix norms. We decided to analytically extend the obtained results to the derivation of explicit formulae for solving the YB-like matrix equation. Furthermore, algorithms for computing the solutions are developed corresponding to the suggested methods in some computer algebra systems. The main features of the proposed approach are highlighted and illustrated by numerical experiments.
5
Lindström, M., S. Miihkinen, and D. Norrbo. "Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces." Advances in Mathematics 408 (October 2022): 108598. http://dx.doi.org/10.1016/j.aim.2022.108598.
Full text
6
Ferjani, Imen, Aref Jeribi, and Bilel Krichen. "On relative essential spectra of a 3 x 3 operator matrix involving relative generalized weak demicompactness." Filomat 34, no. 13 (2020): 4271–86. http://dx.doi.org/10.2298/fil2013271f.
Full textAbstract:
In this paper, we investigate the relative essential spectra of a 3 x 3 block matrix operator with unbounded entries and with domain consisting of vectors satisfying certain relations between their components. Our results are formulated in term of relative generalized weak demicompactness and measure of non-strict-singularity.
7
Li, Songxiao, and Jizhen Zhou. "Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space." AIMS Mathematics 6, no. 4 (2021): 3305–18. http://dx.doi.org/10.3934/math.2021198.
Full text
8
Miraldo, Pedro, and João R. Cardoso. "On the Generalized Essential Matrix Correction: An Efficient Solution to the Problem and Its Applications." Journal of Mathematical Imaging and Vision 62, no. 8 (June 6, 2020): 1107–20. http://dx.doi.org/10.1007/s10851-020-00961-w.
Full textAbstract:
Abstract This paper addresses the problem of finding the closest generalized essential matrix from a given $$6\times 6$$ 6 × 6 matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not been addressed in the literature yet. Although it can be solved directly, it involves a large number of constraints, and any optimization method to solve it would require much computational effort. We start by deriving a couple of unconstrained formulations of the problem. After that, we convert the original problem into a new one, involving only orthogonal constraints, and propose an efficient algorithm of steepest descent type to find its solution. To test the algorithms, we evaluate the methods with synthetic data and conclude that the proposed steepest descent-type approach is much faster than the direct application of general optimization techniques to the original formulation with 33 constraints and to the unconstrained ones. To further motivate the relevance of our method, we apply it in two pose problems (relative and absolute) using synthetic and real data.
9
Wei, Jiao, Xianguo Geng, Xin Wang, and Yunyun Zhai. "Finite genus solutions of the generalized Merola–Ragnisco–Tu lattice hierarchy." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 083503. http://dx.doi.org/10.1063/5.0088138.
Full textAbstract:
Resorting to the zero-curvature equation and the Lenard recursion equations, the generalized Merola–Ragnisco–Tu lattice hierarchy associated with a 3 × 3 discrete matrix spectral problem is derived. With the aid of the characteristic polynomial of the Lax matrix for the generalized Merola–Ragnisco–Tu lattice hierarchy, a trigonal curve is defined, on which we construct the Baker–Akhiezer function, two meromorphic functions, three kinds of Abelian differentials, and Riemann theta function. By analyzing the asymptotic properties of the Baker–Akhiezer function and two meromorphic functions, especially their asymptotic expansions near three infinite points and three zero points, we obtain their essential singularities and divisors. Finally, we obtain the finite genus solutions of the generalized Merola–Ragnisco–Tu lattice hierarchy in terms of the Riemann theta function.
10
Tian, Yongge. "Characterizations of the group invertibility of a matrix revisited." Demonstratio Mathematica 55, no. 1 (January 1, 2022): 866–90. http://dx.doi.org/10.1515/dema-2022-0171.
Full textAbstract:
Abstract A square complex matrix A A is said to be group invertible if there exists a matrix X X such that A X A = A AXA=A , X A X = X XAX=X , and A X = X A AX=XA hold, and such a matrix X X is called the group inverse of A A . The group invertibility of a matrix is one of the fundamental concepts in the theory of generalized inverses, while group inverses of matrices have many essential applications in matrix theory and other disciplines. The purpose of this article is to reconsider the characterization problem of the group invertibility of a matrix, as well as the constructions of various algebraic equalities in relation to group invertible matrices. The coverage includes collecting and establishing a family of existing and new necessary and sufficient conditions for a matrix to be group invertible and giving many algebraic matrix equalities that involve Moore-Penrose inverses and group inverses of matrices through the skillful use of a series of highly selective formulas and facts about ranks, ranges, and generalized inverses of matrices, as well as block matrix operations.
Dissertations / Theses on the topic "Generalized Essential Matrix"
1
Kim, Jae-Hak, and Jae-Hak Kim@anu edu au. "Camera Motion Estimation for Multi-Camera Systems." The Australian National University. Research School of Information Sciences and Engineering, 2008. http://thesis.anu.edu.au./public/adt-ANU20081211.011120.
Full textAbstract:
The estimation of motion of multi-camera systems is one of the most important tasks in computer vision research. Recently, some issues have been raised about general camera models and multi-camera systems. Using many cameras as a single camera is studied [60], and the epipolar geometry constraints of general camera models is theoretically derived. Methods for calibration, including a self-calibration method for general camera models, are studied [78, 62]. Multi-camera systems are an example of practically implementable general camera models and they are widely used in many applications nowadays because of both the low cost of digital charge-coupled device (CCD) cameras and the high resolution of multiple images from the wide field of views. To our knowledge, no research has been conducted on the relative motion of multi-camera systems with non-overlapping views to obtain a geometrically optimal solution. ¶
In this thesis, we solve the camera motion problem for multi-camera systems by using linear methods and convex optimization techniques, and we make five substantial and original contributions to the field of computer vision. First, we focus on the problem of translational motion of omnidirectional cameras, which are multi-camera systems, and present a constrained minimization method to obtain robust estimation results. Given known rotation, we show that bilinear and trilinear relations can be used to build a system of linear equations, and singular value decomposition (SVD) is used to solve the equations. Second, we present a linear method that estimates the relative motion of generalized cameras, in particular, in the case of non-overlapping views. We also present four types of generalized cameras, which can be solvable using our proposed, modified SVD method. This is the first study finding linear relations for certain types of generalized cameras and performing experiments using our proposed linear method. Third, we present a linear 6-point method (5 points from the same camera and 1 point from another camera) that estimates the relative motion of multi-camera systems, where cameras have no overlapping views. In addition, we discuss the theoretical and geometric analyses of multi-camera systems as well as certain critical configurations where the scale of translation cannot be determined. Fourth, we develop a global solution under an L∞ norm error for the relative motion problem of multi-camera systems using second-order cone programming. Finally, we present a fast searching method to obtain a global solution under an L∞ norm error for the relative motion problem of multi-camera systems, with non-overlapping views, using a branch-and-bound algorithm and linear programming (LP). By testing the feasibility of LP at the earlier stage, we reduced the time of computation of solving LP.¶
We tested our proposed methods by performing experiments with synthetic and real data. The Ladybug2 camera, for example, was used in the experiment on estimation of the translation of omnidirectional cameras and in the estimation of the relative motion of non-overlapping multi-camera systems. These experiments showed that a global solution using L∞ to estimate the relative motion of multi-camera systems could be achieved.
2
Curto, Eva Raquel Belém. "Localização de cápsulas endoscópicas multi-câmara." Master's thesis, 2018. http://hdl.handle.net/10316/86660.
Full textAbstract:
Dissertação de Mestrado Integrado em Engenharia Electrotécnica e de Computadores apresentada à Faculdade de Ciências e TecnologiaDoenças do intestino delgado como a hemorragia Gastrointestinal obscura, a doeça de Crohn, adoença celíaca e tumores são difíceis de diagnosticar e tratar uma vez que as técnicas de endoscopiatradicionais provocam imensa dor e desconforto e não é possível visualizar toda a extensão dointestino delgado recorrendo a endoscópios com fios. Com a introdução no mercado da CápsulaEndoscópica Sem Fios começa a existir nos sistemas de saúde uma alternativa mais cómoda e eficazde analisar todo o canal GI. Tem havido várias tentativas por parte de empresas e investigadores deimplementar sistemas que localizem as cápsulas uma vez que ainda não existe nenhuma soluçãosuficientemente rigorosa.Esta dissertação tem como finalidade a localização de uma cápsula endoscópica, mais precisamenteda PillCam Colon 2, uma cápsula que possui duas câmaras dispostas nas extremidades. Nesteâmbito, procedeu-se à calibração das câmaras da cápsula, obtendo-se os seus parâmetros intrínsecos.Foram implementados em MatLab dois algoritmos distintos destinados a resolver problemas deestimação de movimento 6D que envolvam campos visuais não sobrepostos. Num dos algoritmos,o movimento é estimado individualmente a menos de um fator de escala para cada câmara e sódepois é considerada a ligação rígida entre as câmaras para a estimação da escala da translação. Jáno segundo algoritmo, para se estimar o movimento o sistema de câmaras é considerado como umtodo através do conceito de câmara generalizada. A propósito ainda deste último algoritmo sãoestudados em detalhe o tipo e o número de correspondências que se pode usar no caso em estudo.Os métodos implementados foram testados num ambiente simulado tendo sido também adicionadoruído de modo a testar a robustez destes caso se usassem imagens reais.Os métodos descritos na dissertação envolvem um conhecimento alargado sobre visão porcomputador, nomeadamente transformações rígidas, geometria epipolar, estimação da matrizessencial, câmaras generalizadas, coordenadas de Plücker, entre outros.
Diseases of the small intestine such as obscure gastrointestinal haemorrhage, Crohn’s disease, Celiacdisease and tumors are difficult to diagnose and treat since endoscopic techniques cause immensepain and discomfort, and it is not possible to visualize the full extent of the small intestine usingendoscopes with wires. With the introduction in market of the Wireless Capsule Ensoscope beginsto exist in health systems a more comfortable and effective alternative to analyze the entire GIchannel. There have been several attempts by companies and researchers to implement systemsthat locate the capsules since there is still no solution sufficiently rigorous.This dissertation aims to locate an capsule endoscope, more precisely of PillCam Colon 2, acapsule that has two cameras arranged at the ends. In this context, calibration of the capsulecameras was carried out, obtaining its intrinsic parameters. Were been implemented two differentalgorithms to solve 6D motion estimation involving non-overlapping visual fields. In one of thealgorithms, movement is estimated individually up to scale for each camera and the rigid connectionbetween the cameras only is considered for the estimation of the translation scale. In the secondalgorithm, to estimate the movement, the camera system is considered as a whole through theconcept of generalized camera. With regard to this last algorithm are studied in detail the type andnumber of correspondences that can be used in the case under study.The implemented methods were tested in a simulated environment having also been added noisein order to test their robustness in case of real images were used.The methods described in the dissertation involve a broad knowledge of computer vision, inparticular concepts of: rigid transformations, epipolar geometry, estimation of essential matrix,generalized cameras, Plücker coordinates, and others.
3
Kim, Jae-Hak. "Camera Motion Estimation for Multi-Camera Systems." Phd thesis, 2008. http://hdl.handle.net/1885/49364.
Full textAbstract:
The estimation of motion of multi-camera systems is one of the most important tasks in computer vision research. Recently, some issues have been raised about general camera models and multi-camera systems. Using many cameras as a single camera is studied [60], and the epipolar geometry constraints of general camera models is theoretically derived. Methods for calibration, including a self-calibration method for general camera models, are studied [78, 62]. Multi-camera systems are an example of practically implementable general camera models and they are widely used in many applications nowadays because of both the low cost of digital charge-coupled device (CCD) cameras and the high resolution of multiple images from the wide field of views. To our knowledge, no research has been conducted on the relative motion of multi-camera systems with non-overlapping views to obtain a geometrically optimal solution. ¶ In this thesis, we solve the camera motion problem for multi-camera systems by using linear methods and convex optimization techniques, and we make five substantial and original contributions to the field of computer vision. ...
Book chapters on the topic "Generalized Essential Matrix"
1
Haddad, Wassim M., and Sergey G. Nersesov. "Large-Scale Impulsive Dynamical Systems." In Stability and Control of Large-Scale Dynamical Systems. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153469.003.0010.
Full textAbstract:
This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.
2
Pawlowsky-Glahn, Vera, and Richardo A. Olea. "Introduction." In Geostatistical Analysis of Compositional Data. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195171662.003.0007.
Full textAbstract:
Geological data, notably geochemical data, often take the form of a regionalized composition. The concept of regionalized composition combines the concepts of composition and coregionalization. A composition, also known in the literature as a closed array (Chayes 1962), is a random vector whose components add up to a constant. A coregionalization is a set of two or more regionalized variables defined over the same spatial domain, which is modeled as a realization of a vector random function. Here the term regionalized composition is used both for the vector random function used to model a composition and for the realization that we can observe. A regionalized composition can be, for example, a heavy-mineral suite along a river valley. The minerals are quantitatively determined through frequency counts and represented as percent-proportions of the entire heavy-mineral occurrence. Another example is the set of grades in a lead-copper-zinc deposit. In this instance, all components of each specimen are not quantitatively recorded and the grades are also not expressed as proportions of the whole of the measured components: only a small fraction of the composition in ppm is accounted for in each specimen. The problem with the statistical analysis of compositions has been stated historically in terms of correlations: the covariances are subject to essential nonstochastic controls, i.e., distortions which are due to the constant-sum constraint. These numerically induced covariances and correlations arise also with regionalized compositions and are called spurious spatial correlations. They falsify the picture of the spatial covariance structure and can lead to misinterpretations. This problem arises not only when the whole regionalized composition is analyzed, but also when interest lies only in a subvector. A second problem, singularity of the covariance matrix of a composition, has generally been considered only from a numerical point of view. Singularity is a direct consequence of the constant-sum constraint and, as in other multivariate methods, it rules out the use of estimation techniques such as cokriging of all components. Numerically the problem can be tackled either by taking generalized inverses or, equivalently, leaving one component out to avoid singularity of the matrices of coefficients.
Conference papers on the topic "Generalized Essential Matrix"
1
Zhao, Ji, Wanting Xu, and Laurent Kneip. "A Certifiably Globally Optimal Solution to Generalized Essential Matrix Estimation." In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2020. http://dx.doi.org/10.1109/cvpr42600.2020.01205.
Full text
2
Arias Ortiz, Daniela, Nabila Bounceur, and Tadeusz W. Patzek. "Validation and Analysis of the Physics-Based Scaling Curve Method for Ultimate Recovery Prediction in Hy-Draulically Fractured Shale Gas Wells." In SPE Annual Technical Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/210350-ms.
Full textAbstract:
Abstract Patzek et al. (2013, 2014) proposed the generalized physics-based scaling curve method as an alternative approach to the empirical decline curve analysis that predicted shale gas well production. Independently, (Patzek, 2019; Patzek et al., 2019) also introduced the Generalized Extreme Value statistics to evaluate cohorts of shale wells and their survival rates. In this work, we built a conceptual reservoir model of a typical, hydraulically fractured well in the northeast Pennsylvania Marcellus shale using a commercial reservoir simulator (CMG-GEM) to validate the generalized master curve numerically. We use the simulated gas production as the input data to estimate the generalized reservoir scaling curve, and we compare it to the master curve presented in Saputra et al. (2022). Our results reveal that the physical scaling method captures the physics behind gas production from mudrock plays. Our reservoir simulations agree with the master curve. We conclude that the simple method is an excellent alternative to the current industrial forecasting methods as it is computationally cost-effective, more flexible, and requires fewer input data. Also, the numerical reservoir simulations confirm the behavior of the generalized scaling curve with the variation of selected input factors. We complemented this study by conducting a global sensitivity analysis (GSA) to systematically examine the impacts of hydraulic fracture half-length and spacing, unstimulated shale permeability and gas adsorption on the variations of two master curve scaling parameters, the gas mass in the stimulated reservoir volume (MSRV), and the characteristic pressure interference time (τ). GSA using a reservoir simulator is prohibitive. Therefore, we implement and validate a Gaussian process emulator that represents probabilistically the scaling parameters estimated from the reservoir simulation output. We calibrate the emulator with a small set of experiments sampled with a space-filling design. The conducted study provides new insights into the relationship between the production scaling variables MSRV and τ and the reservoir parameters. The results reveal the high importance and nonlinear effects of the hydraulic fracture height, half-length, maximum gas volume adsorbed, and matrix porosity in varying the scaling variable MSRV. Also, the unstimulated matrix permeability and the hydraulic fracture spacing contribute significantly to nonlinear variations of the scaling variable, τ. Finally, gas adsorption has a small effect on the cumulative gas produced but significantly affects the scaling factor MSRV. Thus, gas adsorption becomes essential when estimating the ultimate recovery factor in the Marcellus shale wells.
3
Rao, Singiresu S. "Meshless Local Petrov-Galerkin Method for Heat Transfer Analysis." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64554.
Full textAbstract:
A meshless local Petrov-Galerkin (MLPG) method is proposed to obtain the numerical solution of nonlinear heat transfer problems. The moving least squares scheme is generalized, to construct the field variable and its derivative continuously over the entire domain. The essential boundary conditions are enforced by the direct scheme. The radiation heat transfer coefficient is defined, and the nonlinear boundary value problem is solved as a sequence of linear problems each time updating the radiation heat transfer coefficient. The matrix formulation is used to drive the equations for a 3 dimensional nonlinear coupled radiation heat transfer problem. By using the MPLG method, along with the linearization of the nonlinear radiation problem, a new numerical approach is proposed to find the solution of the coupled heat transfer problem. A numerical study of the dimensionless size parameters for the quadrature and support domains is conducted to find the most appropriate values to ensure convergence of the nodal temperatures to the correct values quickly. Numerical examples are presented to illustrate the applicability and effectiveness of the proposed methodology for the solution of heat transfer problems involving radiation with different types of boundary conditions. In each case, the results obtained using the MLPG method are compared with those given by the FEM method for validation of the results.
4
Bhagwan, Robbin, Alexander Schwagerus, Christof Weis, Peter Habisreuther, Nikolaos Zarzalis, Michael Huth, Berthold Koestlin, and Stefan Dederichs. "Combustion Characteristics of Natural Gas Fueled, Premixed Turbulent Jet Flame Arrays Confined in a Hexagonal Combustor." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90286.
Full textAbstract:
Abstract In order to extend the operation regime of existing gas turbine combustion systems to lower the minimum loads, the applicability of matrix burners (arrays of jet flames) as an alternative to conventional swirl stabilized burners has been considered. In comparison to well-studied single jet flame systems, the effects of geometry and thermodynamic parameters on characteristics of matrix burner systems have not been studied in detail. Information, which is essential for design processes e.g. scaling of matrix burners, is not yet available in public domain. This work involves a systematic investigation of a matrix burner system operating at highly turbulent flow conditions (Reynolds Number ≈ 20000) prevailing in gas turbine combustion systems. In order to understand the effects of geometrical scaling, three variants of jet diameter have been investigated. A detailed test campaign including lean blow out limits detection, velocity field measurement and hydroxyl radical (OH*) chemiluminescence recording has been conducted. Influence of variation in stoichiometry and exit velocity of fuel-air mixture has been captured. The results show that it is possible to generalize the scaling of the matrix burner using the well-known Peclet criterion.
5
Strawbridge, Zeke, Daniel A. McAdams, and Robert B. Stone. "A Computational Approach to Conceptual Design." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dtm-34001.
Full textAbstract:
Design research has generated many computational tools to aid the designer over the years. Most of these tools are focused on either the preliminary steps of customer need gathering or the concluding steps of embodiment or detail design. The conceptual design phase has seen fewer computational tools even though well known methods are available such as brainstorming, intrinsic and extrinsic searches and morphological analysis. In this paper a generalized computational conceptual design tool is presented to aid designers at the conceptual design stage. It relies on storing and reusing existing design knowledge to create new concept variants. Concept variants are computed using matrix manipulations, essentially creating a mathematical morphological matrix. The concept generator produces quick concepts that can be used for concept selection or as a basis for generating additional concept variants through non-computational, creative techniques.
6
Hettiger, Christof. "Applied Structural Simulation in Railcar Design." In 2017 Joint Rail Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/jrc2017-2330.
Full textAbstract:
Fifty years ago, the railcar industry relied entirely on classical analysis methods using fundamental solid mechanics theory to establish design and manufacturing protocols. While this method produced working designs, the assumptions required by this type of analysis often led to overdesigned railcars. In the 1950s, the generalized mathematical approach of Finite Element Analysis (FEA) was developed to model the structural behaviors of mechanical systems. FEA involves creating a numerical model by discretizing a continuous system into a finite system of grid divisions. Each grid division, or element, has an inherent geometric shape and each element is comprised of points which are referred to as nodes. The connected pattern of nodes and elements is called a mesh. A solver organizes the mesh into a matrix of differential equations and computes the displacements using linear algebraic operations from which strains and stresses are obtained. The rapid development of computing technology provided the catalyst to drive FEA from research into industry. FEA is currently the standard approach for improving product design cycle times that were previously achieved by trial and error. Moreover, simulation has improved design efficiency allowing for greater advances in weight, strength, and material optimization. While FEA had its roots planted in the aerospace industry, competitive market conditions have driven simulation into many other professional fields of engineering. For the last few decades, FEA has become essential to the submittal of new railcar designs for unrestricted interchange service across North America. All new railcar designs must be compliant to a list of structural requirements mandated by the Association of American Railroads (AAR), which are listed in its MSRP (Manual of Standards and Recommended Practices) in addition to recommended practices in Finite Element (FE) modeling procedures. The MSRP recognizes that these guidelines are not always feasible to completely simulate, allowing the analyst to justify situations where deviations are necessary. Benefits notwithstanding, FEA has inherent challenges. It is understood that FEA does not provide exact solutions, only approximations. While FEA can provide meaningful insight into actual physical behavior leading to shorter development times and lower costs, it can also create bogus solutions that lead to potential safety and engineering risks. Regardless of how appropriate the FEA assumptions may be, engineering judgment is required to interpret the accuracy and significance of the results. A constant balance is made between model fidelity and computational solve time. The purpose of this paper is to discuss the FEA approach to railcar analysis that is used by BNSF Logistics, LLC (BNSFL) in creating AAR compliant railcar designs. Additionally, this paper will discuss the challenges inherent to FEA using experiences from actual case studies in the railcar industry. These challenges originate from assumptions that are made for the analysis including element types, part connections, and constraint locations for the model. All FEA terminology discussed in this paper is written from the perspective of an ANSYS Mechanical user. Closing remarks will be given about where current advances in FEA technology may be able to further improve railcar industry standards.
7
Ortner, Susan R. "A Microstructure-Based Probabilistic Model for Cleavage in RPV Steels." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93678.
Full textAbstract:
In both simple ferrite-carbide materials, and more complex ferritic steels, cleavage is mediated by the fracture of the particles they contain. If particle cracking is easy, then extension of the resulting particle-sized microcracks into the ferrite matrix, can become the critical step in inducing fracture. Under these circumstances, brittle fracture is essentially stress-controlled, and several models use this as a basis for failure prediction. Fracture toughness data from a series of MnMoNi steels are presented, together with observations of fracture initiation sites, and calculations of the stresses and strains pertaining to these locations at failure, to show that there are circumstances under which particle cracking is not easy. A strain criterion is found to describe the probability of particle cracking effectively. A previously-published, stress-based model is generalised to include the strain criterion. The more general model correlates initiation site properties with K, and predicts a marked temperature-dependence of K (i.e. a ductile-to-brittle transition), even though the only temperature-dependent input parameters are the flow properties. Other input parameters for the model are linked explicitly to the microstructure. The relative dominance of particle cracking and microcrack extension in cleavage depends most strongly on initiating particle type, and final quench severity.