Relevant bibliographies by topics / Elastic boundary condition

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Elastic boundary condition'

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Published: 12 April 2025

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Journal articles on the topic "Elastic boundary condition"

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Randall, C. J. "Absorbing boundary condition for the elastic wave equation." GEOPHYSICS 53, no. 5 (May 1988): 611–24. http://dx.doi.org/10.1190/1.1442496.

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Extant absorbing boundary conditions for the elastic wave equation are generally effective only for waves nearly normally incident upon the boundary. High reflectivity is exhibited for waves traveling obliquely to the boundary. In this paper, a new and efficient absorbing boundary condition for two‐dimensional and three‐dimensional finite‐difference calculations of elastic wave propagation is presented. Compressional and shear components of the incident vector displacement fields are separated by calculating intermediary scalar potentials, allowing the use of Lindman’s boundary condition for scalar fields, which is highly absorbing for waves incident at any angle. The elastic medium is assumed to be homogeneous in the region immediately adjacent to the boundary. The reflectivity matrix of the resulting absorbing boundary for elastic waves is calculated, including the effects of finite‐difference truncation error. For effectively all angles of incidence, reflectivities are much smaller than those of the commonly employed paraxial absorbing boundaries, and the boundary condition is stable for any physical Poisson’s ratio. The nearly complete absorption predicted by the reflectivity matrix calculations, even at near grazing incidence, is demonstrated in a finite‐difference application.
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Zhao, Zhencong, Jingyi Chen, Xiaobo Liu, and Baorui Chen. "Frequency-domain elastic wavefield simulation with hybrid absorbing boundary conditions." Journal of Geophysics and Engineering 16, no. 4 (August 1, 2019): 690–706. http://dx.doi.org/10.1093/jge/gxz038.

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Abstract The frequency-domain seismic modeling has advantages over the time-domain modeling, including the efficient implementation of multiple sources and straightforward extension for adding attenuation factors. One of the most persistent challenges in the frequency domain as well as in the time domain is how to effectively suppress the unwanted seismic reflections from the truncated boundaries of the model. Here, we propose a 2D frequency-domain finite-difference wavefield simulation in elastic media with hybrid absorbing boundary conditions, which combine the perfectly matched layer (PML) boundary condition with the Clayton absorbing boundary conditions (first and second orders). The PML boundary condition is implemented in the damping zones of the model, while the Clayton absorbing boundary conditions are applied to the outer boundaries of the damping zones. To improve the absorbing performance of the hybrid absorbing boundary conditions in the frequency domain, we apply the complex coordinate stretching method to the spatial partial derivatives in the Clayton absorbing boundary conditions. To testify the validity of our proposed algorithm, we compare the calculated seismograms with an analytical solution. Numerical tests show the hybrid absorbing boundary condition (PML plus the stretched second-order Clayton absorbing condition) has the best absorbing performance over the other absorbing boundary conditions. In the model tests, we also successfully apply the complex coordinate stretching method to the free surface boundary condition when simulating seismic wave propagation in elastic media with a free surface.
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Keller, Joseph B., and Marcus J. Grote. "Exact Nonreflecting Boundary Condition For Elastic Waves." SIAM Journal on Applied Mathematics 60, no. 3 (January 2000): 803–19. http://dx.doi.org/10.1137/s0036139998344222.

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Taylor, Adam G., and Jae H. Chung. "Analysis of tangential contact boundary value problems using potential functions." Royal Society Open Science 6, no. 3 (March 2019): 182106. http://dx.doi.org/10.1098/rsos.182106.

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This paper presents an analysis technique of high-order contact potential problems and its application to an elastic settlement analysis of a shallow foundation system subjected to a combined traction boundary condition. Closed-form solutions of potential functions are derived for an elastic half-space subjected to bilinear tangential traction boundary conditions over rectangular surface regions. Using the principle of superposition, the present solutions provide a means to form an approximate and continuous solution of elastic contact problems with higher-order tangential boundary conditions. As an application example, an elastic settlement analysis of a rigid footing founded on a dense granular soil is performed under a tangential traction boundary condition prescribed in an analogy with the stress equilibrium states of static sandpiles. A generalized solution approach to combined normal and tangential traction boundary value problems is discussed in the context of foundation engineering.
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LANGE, A., J. ZHOU, and N. SAFFARI. "OPTIMISED ABSORBING BOUNDARY CONDITIONS FOR ELASTIC-WAVE PROPAGATION." Journal of Computational Acoustics 09, no. 03 (September 2001): 1005–14. http://dx.doi.org/10.1142/s0218396x01001091.

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Second-order absorbing boundary conditions for numerical modeling of elastic-wave propagation are studied. The corresponding reflection coefficients are derived, from which a necessary and sufficient condition for complete absorption at normal incidence is deduced. We define a family of absorbing boundary conditions from symmetrically specified zero reflection incidences. Conditions to avoid singular reflection coefficients are given for this case, these ensure that the solutions of the elastic wave equation also satisfy the boundary conditions. These are then optimised over a wide range of materials, and absorbing boundary conditions that give an efficient absorption for the whole range are obtained. We also compare the results with absorbing boundary conditions developed from the least-squares solution of the system requiring complete absorption at all incidences. The best set of conditions are presented and compared with Clayton and Engquist6 (A2) condition.
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Peng, Chengbin, and M. Nafi Toksöz. "An optimal absorbing boundary condition for elastic wave modeling." GEOPHYSICS 60, no. 1 (January 1995): 296–301. http://dx.doi.org/10.1190/1.1443758.

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Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.
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Yin, Yuhan, and Juan Liu. "Hybrid Method for Inverse Elastic Obstacle Scattering Problems." Mathematics 11, no. 8 (April 20, 2023): 1939. http://dx.doi.org/10.3390/math11081939.

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The problem of determining the shape of an object from knowledge of the far-field of a single incident wave in two-dimensional elasticity was considered. We applied an iterative hybrid method to tackle this problem. An advantage of this method is that it does not need a forward solver, and therefore, the exact boundary condition is not essential. By deriving the Fréchet derivatives of two boundary operators, we established reconstruction algorithms for objects with Dirichlet, Neumann, and Robin boundary conditions; by introducing a general boundary condition, we also established the reconstruction algorithm for objects with unknown physical properties. Numerical experiments showed the effectiveness of the proposed method.
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Ben-Haim, Yakov, and H. G. Natke. "Sequential Adaptation in Estimating Elastic Boundary-Condition Influence Matrices." Journal of Dynamic Systems, Measurement, and Control 115, no. 3 (September 1, 1993): 370–78. http://dx.doi.org/10.1115/1.2899112.

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A method is discussed for adaptive estimation of the boundary-condition influence matrix of a linear elastic system, based on modal measurements (eigenvalues and eigenvectors) and on knowledge of the influence matrix of the system with respect to reference boundary conditions. The estimation is terminated adaptively by an algorithm motivated by the concept of sequential analysis. The boundary-condition influence matrix is re-estimated with measurement of each additional mode, until a termination criterion indicates that adequate accuracy has been attained. The advantage of adaptive termination of the estimation is the enhanced computational (and possibly instrumental) efficiency of estimating with minimal modal data. An analytical technique for comparing the adaptive termination with a reasonable non-adaptive method has been developed and demonstrated by application to a uniform beam. When uncertainty in the boundary conditions is represented by convex models, it is shown that the adaptive estimation can terminate much earlier than the non-adaptive procedure.
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Mittet, Rune. "Implementation of the Kirchhoff integral for elastic waves in staggered‐grid modeling schemes." GEOPHYSICS 59, no. 12 (December 1994): 1894–901. http://dx.doi.org/10.1190/1.1443576.

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Implementation of boundary conditions in finite‐difference schemes is not straightforward for the elastic wave equation if a staggered grid formulation is used. Reverse time migration of VSP data requires a proper description of the recording surface so as not to excite false P‐ and S‐waves. Such contributions may cause artifacts in the imaging procedure. The boundary conditions for the elastic stress tensor can be implemented numerically in a staggered coarse grid modeling scheme by using band‐limited spatial delta‐functions and band‐limited first‐order derivatives of these spatial delta‐functions. A representation theorem for elastic waves is derived to test the implementation of the spatial part of the boundary condition. The implementation is tested in a 2-D numerical experiment for a closed, but curved, boundary S enclosing a volume V. The test condition is that within the volume V, the difference between the forward modeled field and the retropropagated field should be equal to zero. Both P‐ and S‐waves are properly recovered in a 2-D reverse time modeling example. The numerical artifacts related to the proposed spatial approximation of the boundary condition are found to be negligible.
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Yurchuk, V. M., and S. V. Sinchilo. "Torsional elastic waves. Some aspects of nonlinear analysis." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 2 (2023): 172–75. http://dx.doi.org/10.17721/1812-5409.2023/2.31.

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The features of the use of boundary conditions in the nonlinear problem of torsional wave propagation for an elastically deformable medium with an external boundary are analyzed. The formulation and wave analysis in the linear (classical) approach are briefly described, since the linear solution is used in the work as a first approximation in the nonlinear approach. The first feature for a torsional wave is a significant complication in the nonlinear approach of the boundary conditions due to the difference between the shape of the boundary before and after the deformation (in the linear approach, the shape of the boundary does not change). The second feature is the significant complication of the mathematical representation of the boundary conditions due to the appearance of additional nonlinear terms. For a torsional wave, it was found that the use of the condition of absence of stresses on the boundary surface (assumption of a free boundary) may not be completely correct.
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Dissertations / Theses on the topic "Elastic boundary condition"

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Khatla, Wissem-Eddine. "Écoulements modèles de films minces géo-inspirés : étalement et coalescence de cloques visqueuses." Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLS060.

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Dans ce projet, nous proposons une série d’expériences modèles à l’échelle du laboratoire pour explorer la dynamiqueet les instabilités des films liquides minces inspirés par la géophysique.Nous étudions des phénomènes similaires aux laccolithes, où l’écoulement de magma déforme les couches rocheusesenvironnantes. Dans la limite où leur hauteur h est très faible devant leur taille horizontale R, ces formations dynamiquespeuvent être raisonnablement comparées à des cloques liquides minces recouvertes d’un film élastique. Nous proposonsainsi de revisiter les expériences classiques de la dynamique de gouttes en surface libre en modifiant la condition limiteimposée par la nature de l’interface.Nous tenterons de répondre à plusieurs questions relatives à cette configuration.Quelle est la forme et la dynamique d’une poche de fluide piégée sous une membrane élastique ? Comment se dé-roule la coalescence de deux poches voisines avec cette nouvelle condition limite ? Comment les régimes dynamiquesd’étalement en sont-ils affectés ?Pour répondre à ces questions, nous avons mis en place un dispositif expérimental afin d’observer et de caractériser cephénomène d’étalement en utilisant des techniques de démodulation FCD que nous avons adaptées à notre configura-tion.Nous injectons de l’huile végétale de viscosité dynamique μ, à débit contrôlé Q, à travers une plaque de PMMA surlaquelle nous déposons un film élastique d’épaisseur millimétrique. Nous étudions trois configurations principales :1. L’étalement d’une cloque visqueuse unique.2. La coalescence de deux cloques identiques.3. Une instabilité de Rayleigh-Taylor en présence d’une membrane élastique.Pour chaque configuration étudiée, nous commençons par reconstruire la forme générale des cloques obtenues et carto-graphons leur champ de hauteur h(r, t) au cours du temps. Nous montrons la présence de plusieurs régimes d’expansionqui évoluent selon des lois de puissance précises que nous vérifions à la fois théoriquement et expérimentalement. Pourles deux premières études, nous tentons systématiquement d’ajuster la forme de chaque régime à un comportementauto-similaire associé. En complément de cette double approche, une analyse numérique fut également développée envue d’une comparaison avec les données expérimentales obtenues pour les différentes configurations testées
In this project, we propose a series of laboratory-scale model experiments to explore the dynamics and instabilities of geophysically inspired thin liquid films.We are studying phenomena similar to laccoliths, where magma flow deforms the surrounding rock layers. In the limit where their height is very small compared to their horizontal size, these dynamic formations can be reasonably compared to thin liquid blisters covered by an elastic film. We thus propose to revisit classical experiments on free-surface drop dynamics by modifying the boundary condition imposed by the nature of the interface.What is the shape and dynamics of a fluid pocket trapped beneath an elastic membrane? How does the coalescence of two adjacent pockets proceed under this new boundary condition? How are dynamic spreading regimes affected?To answer these questions, we set up an experimental device to observe and characterize this spreading phenomenon, using demodulation techniques that we adapted to our configuration.We inject vegetable oil, at a controlled flow rate, through a PMMA plate onto which we deposit an elastic film of millimetric thickness. We are studying three main configurations:1 Spreading of a single viscous blister.2 The coalescence of two identical blisters.3 A Rayleigh-Taylor instability in the presence of an elastic membrane.For each configuration studied, we begin by reconstructing the general shape of the blisters obtained and map their height field over time. We show the presence of several expansion regimes that evolve according to precise power laws, which we verify both theoretically and experimentally. For the first two studies, we systematically attempt to fit the shape of each regime to an associated self-similar behavior.To complement this dual approach, a numerical analysis was also developed for comparison with the experimental data obtained for the different configurations tested
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Braun, Michael Rainer. "Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26566.

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Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Jacobs, Laurence; Committee Co-Chair: Qu, Jianmin; Committee Member: DesRoches, Reginald. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Tjandrawidjaja, Yohanes. "Some contributions to the analysis of the Half-Space Matching Method for scattering problems and extension to 3D elastic plates." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLY012.

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Cette thèse porte sur la Half-Space Matching Method qui a été développée pour traiter certains problèmes de diffraction dans des domaines complexes infinis pour lesquels les méthodes numériques existantes ne s'appliquent pas. En 2D, elle consiste à coupler plusieurs représentations en ondes planes dans des demi-espaces entourant les obstacles et une représentation éléments finis dans un domaine borné. Afin d'assurer la compatibilité entre les différentes représentations, les traces de la solution sont liées par des équations intégrales de Fourier posées sur les frontières infinies des demi-espaces. Dans le cas d'un milieu dissipatif, il a été montré que ce système d'équations intégrales est coercif plus compact dans un cadre L².Dans cette thèse, nous établissons des estimations d'erreur par rapport aux paramètres de discrétisation (à la fois pour les variables spatiales et les variables de Fourier). Pour traiter le cas non-dissipatif, nous proposons une version modifiée de la Half-Space Matching Method, obtenue en appliquant une dilatation complexe aux inconnues afin de retrouver le cadre L².Nous étendons ensuite la Half-Space Matching Method aux problèmes de diffraction dans une plaque élastique infinie 3D en vue d'applications au Contrôle Non Destructif. La difficulté par rapport au cas 2D vient de la décomposition sur les modes de Lamb utilisée dans les représentations de demi-plaque. La relation de bi-orthogonalité des modes des Lamb impose de considérer comme inconnues non seulement le champ de déplacement, mais aussi le champ de contrainte sur les bandes infinies au bord des demi-plaques. Certaines questions théoriques soulevées par cette formulation multi-inconnues sont étudiées dans le cas 2D scalaire. Des connexions avec les méthodes intégrales sont aussi abordées dans le cas où la fonction de Green est connue, au moins partiellement dans chaque sous-domaine.Les différentes versions de la méthode ont été mises en oeuvre dans la bibliothèque XLiFE++ et des résultats numériques sont présentés pour les cas 2D et 3D
This thesis focuses on the Half-Space Matching Method which was developed to treat some scattering problems in complex infinite domains, when usual numerical methods are not applicable. In 2D, it consists in coupling several plane-wave representations in half-spaces surrounding the obstacle(s) with a Finite Element computation of the solution in a bounded domain. To ensure the matching of all these representations, the traces of the solution are linked by Fourier-integral equations set on the infinite boundaries of the half-spaces. In the case of a dissipative medium, this system of integral equations was proved to be coercive plus compact in an L² framework.In the present thesis, we derive error estimates with respect to the discretization parameters (both in space and Fourier variables). To handle the non-dissipative case, we propose a modified version of the Half-Space Matching Method, which is obtained by applying a complex-scaling to the unknowns, in order to recover the L² framework.We then extend the Half-Space Matching Method to scattering problems in infinite 3D elastic plates for applications to Non-Destructive Testing. The additional complexity compared to the 2D case comes from the decomposition on Lamb modes used in the half-plate representations. Due to the bi-orthogonality relation of Lamb modes, we have to consider as unknowns not only the displacement, but also the normal stress on the infinite bands limiting the half-plates. Some theoretical questions concerning this multi-unknown formulation involving the trace and the normal trace are studied in a 2D scalar case. Connections with integral methods are also addressed in the case where the Green's function is known, at least partially in each subdomain.The different versions of the method have been implemented in the library XLiFE++ and numerical results are presented for both 2D and 3D cases
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Schmidt, Andreas [Verfasser], Reinhard [Akademischer Betreuer] Farwig, and Mads [Akademischer Betreuer] Kyed. "The Navier-Stokes Equations with Elastic Boundary and Boundary Conditions of Friction Type / Andreas Schmidt ; Reinhard Farwig, Mads Kyed." Darmstadt : Universitäts- und Landesbibliothek, 2021. http://d-nb.info/1236344863/34.

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Dydo, James R. "Development of efficient solutions to elastic contact problems with various non-infinite boundary conditions /." The Ohio State University, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487844948076341.

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Venter, Gerhardus. "Sensitivity analysis with respect to elastic boundary conditions and laser spatial variables within experimental spatial dynamic modeling." Thesis, This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-01102009-063257/.

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Crooks, Matthew Stuart. "Application of an elasto-plastic continuum model to problems in geophysics." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/application-of-an-elastoplastic-continuum-model-to-problems-in-geophysics(56bc2269-3eb2-47f9-8482-b62e8e053b76).html.

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A model for stress and strain accumulation in strike slip earthquake faults is presented in which a finite width cuboidal fault region is embedded between two cuboidal tectonic plates. Elasto-plastic continuum constitutive equations model the gouge in the fault and the tectonic plates are linear elastic solids obeying the generalised Hooke's law. The model predicts a velocity field which is comparable to surface deformations. The plastic behaviour of the fault material allows the velocities in the tectonic plate to increase to values which are independent of the distance from the fault. Both of the non-trivial stress and strain components accumulate most significantly in the vicinity of the fault. The release of these strains during a dynamic earthquake event would produce the most severe deformations at the fault which is consistent with observations and the notion of an epicenter. The accumulations in the model, however, are at depths larger than would be expected. Plastic strains build up most significantly at the base of the fault which is in yield for the longest length of time but additionally is subject to larger temperatures which makes the material more ductile. The speed of propagation of the elasto-plastic boundary is calculated and its acceleration towards the surface of the fault may be indicative of a dynamic earthquake type event.
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Croënne, C., J. O. Vasseur, Matar O. Bou, M. F. Ponge, P. A. Deymier, A. C. Hladky-Hennion, and B. Dubus. "Brillouin scattering-like effect and non-reciprocal propagation of elastic waves due to spatio-temporal modulation of electrical boundary conditions in piezoelectric media." AMER INST PHYSICS, 2017. http://hdl.handle.net/10150/623049.

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The properties of a one-dimensional phononic crystal made of identical piezoelectric elements separated by thin metallic electrodes connected to the ground are studied theoretically for cases where the locations of the electrical connections change as a function of time with a specific speed. This spatio-temporal modulation of the electrical boundary conditions results in significant non-linear effects that are evidenced numerically. The interaction between an incident harmonic longitudinal wave and the time-dependent phononic crystal is shown to lead to frequency splitting analogous to Brillouin scattering. Moreover, the boundaries of the Bragg bandgaps are strongly affected, and for some specific modulation speed, one-way wave propagation can be achieved. Published by AIP Publishing.
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Bouzaher, Abdallah. "Réseau bipériodique de dislocations d'hétéro-interface en élasticité anisotrope." Grenoble INPG, 1993. http://www.theses.fr/1993INPG0089.

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Dans ce travail un modele original de calcul des champs elastiques des reseaux hexagonaux de dislocations d'hetero-interfaces est propose en elasticite anisotrope. Les conditions aux limites sont les suivantes: a) les dislocations sont intrinseques et n'engendrent pas de contraintes a longue distance. B) la condition de raccordement des deux milieux a l'interface est representee par un deplacement relatif lineaire a l'interieur d'un hexagone, et discontinue le long de ses cotes. Les champs des deplacements et des contraintes sont etablis et calcules numeriquement par des programmes fortran. Une formule analytique, obtenue par integration, est etablie pour determiner l'energie elastique stockee par unite de surface du joint. Elle est appliquee dans les cas suivants: a) hetero-interface cu/fe, b) hetero-interface cosi#2/si, c) hetero-interface gamma/gamma dans les superalliages, d) joints de torsion dans les metaux cfc
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Brenot, Dominique. "Transmission du son à l'intérieur d'une structure axisymétrique." Paris 6, 1986. http://www.theses.fr/1986PA066022.

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Problème de la transmission du son sur l'axe d'une structure élastique fermée à symétrie de révolution. Problème de Neumann, associé à la pression acoustique par la méthode de la phase stationnaire et problème de structure par une méthode d'éléments finis.
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Books on the topic "Elastic boundary condition"

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United States. National Aeronautics and Space Administration., ed. The Schwinger variational method. [Washington, DC: National Aeronautics and Space Administration, 1995.

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Serikov, Sergey. Impact on impact strength. ru: INFRA-M Academic Publishing LLC., 2024. http://dx.doi.org/10.12737/2161513.

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The main purpose of the monograph is to identify the main patterns in assessing the operational reliability of metals on the basis of a mathematical model of unsteady deformation of an isotropic viscoplastic medium, with specified boundary, initial conditions and energy criterion of destruction. A physically based computational and experimental method for metal identification is formulated. Practical examples of the efficiency of the method for a wide class of materials are given: structural steels, titanium, aluminum and copper alloys. The assessment of the operational reliability of metals is based on a comparison of matrices containing seven parameters: tensile strength, yield strength, elongation, coefficient of dynamic viscosity, specific energy of fracture, rate of deformation, temperature. The book also pays a lot of attention to experimental data on the classical value of impact strength. It is shown that it actually reflects the properties of the material in the range of elastic-brittle state, but not in the scheme of a viscoplastic medium. It is intended for scientific and engineering workers, students involved in metal science and fracture mechanics.
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Book chapters on the topic "Elastic boundary condition"

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Arnold, Anton, and Matthias Ehrhardt. "A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics." In Finite Difference Methods,Theory and Applications, 15–24. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-20239-6_2.

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Lu, Guo Yun, and Shan Yuan Zhang. "Elastic-Plastic Dynamic Response of the Tube with Free Boundary Condition Subjected to Impact." In Engineering Plasticity and Its Applications, 263–68. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-433-2.263.

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Bare, Z., J. Orlik, and G. Panasenko. "Asymptotic Approximations of a Thin Elastic Beam with Auxiliary Coupled 1D System due to Robin Boundary Condition." In Trends in Mathematics, 637–48. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_69.

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Bracamonte, Johane, John S. Wilson, and Joao S. Soares. "Modeling Patient-Specific Periaortic Interactions with Static and Dynamic Structures Using a Moving Heterogeneous Elastic Foundation Boundary Condition." In Functional Imaging and Modeling of the Heart, 315–27. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78710-3_31.

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Fridman, Vladimir. "Discontinuous Functions. Complicated Boundary Conditions." In Theory of Elastic Oscillations, 123–39. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-4786-2_6.

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Thomson, Gavin R., and Christian Constanda. "Problems with Robin Boundary Conditions." In Stationary Oscillations of Elastic Plates, 153–75. Boston: Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8241-5_9.

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Santos, Juan Enrique, and Patricia Mercedes Gauzellino. "Absorbing boundary conditions in elastic and poroelastic media." In Numerical Simulation in Applied Geophysics, 97–119. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48457-0_5.

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Barishpolsky, B. M. "Analysis of Generalized Elastic Problems with Superfluous Boundary Conditions." In Computational Mechanics ’88, 1359–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61381-4_360.

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Jiang, Zhongyu, Yajun Zhang, Huaqing Liu, and Xuanxuan Li. "Symplectic Elastic Solution of Multi-layer Thick-Walled Cylinder Under Different Interlayer Constraints." In Lecture Notes in Civil Engineering, 238–53. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1260-3_21.

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AbstractMulti-layer thick-walled cylinder is a common supporting structure in engineering, which is widely used in various engineering fields. Considering the complex boundary conditions and the different interlayer constraints, it is difficult to solve the theoretical solution of multi-layer thick walled cylinder. In this paper, the general solution expressions of displacement and stress of multi-layer thick-walled cylinder are derived in Hamiltonian mechanics system. The complex boundary conditions are transformed into the form of algebraic sum by Fourier series expansion, and the complex boundary problems are solved by superimposing the special solutions of each order expansion term. At the same time, according to the characteristics of different interlayer constraints, the corresponding conditions of interlayer continuous smooth are proposed. Combined with the boundary conditions of thick-walled cylinder, the linear equations with undetermined coefficients are established. By solving the equations, the mechanical problems of multi-layer thick-walled cylinder are finally solved. By comparing the mechanical responses of multi-layer thick-walled cylinder under different constraint conditions, it is concluded that the overall mechanical performance of the tight interlayer connection is better, and the circumfluence stress component is more prominent than other stress components. Finally, the influence of lateral pressure coefficient and elastic modulus ratio on the circumferential stress of multi-layer thick-walled cylinder is discussed. These research results provide the necessary theoretical basis for solving the mechanical problems of multi-layer thick-walled cylinders.
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Sofronov, I. L., and N. A. Zaitsev. "Transparent Boundary Conditions for the Elastic Waves in Anisotropic Media." In Hyperbolic Problems: Theory, Numerics, Applications, 997–1004. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75712-2_105.

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Conference papers on the topic "Elastic boundary condition"

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Kimura, K., K. Sawada, and H. Kushima. "Long-Term Creep Strength Property of Advanced Ferritic Creep Resistant Steels." In AM-EPRI 2010, edited by D. Gandy, J. Shingledecker, and R. Viswanathan, 732–51. ASM International, 2010. http://dx.doi.org/10.31399/asm.cp.am-epri-2010p0732.

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Abstract Long-term creep strength property of creep strength enhanced ferritic steels was investigated. Stress dependence of minimum creep rate was divided into two regimes with a boundary condition of macroscopic elastic limit which corresponds to 50% of 0.2% offset yield stress (Half Yield). High rupture ductility was observed in the high stress regime above Half Yield, and it was considered to be caused by relatively easy creep deformation throughout grain interior with the assistance of external stress. Grades T23, T/P92 and T/P122 steels represented marked drop in rupture ductility at half yield with decrease in stress. It was considered to be caused by inhomogeneous recovery at the vicinity of prior austenite grain boundary, because creep deformation was concentrated in a tiny recovered area. High creep rupture ductility of Grade P23 steel should be associated with its lower creep strength. It was supposed that recovery of tempered martensitic microstructure of T91 steel was faster than those of the other steels and as a result of that it indicated significant drop in long-term creep rupture strength and relatively high creep rupture ductility. The long-term creep rupture strength at 600°C of Grade 91 steel decreased with increase in nickel content and nickel was considered to be one of the detrimental factors reducing microstructural stability and long-term creep strength. The causes affecting recovery of microstructure should be elucidated in order to obtain a good combination of creep strength and rupture ductility for long-term.
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Peng, Chengbin, and M. Nafi Toksöz. "An optimal absorbing boundary condition for elastic wave modeling." In SEG Technical Program Expanded Abstracts 1993. Society of Exploration Geophysicists, 1993. http://dx.doi.org/10.1190/1.1822294.

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Min, D. J., C. Shin, H. S. Yoo, J. K. Hong, and M. K. Park. "Free Surface Boundary Condition in Finite-Difference Elastic Wave Modeling." In 64th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2002. http://dx.doi.org/10.3997/2214-4609-pdb.5.p264.

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Kim, Minsu, Yongjun Lee, Woo Kyoung Han, and Kyong Hwan Jin. "Learning Residual Elastic Warps for Image Stitching under Dirichlet Boundary Condition." In 2024 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV). IEEE, 2024. http://dx.doi.org/10.1109/wacv57701.2024.00397.

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Du*, Qizhen, Mingqiang Zhang, Gang Fang, Xufei Gong, and Chengfeng Guo. "Relatively amplitude-preserved ADCIGs based on elastic RTM by modifying the initial condition as the boundary condition." In SEG Technical Program Expanded Abstracts 2014. Society of Exploration Geophysicists, 2014. http://dx.doi.org/10.1190/segam2014-0448.1.

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Ponce‐Correa, Gustavo J., and John C. Mutter. "A free boundary condition for the elastic wave equation in the pseudospectral method." In SEG Technical Program Expanded Abstracts 1997. Society of Exploration Geophysicists, 1997. http://dx.doi.org/10.1190/1.1885693.

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Sadasivam, Balaji, Alpay Hizal, and Dwayne Arola. "Abrasive Waterjet Peening With Elastic Prestress: Effect of Boundary Conditions." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67547.

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Abrasive Waterjet Peening (AWJP) has emerged as a potential surface treatment process for metal implants and prosthetic devices. An elastic tensile prestress has been shown to increase the magnitude and depth of residual stress that can be obtained. In the present investigation, the subsurface residual stress fields resulting from AWJ peening of Ti6Al4V with load control and displacement control elastic prestress were compared. Prestress ranged from 0 to 75% of the material’s yield strength and the subsurface residual stress distribution was quantified using the layer removal technique. Results showed that the surface residual stress was dependent on the boundary conditions for prestress levels less than 60% of the materials yield strength. The magnitude of surface residual stress and the stored elastic energy were up to 50% and 100% larger respectively when load controlled boundary conditions were used. However, the boundary condition did not affect the depth of compressive residual stress.
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Xu, Tian, and Yong Lei. "Identification of Young’s Modulus and Equivalent Spring Constraint Boundary Conditions of the Object With Incomplete Displacement Boundary Conditions." In ASME 2020 15th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/msec2020-8396.

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Abstract In endoscopic surgery, the surgical navigation needs to calculate the internal deformation of the soft tissue by biomechanical model which needs to determine the elastic properties and boundary conditions. However, these information cannot be obtained accurately in a real operation scenario. For example, only a limited portion of a liver surface can be observed in a hepatic surgery under endoscope while its elastic properties remain unknown. In addition, simple boundary conditions such as fixed constraints and free-force constraints are not physically adequate to simulate the elastic effect of ligaments attached to the liver. Biomechanical models of the soft tissue have been thoroughly studied in recent years. In these studies, boundary conditions play an important role in identification of elastic properties for mechanical model based methods. But they rarely combine these unknown conditions together to construct the model, and instead set boundary conditions or elastic properties as known for simplification. In this paper, we present a novel method to identify the Young’s modulus and equivalent spring constraint boundary conditions of a partially observed soft object with incomplete boundary conditions. The spring constraint boundary condition is applied to alternate the conventional displacement boundary conditions (e.g. free constraint and fixed constraint) and an inverse algorithm based on the standard finite element method (FEM) and Gauss-Newton (GN) method is developed, which takes external forces and displacements of observable nodes as inputs. A series of numerical simulation experiments are implemented and the analysis of simulation results show the feasibility of the proposed method.
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Xie, Xiao‐Bi, and Ru‐Shan Wu. "Free surface boundary condition and the source term for one‐way elastic wave method." In SEG Technical Program Expanded Abstracts 1997. Society of Exploration Geophysicists, 1997. http://dx.doi.org/10.1190/1.1885799.

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Liu, Yang, and Mrinal K. Sen. "A hybrid absorbing boundary condition for elastic wave modeling with staggered‐grid finite difference." In SEG Technical Program Expanded Abstracts 2010. Society of Exploration Geophysicists, 2010. http://dx.doi.org/10.1190/1.3513458.

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