Relevant bibliographies by topics / Elastostatic solution

Academic literature on the topic 'Elastostatic solution'

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Published: 14 March 2023

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Journal articles on the topic "Elastostatic solution"

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Charalambopoulos, Antonios, Theodore Gortsas, and Demosthenes Polyzos. "On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution." Mathematics 10, no. 7 (April 2, 2022): 1152. http://dx.doi.org/10.3390/math10071152.

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The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradient parameters become zero. Through functional theory considerations, a solution representation of the one-intrinsic-parameter strain gradient elastostatic equation that comprises the classical elastic solution of the corresponding boundary value problem is rigorously provided for the first time. Next, that solution representation is employed to give an answer to contradictions arising by two well-known first-strain gradient elastic models proposed in the literature to describe the strain gradient elastostatic bending behavior of Bernoulli–Euler beams.
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Stolle, Dieter F. E., and Gabriel Sedran. "Influence of inertia on falling weight deflectometer (FWD) test response." Canadian Geotechnical Journal 32, no. 6 (December 1, 1995): 1044–48. http://dx.doi.org/10.1139/t95-101.

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This note addresses the appropriateness of adopting an elastostatic model for backcalculating in situ layer moduli from falling weight deflectometer (FWD) data. By approximating the elastodynamic displacement field using an elastostatic solution for a given load distribution, it is shown via Ritz vector analyses that elastostatic fields do not accurately represent the displacements associated with pavements subjected to FWD-type loading. Some improvement is, however, possible by including first-order corrections for inertial forces. The main conclusion stemming from the analyses is that elastostatic models should not be used to estimate in situ moduli. Key words : pavement, elastodynamic analysis, Ritz vectors, back-calculation, structural integrity.
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Providakis, Costas P., and Dimitri E. Beskos. "Dynamic Analysis of Plates by Boundary Elements." Applied Mechanics Reviews 52, no. 7 (July 1, 1999): 213–36. http://dx.doi.org/10.1115/1.3098936.

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A review of boundary element methods for the numerical treatment of free and forced vibrations of flexural plates is presented. The integral formulation and the corresponding numerical solution from the direct boundary element method viewpoint are described for elastic or inelastic flexural plates experiencing small deformations. When the material is elastic the formulation can be either in the frequency or the time domain in conjunction with the elastodynamic or the elastostatic fundamental solution of the corresponding flexural plate problem. When use is made of the elastodynamic fundamental solution, the discretization is essentially restricted to the perimeter of the plate, while an interior discretization in addition to the boundary one is needed when the elastostatic fundamental solution is employed in the formulation. However, the great simplicity of the elastostatic fundamental solution leads eventually to more efficient schemes. Besides, through dual reciprocity techniques one can again restrict the discretization to the plate perimeter. Free vibrations are solved by the determinant method when use is made of the elastodynamic fundamental solution, or by generalized eigenvalue analysis when use is made of the elastostatic fundamental solution. Forced vibrations are solved either in the frequency domain in conjunction with Fourier or Laplace transform or the time domain in conjunction with a step-by-step time integration. When the material is inelastic the problem is formulated incrementally in the time domain in conjunction with the elastostatic fundamental solution and the plate response is obtained through step-by-step time integration. Special formulations such as indirect, Green’s function, symmetric, dual and multiple reciprocity, or boundary collocation ones are also reviewed. Effects such as those of corners, viscoelasticity, anisotropy, inhomogeneity, in-plane forces, shear deformation and rotatory inertia, variable thickness, internal supports, elastic foundation and large defections are discussed as well. Representative numerical examples serve to illustrate boundary element methods and demonstrate their advantages over other numerical methods. This review article includes 150 references.
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Chen, Ying-Ting, and Yang Cao. "A Coupled RBF Method for the Solution of Elastostatic Problems." Mathematical Problems in Engineering 2021 (January 22, 2021): 1–15. http://dx.doi.org/10.1155/2021/6623273.

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Radial basis function (RBF) has been widely used in many scientific computing and engineering applications, for instance, multidimensional scattered data interpolation and solving partial differential equations. However, the accuracy and stability of the RBF methods often strongly depend on the shape parameter. A coupled RBF (CRBF) method was proposed recently and successfully applied to solve the Poisson equation and the heat transfer equation (Appl. Math. Lett., 2019, 97: 93–98). Numerical results show that the CRBF method completely overcomes the troublesome issue of the optimal shape parameter that is a formidable obstacle to global schemes. In this paper, we further extend the CRBF method to solve the elastostatic problems. Discretization schemes are present in detail. With two elastostatic numerical examples, it is found that both numerical solutions of the CRBF method and the condition numbers of the discretized matrices are almost independent of the shape parameter. In addition, even if the traditional RBF methods take the optimal shape parameter, the CRBF method achieves better accuracy.
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YUUKI, Ryoji, Sang-Bong CHO, Toshiro MATSUMOTO, and Hiroyuki KISU. "Efficient boundary element elastostatic analysis using Hetenyi's fundamental solution." Transactions of the Japan Society of Mechanical Engineers Series A 53, no. 492 (1987): 1581–89. http://dx.doi.org/10.1299/kikaia.53.1581.

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Sanders, E. D., M. A. Aguiló, and G. H. Paulino. "Optimized lattice-based metamaterials for elastostatic cloaking." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2253 (September 2021): 20210418. http://dx.doi.org/10.1098/rspa.2021.0418.

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An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.
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Sharp, S., and S. L. Crouch. "Boundary Integral Methods for Thermoelasticity Problems." Journal of Applied Mechanics 53, no. 2 (June 1, 1986): 298–302. http://dx.doi.org/10.1115/1.3171755.

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The boundary integral method for solving transient heat flow problems is extended to calculate thermally induced stresses and displacements. These results are then corrected by means of an elastostatic solution to satisfy the boundary conditions.
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Tsagareli, Ivane. "Explicit Solution of Elastostatic Boundary Value Problems for the Elastic Circle with Voids." Advances in Mathematical Physics 2018 (June 10, 2018): 1–6. http://dx.doi.org/10.1155/2018/6275432.

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We solve the static two-dimensional boundary value problems for an elastic porous circle with voids. Special representations of a general solution of a system of differential equations are constructed via elementary functions which make it possible to reduce the initial system of equations to equations of simple structure and facilitate the solution of the initial problems. Solutions are written explicitly in the form of absolutely and uniformly converging series. The question pertaining to the uniqueness of regular solutions of the considered problems is investigated.
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Zhao, Bao Sheng, and Di Wu. "Boundary Conditions for Torsional Circular Shaft with Two-Dimensional Dodecagonal Quasicrystals." Advanced Materials Research 580 (October 2012): 411–14. http://dx.doi.org/10.4028/www.scientific.net/amr.580.411.

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Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, a set of necessary conditions on the end-data of torsional circular shaft in two-dimensional dodecagonal quasicrystals (2D dodecagonal QCs) for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, using the reciprocal theorem, these necessary conditions for the end-data to induce only a decaying elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the torsional circular shaft in 2D dodecagonal QCs. The results of the present paper enable us to establish a set of boundary conditions.
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Yuan, Huina, and Ziyang Pan. "Discussion on the Time-Harmonic Elastodynamic Half-Space Green’s Function Obtained by Superposition." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/2717810.

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The time-harmonic elastodynamic half-space Green’s function derived by Banerjee and Mamoon by way of superposition is discussed and examined against another semianalytical solution and a numerical solution. It is shown that Banerjee and Mamoon’s solution gives infinitez-displacement response when the depth of the source goes to infinity, which is unreasonable and does not agree with other solutions. A possible problem in the derivation is that it is inappropriate to directly extend the results of Mindlin’s superposition method for the elastostatic half-space problem to the dynamic case. The superposition of the six full-space elastodynamic solutions does not satisfy the required boundary conditions of the half-space elastodynamic problem as in the static case and thus does not solve the dynamic half-space problem.
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Dissertations / Theses on the topic "Elastostatic solution"

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Ching, Hsu-Kuang. "Solution of Linear Elastostatic and Elastodynamic Plane Problems by the Meshless Local Petrov-Galerkin Method." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/28885.

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The meshless local Petrov-Galerkin (MLPG) method is used to numerically find an approximate solution of plane strain/stress linear elastostatic and elastodynamic problems. The MLPG method requires only a set of nodes both for the interpolation of the solution variables and the evaluation of various integrals appearing in the problem formulation. The monomial basis functions in the MLPG formulation have been enriched with those for the linear elastic fracture mechanics solutions near a crack tip. Also, the diffraction and the visibility criteria have been added to make the displacement field discontinuous across a crack. A computer code has been developed in Fortran and validated by comparing computed solutions of three static and one dynamic problem with their analytical solutions. The capabilities of the code have been extended to analyze contact problems in which a displacement component and the complementary traction component are prescribed at the same point of the boundary. The code has been used to analyze stress and deformation fields near a crack tip and to find the stress intensity factors by using contour integrals, the equivalent domain integrals and the J-integral and from the intercepts with the ordinate of the plots, on a logarithmic scale, of the stress components versus the distance ahead of the crack tip. We have also computed time histories of the stress intensity factors at the tips of a central crack in a rectangular plate with plate edges parallel to the crack loaded in tension. These are found to compare favorably with those available in the literature. The code has been used to compute time histories of the stress intensity factors in a double edge-notched plate with the smooth edge between the notches loaded in compression. It is found that the deformation fields near the notch tip are mode-II dominant. The mode mixity parameter can be changed in an orthotropic plate by adjusting the ratio of the Young's moduli in the axial and the transverse direction. The plane strain problem of compressing a linear elastic material confined in a rectangular cavity with rough horizontal walls and a smooth vertical wall has been studied with the developed code. Computed displacements and stresses are found to agree well with the analytical solution of the problem obtained by the Laplace transform technique. The Appendix describes the analysis with the finite element code ABAQUS of the dependence of the energy release rate upon the crack length in a polymeric disk enclosed in a steel ring and having a star shaped hole at its center. A starter crack is assumed to exist in one of the leaflets of the hole. The disk is loaded either by a pressure acting on the surfaces of the hole and the crack or by a temperature rise. Computed values of the energy release rate obtained by modeling the disk material as Hookean are found to be about 30% higher than those obtained when the disk material is modeled as Mooney-Rivlin. The latter set of results accounts for both material and geometric nonlinearities.
Ph. D.
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2

Onwordi, I. C. "Finite element solutions to elastostatic non-conforming contacts." Thesis, Imperial College London, 1986. http://hdl.handle.net/10044/1/38126.

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Iaccarino, Gianni Luca. "Analytical Solution of two Traction-Value Problems in Second-Order Elasticity with Live Loads." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/35137.

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We present a generalization of Signorini's method to the case of live loads which allows us to derive approximate solutions to some pure traction-value problems in finite elastostatics. The boundary-value problems and the corresponding compatibility conditions are formulated in order to determine the displacement of the system up to the second-order of approximation. In particular, we consider the case of homogeneous and isotropic elastic bodies and we solve the following two traction-value problems with live loads:(i) a sphere subjected to the action of a uniform pressure field;(ii)a hollow circular cylinder whose inner and outer surfaces are subjected to uniform pressures. Then, starting from these solutions, we suggest experiments to determine the second-order constitutive constants of the elastic body. Expressions of the second-order material constants in terms of displacements and Lame' coefficients are determined.
Master of Science
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Wakugawa, Jason Masao Knowles James K. "On the existence and uniqueness of the solution to the small-scale nonlinear anti-plane shear crack problem in finite elastostatics /." Diss., Pasadena, Calif. : California Institute of Technology, 1985. http://resolver.caltech.edu/CaltechETD:etd-03212008-094413.

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"Digital computer solution of special electrostatic and elastostatic problems with applications to the mining of tabular deposits." Thesis, 2015. http://hdl.handle.net/10539/16950.

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Gee, Chuen-Ming, and 葛春明. "An Adaptive h Algorithm for Boundary Element Solutions of Plane Elastostatic Problems." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/76501616207074261518.

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碩士
國立台灣工業技術學院
機械工程技術研究所
85
The present study develops an adaptive h method for the boundary element solutions of plane elasto-static problems with multiple subregions. The domainmaterial properties considered include isotropy, orthotropy and anisotropy. First this study derives the boundary element equations of plane elasto- staticproblems with anisotropic medium and the formulas to compute the stress intensity factors of problems of plane linear elastic fracture mechanics. Thenthe error estimation method for the present boundary element solution and themesh refinement procedure are introduced. Finally the present adaptive boundary element mesh refinement model is applied to analyze some general plane elasto-static problems and plane linear elastic fracture mechanics problems to verify the accuracy of this adaptive model. The effect of materialproperty on the distributions of elements, displacements and tractions in the final refined meshis also investigated. From the numerical results, the accuracy and efficiency of the present adaptive boundary element meshrefinement model are verified. The variation of material axes is also found to affect the distributions of elements, displacements and tractions in the final refined mesh.
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Chu, Po-chun, and 朱珀君. "Models of Corner and Crack Singularity of Linear Elastostatics and their Numerical Solutions." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/62948602889329302689.

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碩士
國立中山大學
應用數學系研究所
98
The singular solutions for linear elastostatics at corners are essential in both theory and computation. In this thesis, we seek new singular solutions for corners with the fixed (displacement), the free stress (traction) boundary conditions, and their mixed types, and to explore their corner singularity and provide the algorithms and error estimates in detail. The singular solutions of linear elastostatics are derived, and a number of new models of corner and crack singularity are proposed. Effective numerical methods, such as the collocation Trefftz methods (CTM), the method of fundamental solutions (MFS), the method of particular solutions (MPS) and their combinations: the so called combined method, are developed. Such solutions are useful to examine other numerical methods for singularity problems in linear elastostatics. This thesis consists of three parts, Part I: Basic approaches, Part II: Advanced topics, and Part III: Mixed types of displacement and traction conditions. Contents of Parts I and II have been published in [47,82]. In Part I, the collocation Trefftz methods are used to obtain highly accurate solutions, where the leading coefficient has 14 (or 13) significant digits by the computation with double precision. In part II, two more new models (symmetric and anti-symmetric) of interior crack singularities are proposed, for the corner and crack singularity problems, the combined methods by using many fundamental solutions, but by adding a few singular solutions are proposed. Such a kind of combined methods is significant for linear elastostatics with corners (i.e., the L-shaped domain), because the singular solutions can only be obtained by seeking the power νk of rνk numerically. Hence, only a few singular solutions used may greatly simplify the numerical algorithms; Part III is a continued study of Parts I and II, to explore mixed type of displacement and free traction boundary conditions. To our best knowledge, this is the first time to provide the particular solutions near the corner with mixed types of boundary conditions and to report their numerical computation with different boundary conditions on the same corner edge in linear elastostatics. This thesis explores corner singularity and its numerical methods, to form a systematic study of basic theory and advanced computation for linear elastostatics.
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Wakugawa, Jason Masao. "On the Existence and Uniqueness of the Solution to the Small-Scale Nonlinear Anti-Plane Shear Crack Problem in Finite Elastostatics." Thesis, 1985. https://thesis.library.caltech.edu/1050/1/Wakugawa_jm_1985.pdf.

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This thesis addresses the issue of existence and uniqueness of the solution to the small-scale nonlinear anti-plane shear crack problem in finite elastostatics. The hodograph transformation, commonly used in the theory of compressible fluid flows, plays an essential role. Existence is established by exhibiting an exact closed form solution, constructed via the hodograph transformation. Uniqueness is established by first proving the uniqueness of the solution to a related boundary-value problem, which is linear by virtue of the hodograph transformation, and then examining the implications of this result on the original problem. The possibility of making some of the conditions imposed on the solution to the small-scale nonlinear crack problem less restrictive is then investigated. This leads to several further results, including estimates of the nonvanishing shear stress component of the stress tensor along the crack faces.

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Books on the topic "Elastostatic solution"

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Victor, Li, and United States. National Aeronautics and Space Administration, eds. Vector image method for the derivation of elastostatic solutions for point sources in a plane layered medium. Cambridge, Ma: Dept. of Civil Engineering, Massachusetts Institute of Technology, 1986.

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Jentsch, Lothar. Zur Existenz Von Regulären lösungen der Elastostatik Stückweise Homogener Körper Mit Neuen Kontaktbedingungen an Den Trennflächen Zwischen Zwei Homogenen Teilen. de Gruyter GmbH, Walter, 2022.

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Book chapters on the topic "Elastostatic solution"

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Gerstle, W. H., N. N. V. Prasad, and M. Xie. "Solution Method for Coupled Elastostatic BEM and FEM Domains." In Boundary Element Technology VII, 213–26. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2872-8_15.

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Sawada, T. "Solution Errors in BEM of 2-D Elastostatic Problem." In Computational Mechanics ’88, 69–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61381-4_16.

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Muci-Küchler, K. H., and T. J. Rudolphi. "Application of Tangent Derivative Boundary Integral Equations to the Solution of Elastostatic Problems." In Boundary Element Technology VII, 757–74. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2872-8_51.

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Kassab, Alain J., F. A. Moslehy, T. W. Ulrich, and J. Pollard. "Inverse Boundary Element Solution for Locating Subsurface Cavities in Thermal and Elastostatic Problems." In Computational Mechanics ’95, 3024–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79654-8_499.

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Kythe, Prem K. "Elastostatics." In Fundamental Solutions for Differential Operators and Applications, 138–61. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-4106-5_7.

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Poullikkas, Andreas, Andreas Karageorghis, and Georgios Georgiou. "The Method of Fundamental Solutions in Three-Dimensional Elastostatics." In Parallel Processing and Applied Mathematics, 747–55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-48086-2_83.

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Eslami, Reza, Richard B. Hetnarski, Jozef Ignaczak, Naotake Noda, Naobumi Sumi, and Yoshinobu Tanigawa. "Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics." In Theory of Elasticity and Thermal Stresses, 209–18. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6356-2_8.

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Eslami, Reza, Richard B. Hetnarski, Jozef Ignaczak, Naotake Noda, Naobumi Sumi, and Yoshinobu Tanigawa. "Solutions to Particular Two-Dimensional Boundary Value Problems of Elastostatics." In Theory of Elasticity and Thermal Stresses, 219–44. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6356-2_9.

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Labisch, Franz Karl. "Some Remarks on the Morphology of Non-Unique Solutions in Nonlinear Elastostatics." In Bifurcation: Analysis, Algorithms, Applications, 177–84. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7241-6_19.

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Liolios, A. A. "Upper and Lower Solution Bounds in Unilateral Contact Elastostatics under Second-Order Geometric Effects." In Contact Mechanics, 37–40. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1983-6_6.

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Conference papers on the topic "Elastostatic solution"

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Sakurai, H. "Analytical solution of a two-dimensional elastostatic problem of functionally graded materials via the Airy stress function." In MATERIALS CHARACTERISATION 2011. Southampton, UK: WIT Press, 2011. http://dx.doi.org/10.2495/mc110111.

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Barber, J. R., and P. Hild. "Non-Uniqueness, Eigenvalue Solutions and Wedged Configurations Involving Coulomb Friction." In ASME/STLE 2004 International Joint Tribology Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/trib2004-64368.

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It is well known that the conventional Coulomb friction condition can lead to non-uniqueness of solution in elastostatic solutions if the friction coefficient is sufficiently high. Interest in this field has centered on discrete formulations, particularly with reference to the finite element method. More recently Hild has demonstrated the existence of a multiplicity of non-unique solutions to a simple problem in two-dimensional continuum elasticity and showed how to determine the conditions for such states to exist by formulating an eigenvalue problem. Both the discrete and continuum examples of non-uniqueness seem to be related to the well known physical phenomenon whereby a frictional system can become locked or ‘wedged’ in a state of stress even when no external loads are applied (the homogeneous problem), but the equivalence is not complete because of the influence of unilateral inequalities in the physical problem. We shall discuss the relations between these concepts in the context of simple continuum and discrete problems in two-dimensional linear elasticity.
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Yosibash, Zohar, and Barna A. Szabó. "Failure Analysis of Composite Materials and Multi Material Interfaces." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0145.

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Abstract Composite materials and multi-material interface problem usually have one or more singular points. In the neighborhood of these points the solution of two-dimensional linear elastostatic problems is characterized by a series of eigenpairs and their coefficients, called the generalized stress intensity factors (GSIFs). Accurate and reliable computation of the eigenpairs and the GSIFs is important because failure theories directly or indirectly involve these quantities. New efficient and accurate methods for numerical computation of the eigenpairs and the GSIFs, based on the p-version of the finite element method, are presented and demonstrated. Examples, representing two different kinds of singular points demonstrate that the method works well and produces results of high accuracy. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs.
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Naghdabadi, Reza, and Mohsen Asghari. "Some Advantages of the Elliptic Weight Function for the Element Free Galerkin Method." In ASME 2005 Pressure Vessels and Piping Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pvp2005-71455.

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In this paper, an anisotropic weight function in the elliptic form is introduced for the Element Free Galerkin Method (EFGM). In the circular (isotropic) weight function, each node has one characteristic parameter that determines its domain of influence. In the elliptic weight function, each node has three characteristic parameters that are major influence radius, minor influence radius and the direction of the major influence. Using the elliptic weight function each point of the domain may be affected by a less number of nodes in certain conditions. Thus, the computational cost of the method is decreased. In addition, the dependency of the solution on the method that is used for the enforcement of the essential boundary conditions, decreases. As an application of the proposed elliptic weight function, some examples of elastostatic problems are solved and the results are compared with those available in the literature.
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Bora, Jugma N. "Analytical Evaluation of the Integrals Appearing in the Boundary Element Method for Some Problems in Mechanics." In ASME 1991 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/cie1991-0102.

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Abstract The boundary integral equation method or simply the Boundary Element Method (BEM) is now considered to be a powerful tool for solving problems in mechanics. A large number of the line and area integrals appearing for two-dimensional problems, in the BEM, can be represented as linear combinations of four singular functions. These integrals that are generated are products of the approximating polynomials and one or more of the four singular functions. These integrals can be evaluated numerically or analytically. The advantage of numerical integration is that the shape of the boundary can be of any complexity. The big disadvantage is that another source of error, besides the polynomial interpolation, is added into the process due to the approximation of the integrand for numerical integration. The singular nature of the fundamental solutions further exacerbates this disadvantage. In analytical integration, the form of the boundary must be assumed. The usual representation is a sum of straight-line segments. Currently, analytical expressions are available only for a few formulations and they are valid only for zero- and first-order polynomials. In this paper analytical expressions of the integrals are obtained for approximating polynomials of any arbitrary order. The fundamental solutions of the Laplace, Biharmonic and the equation of Plane Elastostatics are considered. The validity and advantage of using these integrals are shown by some simple problems in mechanics that have theoretical solutions.
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Shioya, Ryuji, Masao Ogino, Hiroshi Kawai, and Shinobu Yoshimura. "Advanced General-Purpose Finite Element Solid Analysis System Adventure_Solid on the Earth Simulator: Its Application to Full-Scale Analysis of Nuclear Pressure Vessel." In ASME/JSME 2004 Pressure Vessels and Piping Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/pvp2004-2750.

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We have been developing an advanced general-purpose computational mechanics system, named ADVENTURE, which is designed to be able to analyze a model of arbitrary shape with a 10–100 million degrees of freedom (DOFs) mesh, and additionally to enable parametric and non-parametric shape optimization. Domain-decomposition-based parallel algorithms are implemented in pre-processes (domain decomposition), main processes (system matrix assembling and solutions) and post-process (visualization), respectively. Especially the hierarchical domain decomposition method with a preconditioned iterative solver (HDDM) is adopted in one of the main modules for solid analysis, named ADVENTURE_Solid. The employed preconditioner is the Balancing Domain Decomposition (BDD) type method. The ADVENTURE_Solid has been successfully implemented on a single PC, PC clusters and massively parallel processors such as Hitachi SR8000/MPP. In this study, this solid analysis module is implemented with minor modification on the Earth Simulator consisting of 256 nodes, i.e. 2,048 vector-type processing elements of theoretical peak performance of 16 TFLOPS (Tela FLoating point Operations Per Seconds), and succeeded in solving an elastostatic problem of a nuclear pressure vessel model of 100 million DOFs mesh in 8.5 minutes with 5.1 TFLOPS, which is 31.8% of the peak performance and over 80% parallel efficiency. As the purpose of demonstration of virtual mock-up test, the ADVENTURE_Solid is applied to solve a precise model of the ABWR vessel subjected to two kinds of loading conditions, i.e. (1) quasi-static seismic loading and (2) hydrostatic internal pressure.
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7

Chou, Tsu-Wei, and Baoxing Chen. "Transient Elastic Wave Propagation and Local Dynamic Stress Concentration in Woven Fabric Composites." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-1176.

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Abstract Investigations of the response of composites to time-dependent loadings are of considerable importance in structural analysis of many engineering fields, including aerospace, aeronautic, naval and automotive applications. Wave propagation in woven fabric composites poses major theoretical and experimental challenges. The mathematical modeling of dynamic stress concentrations in woven fabric composites is a fairly difficult task due to the great number of wave interactions between the fiber and the matrix. When composite structures composed of woven fabric preforms are loaded impulsively, stress waves propagate in different constituent phases at different speeds, which results in dynamic normal and shearing stresses at the interfacial bond region as well as at the yarn cross-over points. The concentration of these stresses may initiate unstable delamination and eventually failure of the laminated structure. This paper presents a theoretical study on the elastic wave propagation and local dynamic stress concentration in woven fabric composites. The analysis focuses on the unit cell of an orthogonal woven fabric composite, which is composed of two sets of mutually orthogonal yarns of either the same fiber (non-hybrid fabric) or different fibers (hybrid fabric) in a matrix material. Using the mosaic model for simplifying woven fabric composites and a shear lag approach to take into account the inter-yarn deformation, a one-dimensional analysis has been developed to predict the local elastodynamic and elastostatic behavior. The initial and boundary value problems are formulated and then solved using Laplace transforms. Closed form solutions of the dynamic displacements and stresses in each yarn, and the bond shearing stresses at the interfaces between adjacent yarns, are obtained in the time domain for in-plane, as well as out-of-plane impact loadings. When time tends to infinity, the dynamic solutions approach to their corresponding static solutions, which are also developed in this article. Solutions of certain special cases are identical to those reported in the literature. Lastly, the dynamic stresses and bond shearing stresses of plain weave composites subjected to step uniform impacts are presented and discussed as an example of the general analytical model.
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8

Gommerstadt, B. Y. "The J and M Integrals for a Cylindrical Cavity in a Time-Harmonic Wave Field." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65353.

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The invariant integrals are being widely used in the study of defects and fracture mechanics, mostly in elastostatics. However, the properties and the interpretation of these integrals in elastodynamics, especially in the case of time-harmonic excitation, have remained unexplored. Their study has a variety of engineering and geophysical implications, in particular, for the further development of non-destructive evaluation techniques. This contribution is focused on the derivation of the time average J integral for a cylindrical inhomogeneity and M integral for a cylindrical cavity placed in a monochromatic plane elastic wave of arbitrary wavelength. It is shown in the context of antiplane linear elasticity, that the J integral or the material force acting on the inhomogeneity resembles the radiation pressure force exerted on a dielectric cylinder by the normally incident electromagnetic wave. Based on the existing solution of this electrodynamic problem and the corresponding acoustic problem, the J integral is expressed as a function of the nondimensional wave number in the form of the partial wave expansion of the scattering theory. Employing the same classical method as for the J integral, the closed-form solution for the time average M integral for a traction-free cavity is also obtained as a function of the nondimensional wave number. The M integral, i.e., the expansion moment per unit length on an infinitely long circular cavity, is represented in terms of the scattering phase shifts as in the case of the J integral. Rather different expressions for the cavity are also derived for both integrals, which can be used more conveniently for numerical calculations, and these calculations are carried out for J and M integrals in a wide spectrum of frequencies. Asymptotic approximations of both integrals for low and high frequencies are presented. The long wavelength approximation, including the monopole and dipole contributions, has been provided for the J integral in the form of simple analytical expression. The value of M integral in the vanishing frequency limit is also presented. In the opposite short wavelength limit, the corresponding asymptotic values are derived for both integrals. These solutions which are valid for the empty cavity are extended to the case of inviscid fluid-filled cavity. The obtained results can be used in the area of non-destructive evaluation for the flaw characterization by ultrasonic scattering methods. The derived frequency dependence of the J and M integral can be related to the measurable far-field scattering amplitudes. This relationship is relevant to the inverse-scattering approach, which can be applied to the characterization of materials in an attempt to infer geometrical characteristics of flow structures.
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