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Journal articles on the topic 'Elastostatic solution'

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Published: 14 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Juha, Mario J. "Reproducing Kernel Element Method for Galerkin Solution of Elastostatic Problems." Ingeniería y Ciencia 8, no. 16 (November 30, 2012): 71–96. http://dx.doi.org/10.17230/ingciencia.8.16.4.

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The Reproducing Kernel Element Method (RKEM) is a relatively new technique developed to have two distinguished features: arbitrary high order smoothness and arbitrary interpolation order of the shape functions. This paper provides a tutorial on the derivation and computational implementation of RKEM for Galerkin discretizations of linear elastostatic problems for one and two dimensional space. A key characteristic of RKEM is that it do not require mid-side nodes in the elements to increase the interpolatory power of its shape functions, and contrary to meshless methods, the same mesh used to construct the shape functions is used for integration of the stiffness matrix. Furthermore, some issues about the quadrature used for integration arediscussed in this paper. Its hopes that this may attracts the attention of mathematicians.

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12

Morales, J. L., J. A. Moreno, and F. Alhama. "Numerical solution of 2D elastostatic problems formulated by potential functions." Applied Mathematical Modelling 37, no. 9 (May 2013): 6339–53. http://dx.doi.org/10.1016/j.apm.2013.01.030.

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13

Zhao, Bao Sheng, Yang Gao, and Ying Tao Zhao. "Boundary Conditions for Axisymmetric Circular Cylinder of Cubic Quasicrystal." Advanced Materials Research 160-162 (November 2010): 204–9. http://dx.doi.org/10.4028/www.scientific.net/amr.160-162.204.

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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 axisymmetric circular cylinder in cubic quasicrystal 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 circular cylinder with axisymmetric deformations in cubic quasicrystal. The results of the present paper enable us to establish a set of correct boundary conditions, and mix boundary conditions of which are obtained for the first time.

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14

Ben Gharbia, Ibtihel, Marcella Bonazzoli, Xavier Claeys, Pierre Marchand, and Pierre-Henri Tournier. "Fast Solution of Boundary Integral Equations for Elasticity Around a Crack Network: A Comparative Study." ESAIM: Proceedings and Surveys 63 (2018): 135–51. http://dx.doi.org/10.1051/proc/201863135.

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Because of the non-local nature of the integral kernels at play, the discretization of boundary integral equations leads to dense matrices, which would imply high computational complexity. Acceleration techniques, such as hierarchical matrix strategies combined with Adaptive Cross Approximation (ACA), are available in literature. Here we apply such a technique to the solution of an elastostatic problem, arising from industrial applications, posed at the surface of highly irregular cracks networks.

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15

Ivanychev, D. A. "Solution of the Nonaxisymmetric Elastostatic Problem for a Transversely Isotropic Body of Revolution." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 2 (101) (April 2022): 4–21. http://dx.doi.org/10.18698/1812-3368-2022-2-4-21.

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The paper investigates the elastic equilibrium of transversely isotropic bodies of revolution under the action of stationary surface forces distributed according to the cyclic law. The proposed method for constructing the stress-strain state is a development of the method of boundary states. The method is based on the concept of spaces of internal and boundary states conjugated by an isomorphism. Bases of state spaces are formed and orthonormalized. The desired state is expanded in a series by the elements of the orthonormal basis, and the Fourier coefficients, which are quadratures, of this linear combination are calculated. The basis of the internal state space relies on the general solution of the problem of plane deformation of a transversely isotropic body and the formulas for the transition to a spatial state, the components of which depend on three coordinates. Scalar products in state spaces represent the internal energy of elastic deformation and the work of surface forces on the displacements of the boundary points. The study introduces the solution of the main mixed problem for a circular cylinder made of transversely isotropic siltstone with the axis of anisotropy coinciding with the geometric axis of symmetry. The solution is analytical and the characteristics of the stress-strain state have a polynomial form. The paper presents explicit and indirect signs of convergence of problem solutions and graphically visualizes the results

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16

Tago, J., V. M. Cruz-Atienza, C. Villafuerte, T. Nishimura, V. Kostoglodov, J. Real, and Y. Ito. "Adjoint slip inversion under a constrained optimization framework: revisiting the 2006 Guerrero slow slip event." Geophysical Journal International 226, no. 2 (April 22, 2021): 1187–205. http://dx.doi.org/10.1093/gji/ggab165.

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SUMMARY To shed light on the prevalently slow, aseismic slip interaction between tectonic plates, we developed a new static slip inversion strategy, the ELADIN (ELastostatic ADjoint INversion) method, that uses the adjoint elastostatic equations to compute the gradient of the cost function. ELADIN is a 2-step inversion algorithm to efficiently handle plausible slip constraints. First it finds the slip that best explains the data without any constraint, and then refines the solution by imposing the constraints through a Gradient Projection Method. To obtain a self-similar, physically consistent slip distribution that accounts for sparsity and uncertainty in the data, ELADIN reduces the model space by using a von Karman regularization function that controls the wavenumber content of the solution, and weights the observations according to their covariance using the data precision matrix. Since crustal deformation is the result of different concomitant interactions at the plate interface, ELADIN simultaneously determines the regions of the interface subject to both stressing (i.e. coupling) and relaxing slip regimes. For estimating the resolution, we introduce a mobile checkerboard analysis that allows to determine lower-bound fault resolution zones for an expected slip-patch size and a given stations array. We systematically test ELADIN with synthetic inversions along the whole Mexican subduction zone and use it to invert the 2006 Guerrero Slow Slip Event (SSE), which is one of the most studied SSEs in Mexico. Since only 12 GPS stations recorded the event, careful regularization is thus required to achieve reliable solutions. We compared our preferred slip solution with two previously published models and found that our solution retains their most reliable features. In addition, although all three SSE models predict an upward slip penetration invading the seismogenic zone of the Guerrero seismic gap, our resolution analysis indicates that this penetration might not be a reliable feature of the 2006 SSE.

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17

Dauksher, W., and A. F. Emery. "The solution of elastostatic and elastodynamic problems with Chebyshev spectral finite elements." Computer Methods in Applied Mechanics and Engineering 188, no. 1-3 (July 2000): 217–33. http://dx.doi.org/10.1016/s0045-7825(99)00149-8.

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18

Lee, Jungki, and Mingu Han. "Volume Integral Equation Method Solution for Spheroidal Inclusion Problem." Materials 14, no. 22 (November 18, 2021): 6996. http://dx.doi.org/10.3390/ma14226996.

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In this paper, the volume integral equation method (VIEM) is introduced for the numerical analysis of an infinite isotropic solid containing a variety of single isotropic/anisotropic spheroidal inclusions. In order to introduce the VIEM as a versatile numerical method for the three-dimensional elastostatic inclusion problem, VIEM results are first presented for a range of single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under uniform remote tensile loading. We next considered single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under remote shear loading. The authors hope that the results using the VIEM cited in this paper will be established as reference values for verifying the results of similar research using other analytical and numerical methods.

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19

Ding, Rui, Fu Jun Chen, Quan Shen, and Ling Liu. "The Coupling of Pseudo-Spectral Method and Domain Decomposition Method for the Elastostatic Problem." Applied Mechanics and Materials 580-583 (July 2014): 3071–74. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.3071.

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It presents the coupling of Pseudo-spectral method (PS) and domain decomposition method (DDM) for the elastostatic problem. First, the original problem is decomposed into several sub-problems by DDM. Next combining the advantage of easy programming and high accuracy of Pseudo-spectral method, we can solve these sub-problems in parallel by PS. Finally the global numerical solution is obtained by the partition of unity approximation. Some numerical experiments illustrate the effectiveness and accuracy of our method.

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20

Dong, C. Y., S. H. Lo, and Y. K. Cheung. "Numerical solution of 3D elastostatic inclusion problems using the volume integral equation method." Computer Methods in Applied Mechanics and Engineering 192, no. 1-2 (January 2003): 95–106. http://dx.doi.org/10.1016/s0045-7825(02)00534-0.

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21

Ulrich, T. W., F. A. Moslehy, and A. J. Kassab. "A BEM based pattern search solution for a class of inverse elastostatic problems." International Journal of Solids and Structures 33, no. 15 (June 1996): 2123–31. http://dx.doi.org/10.1016/0020-7683(95)00142-5.

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22

Simonenko, Stanislav, Victor Bayona, and Manuel Kindelan. "Optimal shape parameter for the solution of elastostatic problems with the RBF method." Journal of Engineering Mathematics 85, no. 1 (June 18, 2013): 115–29. http://dx.doi.org/10.1007/s10665-013-9636-7.

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23

LEUNG, C. Y., and S. P. WALKER. "ITERATIVE SOLUTION OF LARGE THREE-DIMENSIONAL BEM ELASTOSTATIC ANALYSES USING THE GMRES TECHNIQUE." International Journal for Numerical Methods in Engineering 40, no. 12 (June 30, 1997): 2227–36. http://dx.doi.org/10.1002/(sici)1097-0207(19970630)40:12<2227::aid-nme154>3.0.co;2-z.

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24

Gregory, R. D., and F. Y. M. Wan. "The Interior Solution for Linear Problems of Elastic Plates." Journal of Applied Mechanics 55, no. 3 (September 1, 1988): 551–59. http://dx.doi.org/10.1115/1.3125829.

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Necessary conditions have been established recently for the prescribed data along the cylindrical edge(s) of an elastic flat plate to induce only an exponentially decaying elastostatic state. The present paper describes how these conditions may be used to determine the interior solution (or its various thin and thick plate theory approximations) of plate problems. The results in turn show that the necessary conditions for a decaying state are also sufficient conditions. Boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems. One of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim. The solution process for this problem illustrates for the first time how the stretching action in the plate interior induced by transverse loads can be properly analyzed.

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25

Lee, Jungki, and Ajit Mal. "A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems." Journal of Applied Mechanics 64, no. 1 (March 1, 1997): 23–31. http://dx.doi.org/10.1115/1.2787282.

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A volume integral equation method is introduced for the solution of elastostatic problems in heterogeneous solids containing interacting multiple inclusions, voids, and cracks. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions and cracks. The influence of interface layers on the interfacial stress field is investigated. The stress intensity factors for microcracks in the presence of interacting inclusions or voids are also calculated for a variety of model geometries. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and boundary integral methods.

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26

Bichurin, M. I., and V. M. Petrov. "Modeling of Magnetoelectric Interaction in Magnetostrictive-Piezoelectric Composites." Advances in Condensed Matter Physics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/798310.

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The paper dwells on the theoretical modeling of magnetoelectric (ME) effect in layered and bulk composites based on magnetostrictive and piezoelectric materials. Our analysis rests on the simultaneous solution of elastodynamic or elastostatic and electro/magnetostatic equations. The expressions for ME coefficients as the functions of material parameters and volume fractions of components are obtained. Longitudinal, transverse, and in-plane cases are considered. The use of the offered model has allowed to present the ME effect in ferrite cobalt-barium titanate, ferrite cobalt-PZT, ferrite nickel-PZT, and lanthanum strontium manganite-PZT composites adequately.

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27

Wheel, M. A. "A geometrically versatile finite volume formulation for plane elastostatic stress analysis." Journal of Strain Analysis for Engineering Design 31, no. 2 (March 1, 1996): 111–16. http://dx.doi.org/10.1243/03093247v312111.

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A finite volume formulation for discretizing and analysing plane elastostatic problems is described. Equilibrium equations which relate the displacements at the centre of a general quadrilateral cell to those in neighbouring cells are developed. After the application of suitable boundary conditions, an iterative method is employed to solve the resulting system of simultaneous equations and produce the displacement field, from which the strain and stress fields are derived subsequently. Stress distributions for a test problem, an elliptic plate pierced by an elliptic hole and loaded on the outer boundary, are determined for meshes of increasing refinement. The distributions are compared with those determined using triangular and quadrilateral finite elements and the analytical solution.

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28

Duan, H. L., J. Wang, Z. P. Huang, and Y. Zhong. "Stress fields of a spheroidal inhomogeneity with an interphase in an infinite medium under remote loadings." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2056 (April 8, 2005): 1055–80. http://dx.doi.org/10.1098/rspa.2004.1396.

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This paper presents the elastostatic solution of the problem of an arbitrarily oriented spheroidal inhomogeneity with an interphase embedded in an infinite medium. The latter is under a remote axisymmetric loading. The complete solution of this problem requires three fundamental solutions, which are obtained by the Papkovich–Neuber displacement potentials and the expansion formulae for spheroidal harmonics. New displacement potentials are given when the remote loading is a longitudinal shear. The influence of the orientation and aspect ratio of the inhomogeneity, and of the remote stress ratio on the stress concentrations at the interfaces and the von Mises equivalent stress in the inhomogeneity, are studied. It is found that the interphase between the inhomogeneity and the surrounding medium significantly alters the stress distribution in, and around, the inhomogeneity. In addition to the general solution for an inhomogeneity with an interphase, the stress field exterior to a spheroidal inhomogeneity without an interphase (the Eshelby problem) is presented in a simple form. It is pointed out that the solution of a spheroidal inhomogeneity with an interphase in an infinite medium subjected to an arbitrary uniform eigenstrain, or a combination of a uniform eigenstrain and an arbitrary remote mechanical loading, can be obtained using the procedure developed in this paper.

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Loloi, Mehdi. "Boundary integral equation solution of three-dimensional elastostatic problems in transversely isotropic solids using closed-form displacement fundamental solutions." International Journal for Numerical Methods in Engineering 48, no. 6 (June 30, 2000): 823–42. http://dx.doi.org/10.1002/(sici)1097-0207(20000630)48:6<823::aid-nme902>3.0.co;2-j.

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30

Ko, Y. Y. "Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems." Journal of Mechanics 36, no. 6 (May 7, 2020): 749–61. http://dx.doi.org/10.1017/jmech.2020.15.

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ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

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Changwen, Mi, and Demitris Kouris. "Nanoparticles and the influence of interface elasticity." Theoretical and Applied Mechanics 35, no. 1-3 (2008): 267–86. http://dx.doi.org/10.2298/tam0803267c.

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In this manuscript, we discuss the influence of surface and interface stress on the elastic field of a nanoparticle, embedded in a finite spherical substrate. We consider an axially symmetric traction field acting along the outer boundary of the substrate and a non-shear uniform eigenstrain field inside the particle. As a result of axial symmetry, two Papkovitch-Neuber displacement potential functions are sufficient to represent the elastic solution. The surface and interface stress effects are fully represented utilizing Gurtin and Murdoch's theory of surface and interface elasticity. These effects modify the traction-continuity boundary conditions associated with the classical continuum elasticity theory. A complete methodology is presented resulting in the solution of the elastostatic Navier's equations. In contrast to the classical solution, the modified version introduces additional dependencies on the size of the nanoparticles as well as the surface and interface material properties.

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Kasparova, E. A., and E. I. Shifrin. "Solution for the Geometric Elastostatic Inverse Problem by Means of Not Completely Overdetermined Boundary Data." Mechanics of Solids 55, no. 8 (December 2020): 1298–307. http://dx.doi.org/10.3103/s0025654420080117.

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33

Hagedorn, P., and W. Schramm. "On the Dynamics of Large Systems With Localized Nonlinearities." Journal of Applied Mechanics 55, no. 4 (December 1, 1988): 946–51. http://dx.doi.org/10.1115/1.3173746.

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In this paper, a certain class of dynamical systems is discussed, which can be decomposed into a large linear subsystem and one or more nonlinear subsystems. For this class of nonlinear systems the dynamic behavior is represented in the time domain by means of an integral equation. A simple numerical procedure for the solution of this integral equation is given. It is also shown how the decomposition of the system can be used in measuring the frequency response of the large linear subsystem, without actually separating it from the nonlinear subsystems. An elastostatic analogy is used to illustrate the ideas and a numerical example is given for a dynamic system.

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34

Das, Subir. "Interaction between line cracks in an orthotropic layer." International Journal of Mathematics and Mathematical Sciences 29, no. 1 (2002): 31–42. http://dx.doi.org/10.1155/s0161171202004982.

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We deal with the interaction between three coplanar Griffith cracks located symmetrically in the mid plane of an orthotropic layer of finite thickness2h. The Fourier transform technique is used to reduce the elastostatic problem to the solution of a set of integral equations which have been solved by using the finite Hilbert transform technique and Cooke's result. The analytical expressions for the stress intensity factors at the crack tips are obtained for largeh. Numerical values of the interaction effect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to each other and crack tip spacing as well as the thickness of the layer.

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MARTINSSON, P. G., and IVO BABUŠKA. "HOMOGENIZATION OF MATERIALS WITH PERIODIC TRUSS OR FRAME MICRO-STRUCTURES." Mathematical Models and Methods in Applied Sciences 17, no. 05 (May 2007): 805–32. http://dx.doi.org/10.1142/s021820250700211x.

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The equations that govern elastostatic equilibrium between a prescribed force field and an unknown displacement field for materials with periodic skeletal micro-structures are studied. It is shown that as the size of the micro-structure tends to zero, the displacement field will converge to the solution of a constant coefficient partial differential equation. This equation is shown to be either a classical or a micro-polar continuum elasticity equation, depending on the micro-structural geometry and the nature of the external load field. Convergence is proved for representative model problems in Sobolev energy norms and in the maximum norm. In addition, it is shown that by considering pseudo-differential homogenized equations, any order of convergence can be achieved.

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36

Vigdergauz, Shmuel. "Planar grained structures with multiple inclusions in a periodic cell: Elastostatic solution and its potential applications." Mathematics and Mechanics of Solids 19, no. 7 (May 24, 2013): 805–20. http://dx.doi.org/10.1177/1081286513488017.

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Penkov, V. B., L. V. Levina, O. S. Novikova, and A. S. Shulmin. "An algorithm for analytical solution of basic problems featuring elastostatic bodies with cavities and surface flaws." Journal of Physics: Conference Series 973 (March 2018): 012016. http://dx.doi.org/10.1088/1742-6596/973/1/012016.

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BLÁZQUEZ, A., V. MANTIČ, F. PARÍS, and J. CAÑAS. "ON THE REMOVAL OF RIGID BODY MOTIONS IN THE SOLUTION OF ELASTOSTATIC PROBLEMS BY DIRECT BEM." International Journal for Numerical Methods in Engineering 39, no. 23 (December 15, 1996): 4021–38. http://dx.doi.org/10.1002/(sici)1097-0207(19961215)39:23<4021::aid-nme36>3.0.co;2-q.

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Ohayon, R., R. Sampaio, and C. Soize. "Dynamic Substructuring of Damped Structures Using Singular Value Decomposition." Journal of Applied Mechanics 64, no. 2 (June 1, 1997): 292–98. http://dx.doi.org/10.1115/1.2787306.

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This paper deals with the theoretical aspects concerning linear elastodynamic of damped continuum medium in the frequency domain. Eigenvalue analysis and frequency response function are studied. The methods discussed here use a dynamic substructuring approach. The first method is based on a mixed variational formulation in which Lagrange multipliers are introduced to impose the linear constraints on the coupling interfaces. A modal reduction of each substructure is obtained using its free-interface modes. A practical construction of a unique solution is carried out using the Singular Value Decomposition (SVD) related only to the frequency-independent Lagrange multiplier terms. The second method is similar to the first one replacing the free-interface modes by the fixed-interface modes and elastostatic operator on the interface of each substructure.

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Haslinger, Jaroslav, Radek Kučera, and Tomáš Ligurský. "Qualitative analysis of 3D elastostatic contact problems with orthotropic Coulomb friction and solution-dependent coefficients of friction." Journal of Computational and Applied Mathematics 235, no. 12 (April 2011): 3464–80. http://dx.doi.org/10.1016/j.cam.2011.02.007.

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41

Vodička, R., V. Mantič, and F. París. "On the removal of the non-uniqueness in the solution of elastostatic problems by symmetric Galerkin BEM." International Journal for Numerical Methods in Engineering 66, no. 12 (2006): 1884–912. http://dx.doi.org/10.1002/nme.1605.

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42

Lahmar, M., A. Haddad, and D. Nicolas. "Elastohydrodynamic analysis of one-layered journal bearings." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 212, no. 3 (March 1, 1998): 193–205. http://dx.doi.org/10.1243/1350650981542001.

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Steady state and dynamic solutions to the problem of isothermal elastohydrodynamic lubrication of single-layered journal bearings are derived and presented. The mathematical problem comprises two parts: fluid and elasticity. The elasticity problem is governed by the elastostatic equations which are solved by application of a complex variable approach using the complex Kolosov-Muskhelishvili potentials. The fluid problem is described by the two-dimensional Reynolds equation which is discretized using a finite difference approach and solved by application of the Gauss-Seidel scheme with the Swift-Stieber boundary conditions. The fluid-structure coupling is achieved by an iterative procedure with an under-relaxation algorithm. The dynamic coefficients are obtained by use of a first-order perturbation approach. The results obtained show that the proposed elasticity model permits a fast solution of the problem, particularly under dynamic conditions. They also show that, under the effect of coating elastic deformation, the contact geometry is modified and the load-carrying capacity decreases while the stability margin of the journal bearing system increases.

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Gurrutxaga-Lerma, Beñat. "Elastodynamic image forces on screw dislocations in the presence of phase boundaries." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2205 (September 2017): 20170484. http://dx.doi.org/10.1098/rspa.2017.0484.

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The elastodynamic image forces acting on straight screw dislocations in the presence of planar phase boundaries are derived. Two separate dislocations are studied: (i) the injected, non-moving screw dislocation and (ii) the injected (or pre-existing), generally non-uniformly moving screw dislocation. The image forces are derived for both the case of a rigid surface and of a planar interface between two homogeneous, isotropic phases. The case of a rigid interface is shown to be solvable employing Head's image dislocation construction. The case of the elastodynamic image force due to an interface is solved by deriving the reflected wave's contribution to the global solution across the interface. This entails obtaining the fundamental solution (Green's function) for a point unit force via Cagniard's method, and then applying the convolution theorem for a screw dislocation modelled as a force distribution. Complete, explicit formulae are provided when available. It is shown that the elastodynamic image forces are generally affected by retardation effects, and that those acting on the moving dislocations display a dynamic magnification that exceed the attraction (or repulsion) predicted in classical elastostatic calculations.

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YAVUZ, Mustafa Murat, and Bahattin KANBER. "Effects of higher order Taylor series terms on the solution accuracy of NI-RPIM for 3D elastostatic problems." TURKISH JOURNAL OF ENGINEERING AND ENVIRONMENTAL SCIENCES 38 (2014): 411–33. http://dx.doi.org/10.3906/muh-1407-24.

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Hamzehei Javaran, S., and S. Shojaee. "The solution of elastostatic and dynamic problems using the boundary element method based on spherical Hankel element framework." International Journal for Numerical Methods in Engineering 112, no. 13 (June 27, 2017): 2067–86. http://dx.doi.org/10.1002/nme.5595.

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Olver, A. V., and D. Dini. "Roughness in lubricated rolling contact: The dry contact limit." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 221, no. 7 (July 1, 2007): 787–91. http://dx.doi.org/10.1243/13506501jet318.

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A difficulty with the standard fast Fourier transform (FFT) perturbation model of roughness in lubricated rolling contacts is that it does not necessarily converge towards the elastic case as the film thickness is reduced; rather it leads to a situation in which all the roughness is completely flattened. This is rarely the case for real engineering surfaces. Here, it is shown that this difficulty can be avoided by carrying out a Fourier transform of the elastostatically flattened roughness and using the resulting (complex) amplitude as the low-film thickness limit of each Fourier component in the elastohydrodynamic lubrication (EHL) analysis. Results give a plausible convergence to the elastostatic solution, which is nevertheless consistent with the expected near-full-film EHL behaviour and which becomes identical to the earlier model for roughness that, statically, can be fully flattened. As expected, hydrodynamic action persists at the finest scale, even for very thin films.

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Patra, R., S. P. Barik, M. Kundu, and P. K. Chaudhuri. "Plane Elastostatic Solution in an Infinite Functionally Graded Layer Weakened by a Crack Lying in the Middle of the Layer." International Journal of Computational Mathematics 2014 (November 25, 2014): 1–9. http://dx.doi.org/10.1155/2014/358617.

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This paper is concerned with an internal crack problem in an infinite functionally graded elastic layer. The crack is opened by an internal uniform pressure p0 along its surface. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude P/2 with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. Elastic parameters λ and μ are assumed to vary along the normal to the plane of crack. The problem is solved by using integral transform technique. The solution of the problem has been reduced to the solution of a Cauchy-type singular integral equation, which requires numerical treatment. The stress-intensity factors and the crack opening displacements are determined and the effects of graded parameters on them are shown graphically.

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Vigdergauz, S. "A planar grained structure with a multiphase nested inclusion in a periodic cell: Elastostatic solution and the equi-stressness." Mathematics and Mechanics of Solids 21, no. 6 (May 29, 2014): 709–24. http://dx.doi.org/10.1177/1081286514536084.

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Vodička, R., V. Mantič, and F. París. "Note on the removal of rigid body motions in the solution of elastostatic traction boundary value problems by SGBEM." Engineering Analysis with Boundary Elements 30, no. 9 (September 2006): 790–98. http://dx.doi.org/10.1016/j.enganabound.2006.04.002.

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50

Stephen, N. G., and M. Z. Wang. "Decay Rates for the Hollow Circular Cylinder." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 747–53. http://dx.doi.org/10.1115/1.2894038.

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The self-equilibrated end load problem for a hollow circular cylinder is considered using the Papkovitch-Neuber solution to the elastostatic displacement equations of equilibrium; both axi- and nonaxisymmetric solutions are derived. The requirement of zero traction on the surface generators of the cylinder leads to an eigenequation whose roots determine the rate of decay with axial coordinate. The locus of the smaller roots is plotted for circumferential harmonic loadings n = 0, 1, 2, and 3, for different wall thicknesses, and supplement previously known decay rates for the solid section and the circular cylindrical shell which are the extremes of diameter ratio. The loci are of considerable intricacy, and for small wall thickness, simple shell theory and two modes of decay for the semi-infinite plate are employed to identify the various modes of decay. Whereas for the solid cylinder the characteristic decay length of Saint-Venant’sprinciple is the radius (or diameter), for the hollow cylinder it becomes possible to discriminate between “wall thickness” and “rmt” modes of decay according to the limiting behavior as the cylinder assumes shell-like proportions; the one exception is “membrane bending” for which self-equilibrating end loading does not decay as thickness tends to zero.

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