Статті в журналах: "Linearly Elastic Analysis"

1

Miara, B., and E. Sanchez-Palencia. "Asymptotic analysis of linearly elastic shells." Asymptotic Analysis 12, no. 1 (1996): 41–54. http://dx.doi.org/10.3233/asy-1996-12103.

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2

Ciarlet, Philippe G. "Mathematical modelling of linearly elastic shells." Acta Numerica 10 (May 2001): 103–214. http://dx.doi.org/10.1017/s0962492901000022.

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The objective of this article is to lay down the proper mathematical foundations of the two-dimensional theory of linearly elastic shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional linear shell theories, by means of asymptotic methods, with the thickness as the ‘small’ parameter.A major virtue of this approach is that it naturally leads to precise mathematical definitions of linearly elastic ‘membrane’ and ‘flexural’ shells. Another noteworthy feature is that it highlights in particular the role played by two fundamental tensors, each associated with a displacement field of the middle surface, the linearized change of metric and linearized change of curvature tensors.More specifically, under fundamentally distinct sets of assumptions bearing on the geometry of the middle surface, on the boundary conditions, and on the order of magnitude of the applied forces, it is shown that the three-dimensional displacements, once properly scaled, converge (in H1, or in L2, or in ad hoc completions) as the thickness approaches zero towards a ‘two-dimensional’ limit that satisfies either the linear two-dimensional equations of a ‘membrane’ shell (themselves divided into two subclasses) or the linear two-dimensional equations of a ‘flexural’ shell. Note that this asymptotic analysis automatically provides in each case the ‘limit’ two-dimensional equations, together with the function space over which they are well-posed.The linear two-dimensional shell equations that are most commonly used in numerical simulations, namely Koiter's equations, Naghdi's equations, and ‘shallow’ shell equations, are then carefully described, mathematically analysed, and likewise justified by means of asymptotic analyses.The existence and uniqueness of solutions to each one of these linear two-dimensional shell equations are also established by means of crucial inequalities of Korn's type on surfaces, which are proved in detail at the beginning of the article.This article serves as a mathematical basis for the numerically oriented companion article by Dominique Chapelle, also in this issue of Acta Numerica.

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3

Kounadis, A. N., and J. G. Mallis. "Elastica type buckling analysis of bars from non-linearly elastic material." International Journal of Non-Linear Mechanics 22, no. 2 (January 1987): 99–107. http://dx.doi.org/10.1016/0020-7462(87)90013-8.

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4

Poon, B., D. Rittel, and G. Ravichandran. "An analysis of nanoindentation in linearly elastic solids." International Journal of Solids and Structures 45, no. 24 (December 2008): 6018–33. http://dx.doi.org/10.1016/j.ijsolstr.2008.07.021.

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5

Ciarlet, Philippe G., and V�ronique Lods. "Asymptotic analysis of linearly elastic shells: ?Generalized membrane shells?" Journal of Elasticity 43, no. 2 (May 1996): 147–88. http://dx.doi.org/10.1007/bf00042508.

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6

Maso, Gianni Dal, Antonio DeSimone, and Maria Giovanna Mora. "Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials." Archive for Rational Mechanics and Analysis 180, no. 2 (February 6, 2006): 237–91. http://dx.doi.org/10.1007/s00205-005-0407-0.

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7

Renardy, M., and D. L. Russell. "Formability of Linearly Elastic Structures with Volume-Type Actuation." Archive for Rational Mechanics and Analysis 149, no. 2 (October 1, 1999): 97–122. http://dx.doi.org/10.1007/s002050050169.

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8

Auricchio, Ferdinando, Carlo Lovadina, and Alexandre L. Madureira. "An asymptotically optimal model for isotropic heterogeneous linearly elastic plates." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 5 (September 2004): 877–97. http://dx.doi.org/10.1051/m2an:2004042.

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9

SABU, N. "ASYMPTOTIC ANALYSIS OF LINEARLY ELASTIC SHALLOW SHELLS WITH VARIABLE THICKNESS." Chinese Annals of Mathematics 22, no. 04 (October 2001): 405–16. http://dx.doi.org/10.1142/s0252959901000401.

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10

Sun, Jun-Yi, Qi Zhang, Xue Li, and Xiao-Ting He. "Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading." Symmetry 13, no. 10 (September 23, 2021): 1770. http://dx.doi.org/10.3390/sym13101770.

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The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

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11

Ciarlet, Philippe G., and Cristinel Mardare. "The intrinsic theory of linearly elastic plates." Mathematics and Mechanics of Solids 24, no. 4 (May 28, 2018): 1182–203. http://dx.doi.org/10.1177/1081286518776047.

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In an intrinsic approach to a problem in elasticity, the only unknown is a tensor field representing an appropriate ‘measure of strain’, instead of the displacement vector field in the classical approach. The objective of this paper is to study the displacement traction problem in the special case where the elastic body is a linearly elastic plate of constant thickness, clamped over a portion of its lateral face. In this respect, we first explicitly compute the intrinsic three-dimensional boundary condition of place in terms of the Cartesian components of the linearized strain tensor field, thus avoiding the recourse to covariant components in curvilinear coordinates and providing an interesting example of actual computation of an intrinsic boundary condition of place in three-dimensional elasticity. Second, we perform a rigorous asymptotic analysis of the three-dimensional equations as the thickness of the plate, considered as a parameter, approaches zero. As a result, we identify the intrinsic two-dimensional equations of a linearly elastic plate modelled by the Kirchhoff–Love theory, with the linearized change of metric and change of curvature tensor fields of the middle surface of the plate as the new unknowns, instead of the displacement field of the middle surface in the classical approach.

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12

Piersanti, Paolo. "Asymptotic analysis of linearly elastic elliptic membrane shells subjected to an obstacle." Journal of Differential Equations 320 (May 2022): 114–42. http://dx.doi.org/10.1016/j.jde.2022.02.053.

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13

Lazopoulos, Konstantinos A., and Anastasios K. Lazopoulos. "On the fractional deformation of a linearly elastic bar." Journal of the Mechanical Behavior of Materials 29, no. 1 (April 20, 2020): 9–18. http://dx.doi.org/10.1515/jmbm-2020-0002.

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AbstractFractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented.

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14

Rungamornrat, Jaroon, and Peerasak Tangnovarad. "Analysis of Linearly Elastic Inextensible Frames Undergoing Large Displacement and Rotation." Mathematical Problems in Engineering 2011 (2011): 1–37. http://dx.doi.org/10.1155/2011/592958.

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This paper presents an efficient semi-analytical technique for modeling two-dimensional, linearly elastic, inextensible frames undergoing large displacement and rotation. A system of ordinary differential equations governing an element is first converted into a system of nonlinear algebraic equations via appropriate enforcement of boundary conditions. Taylor's series expansion is then employed along with the co-rotational approach to derive the best linear approximation of such system and the corresponding exact element tangent stiffness matrix. A standard assembly procedure is applied, next, to obtain the best linear approximation of governing nonlinear equations for the structure. This final system is exploited in the solution search by Newton-Ralphson iteration. Key features of the proposed technique include that (i) exact load residuals are evaluated from governing nonlinear algebraic equations, (ii) an exact form of the tangent stiffness matrix is utilized, and (iii) all elements are treated in a systematic way via direct stiffness strategy. The first two features enhance the performance of the technique to yield results comparable to analytical solutions and independent of mesh refinement whereas the last feature allows structures of general geometries and loading conditions be modeled in a straightforward fashion. The implemented algorithm is tested for various structures not only to verify its underlying formulation but also to demonstrate its capability and robustness.

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15

Rushchitsky, J. J., C. Cattani, and E. V. Terletskaya. "Wavelet Analysis of a Single Pulse in a Linearly Elastic Composite." International Applied Mechanics 41, no. 4 (April 2005): 374–80. http://dx.doi.org/10.1007/s10778-005-0098-0.

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16

Ciarlet, Philippe G., and Véronique Lods. "Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations." Archive for Rational Mechanics and Analysis 136, no. 2 (December 1996): 119–61. http://dx.doi.org/10.1007/bf02316975.

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17

Ciarlet, Philippe G., Véronique Lods, and Bernadette Miara. "Asymptotic analysis of linearly elastic shells. II. Justification of flexural shell equations." Archive for Rational Mechanics and Analysis 136, no. 2 (December 1996): 163–90. http://dx.doi.org/10.1007/bf02316976.

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18

Ciarlet, Philippe G., and Véronique Lods. "Asymptotic Analysis of Linearly Elastic Shells. I. Justification of Membrane Shell Equations." Archive for Rational Mechanics and Analysis 136, no. 2 (December 12, 1996): 119–61. http://dx.doi.org/10.1007/pl00004229.

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19

Ciarlet, Philippe G., Véronique Lods, and Bernadette Miara. "Asymptotic Analysis of Linearly Elastic Shells. II. Justification of Flexural Shell Equations." Archive for Rational Mechanics and Analysis 136, no. 2 (December 12, 1996): 163–90. http://dx.doi.org/10.1007/pl00004230.

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20

Ciarlet, Philippe G., and Véronique Lods. "Asymptotic Analysis of Linearly Elastic Shells. III. Justification of Koiter's Shell Equations." Archive for Rational Mechanics and Analysis 136, no. 2 (December 12, 1996): 191–200. http://dx.doi.org/10.1007/pl00004231.

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21

Yancey, R. N., and Marek-Jerzy Pindera. "Micromechanical Analysis of the Creep Response of Unidirectional Composites." Journal of Engineering Materials and Technology 112, no. 2 (April 1, 1990): 157–63. http://dx.doi.org/10.1115/1.2903302.

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The paper outlines the use of the micromechanics model proposed by Aboudi in predicting the creep response of unidirectional composites consisting of linearly viscoelastic matrices and elastic fibers. The closed-form expressions for the effective elastic moduli given in terms of the phase moduli and volume fractions provided by the micromechanics model facilitate a straightforward application of the viscoelastic Correspondence Principle. The inversion of the effective moduli in the Laplace transform domain to the time domain is subsequently accomplished using the Bellman method. The predictions of the model are compared with the creep response of T300/934 graphite/epoxy unidirectional coupons at two different temperatures. Very good correlation between theory and experiment is illustrated for the linearly viscoelastic response characterized by relatively small creep strains.

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22

Le, Q. V., W. K. Chan, and J. Schwartz. "A two-dimensionalordinary, state-based peridynamic model for linearly elastic solids." International Journal for Numerical Methods in Engineering 98, no. 8 (March 3, 2014): 547–61. http://dx.doi.org/10.1002/nme.4642.

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23

Ciarlet, Philippe G., and Paolo Piersanti. "An obstacle problem for Koiter’s shells." Mathematics and Mechanics of Solids 24, no. 10 (March 3, 2019): 3061–79. http://dx.doi.org/10.1177/1081286519825979.

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In this paper, we define, a priori, a natural two-dimensional Koiter’s model of a ‘general’ linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the ‘unconstrained’ Koiter’s model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a ‘small’ parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the ‘limit’ model obtained in this fashion coincides with the two-dimensional ‘limit’ model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a ‘general’ linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter’s model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a ‘limit’ model.

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24

LUCE, ROBERT, CÉCILE POUTOUS, and JEAN-MARIE THOMAS. "WEAKENED CONDITIONS OF ADMISSIBILITY OF SURFACE FORCES APPLIED TO LINEARLY ELASTIC MEMBRANE SHELLS." Analysis and Applications 06, no. 03 (July 2008): 247–67. http://dx.doi.org/10.1142/s0219530508001158.

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We consider a family of linearly elastic shells of the first kind (as defined in [2]), also known as non inhibited pure bending shells [7]. This family is indexed by the half-thickness ε. When ε approaches zero, the averages across the thickness of the shell of the covariant components of the displacement of the points of the shell converge strongly towards the solution of a "2D generalized membrane shell problem" provided the applied forces satisfy admissibility conditions [1,3]. The identification of the admissible applied forces usually requires delicate analysis. In the first part of this paper, we simplify the general admissibility conditions when applied forces h are surface forces only, and obtain conditions that no longer depend on ε [5]: find hαβ = hαβ in L2(ω) such that for all η = (ηi) in V(ω), ∫ω hi ηi dω = ∫ω hαβγαβ(η)dω where ω is a domain of ℝ2, θ is in [Formula: see text] and [Formula: see text] is the middle surface of the shells, where (γαβ (η)) is the linearized strain tensor of S and V(ω) = {η ∈ H1(ω), η = 0 on γ0}, the shells being clamped along Γ0 = θ(γ0). In the second part, since the simplified admissibility formulation does not allow to conclude directly to the existence of hαβ, we seek sufficient conditions on h for hαβ to exist in L2(ω). In order to get them, we impose more regularity to hαβ and boundary conditions. Under these assumptions, we can obtain from the weak formulation a system of PDE's with hαβ as unknowns. The existence of solutions depends both on the geometry of the shell and on the choice of h. We carry through the study of four representative geometries of shells and identify in each case a special admissibility functional space for h.

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25

Kyrkach, Oleksiy, Havin Valerij Havin, and Borys Kyrkach. "Static analysis of multi-support spindle shafts with nonlinear elastic bearings." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 2 (December 31, 2021): 94–100. http://dx.doi.org/10.20998/2078-9130.2021.2.248079.

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In this paper a mathematical model and computational tool are developed for the static analysis of multi-bearing spindle shafts with nonlinear elastic supports. Based on the Timoshenko beam theory a resolving system of equations is obtained that takes into account the nonlinear dependence of the bearing stiffness on the reaction forces acting upon them. A solution method is proposed and appropriate software is developed that implements the static analysis of multi-support spindle shafts with non-linearly elastic bearings in MATLAB environment. Key words: spindle, shaft, nonlinear elastic support, multi-bearing, nonlinear elastic stiffness, Timoshenko beam.

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26

Sayman, Onur, Ramazan Karakuzu, Behçet Dağhan, and Saim Koçak. "Elastic-Plastic Stress Analysis of Thermoplastic Composite Beams Under Temperature Distributed Linearly." Journal of Thermoplastic Composite Materials 15, no. 3 (May 2002): 193–208. http://dx.doi.org/10.1177/0892705702015003443.

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27

Barboteu, M. "Numerical analysis of a bilateral frictional contact problem for linearly elastic materials." IMA Journal of Numerical Analysis 22, no. 3 (July 1, 2002): 407–36. http://dx.doi.org/10.1093/imanum/22.3.407.

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28

Liu, G. R., and J. D. Achenbach. "A Strip Element Method for Stress Analysis of Anisotropic Linearly Elastic Solids." Journal of Applied Mechanics 61, no. 2 (June 1, 1994): 270–77. http://dx.doi.org/10.1115/1.2901440.

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A new numerical method, the strip element method, is presented for the stress analysis of anisotropic linearly elastic solids. For two-dimensional problems the domain is discretized in one direction into strip elements. By using the principle of virtual work, approximate governing differential equations are derived for the field dependence in the second direction. These differential equations can be solved analytically. For infinite bodies, some special features such as infinite elements and nonreflecting boundary conditions are introduced and a viscoelastic nonreflecting boundary is also presented. Numerical results for static and dynamic problems are presented and compared with exact solutions. Very good agreement is observed. The strip element method maintains the advantages of the finite element method, but it requires much less data storage. The technique can easily be extended to solids that are inhomogeneous in one direction.

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29

Ciarlet, Philippe G., and Véronique Lods. "Asymptotic analysis of linearly elastic shells. III. Justification of Koiter's shell equations." Archive for Rational Mechanics and Analysis 136, no. 2 (December 1996): 191–200. http://dx.doi.org/10.1007/bf02316977.

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30

Topcu, Muzaffer, Gurkan Altan, Hasan Callioglu, and Burcin Deda Altan. "Thermal Elastic-Plastic Stress Analysis of an Aluminium Composite Disc under Linearly Decreasing Thermal Loading." Advanced Composites Letters 17, no. 3 (May 2008): 096369350801700. http://dx.doi.org/10.1177/096369350801700302.

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In this study, an elastic-plastic thermal stress analysis of an orthotropic aluminium metal matrix composite disc with a hole has been investigated analytically for non-linear hardening material behaviour. The aluminium composite disc reinforced curvilinearly by steel fibres is produced under hydraulic press. The mechanical properties of the composite disc are obtained by tests. A computer program is developed to calculate the thermal stresses under a linearly decreasing temperature from inner surface to outer surface. Elastic, elastic-plastic and residual thermal stress distributions are obtained analytically from inner surface to outer surface and they are presented in tables and Fig. s. The elastic-plastic solution is performed for the plastic region expanding around the inner surface. The magnitude of the tangential stress component has been found out in this study to be higher than the magnitude of the radial stress component. Besides, the tangential stress component is compressive at the inner surface and tensile at the outer surface. The magnitude of the tangential residual stress component is the highest at the inner surface of the composite disc.

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31

Pathak, Prabin, and Yi Xia Zhang. "Finite Element Simulation for Nonlinear Finite Element Analysis of FRP Strengthened RC Beams with Bond-Slip Effect." Applied Mechanics and Materials 846 (July 2016): 440–45. http://dx.doi.org/10.4028/www.scientific.net/amm.846.440.

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A new simple, efficient and accurate finite element model denoted as FEM-B is developed for the analysis of structural behavior of FRP strengthened RC beams with bond-slip effect. Geometric nonlinearity and material nonlinear properties of concrete and steel rebar are accounted for this model. Concrete, steel, FRP and adhesive are modelled as Solid 65, Link 180, Shell181 and Solid 45 respectively. Concrete is modelled using Nitereka and Neal’s model for compression, isotropic and linear elastic model before cracking for tension and strength gradually reduces to zero after cracking, whereas steel is assumed to be elastic perfectly plastic material. The material of FRP is considered to be linearly elastic until rupture, and adhesive is assumed to be linearly elastic. The bond slip between concrete, adhesive and FRP is based on the bilinear law, which is modelled using spring element Combin 39.The developed new finite element model FEM-B is validated against experimental results, and demonstrates to be effective for the structural analysis of FRP strengthened RC beams.

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32

Chang, W. V., and S. C. Sun. "Nonlinear Elastic Analysis of the Hardness Test on Rubber-Like Materials." Rubber Chemistry and Technology 64, no. 2 (May 1, 1991): 202–10. http://dx.doi.org/10.5254/1.3538552.

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Abstract Both the Ogden-Tschoegl nonlinear elastic constitutive law and a contact algorithm in the general-purpose finite-element program AFEM have been used to examine the use of IRHD values to relate the elastic properties of elastomers. We are aware that large deformations of rubber specimens and complicated interface conditions are involved in this so-called simple test. However, from the finite-element results, we find that the linearly elastic Hertz contact solution is a reasonably accurate model. This can be attributed to several points. First, the hardness test involves mainly compression and shear deformation and the linearly elastic behavior is more closely followed in rubbers for the above two types of deformation. Second, although nonlinear effects become significant in soft rubbers and higher indentation cases, the ASTM D 1415 standard defines larger indentation depth differences for smaller IRHD values. The definition itself compensates for the nonlinear effects. Third, although the interfacial stress field changed due to different frictional conditions, we calculated the IRHD values only from indentation depth difference and total load applied to the steel ball. Both the indentation depth difference and the total load are obtained from far-field conditions and do not change significantly. We should note that using linear elasticity to correlate the elastic moduli and IRHD values is simply a special case in rubber elasticity. We conveniently get rubber's elastic moduli from IRHD values based on linear elasticity, but the complete rubber-like material behavior has to be obtained from more general experiments and described by a nonlinear constitutive law such as the Ogden-Tschoegl model.

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33

BARAŃSKI, W. "ON INFINITESIMAL STABILITY AND HOMOGENIZATION OF LINEARLY ELASTIC PERIODIC COMPOSITES." Mathematical Models and Methods in Applied Sciences 10, no. 08 (November 2000): 1251–62. http://dx.doi.org/10.1142/s0218202500000616.

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This paper is devoted to the study of infinitesimal stability of linearly elastic periodic composites. A solution of the homogenization problem of infinitesimal stability with respect to Dirichlet's boundary conditions is found. Under some regularity assumptions, it is shown that in this case homogenization commutes with infinitesimal stability. The obtained results are derived in a sequence of steps involving analysis of mutual relations between H-measures, ellipticity, infinitesimal stability and the existence of modes of infinitesimal buckling.

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34

McLeod, J. B., and K. R. Rajagopal. "Inhomogeneous Non-Unidirectional Deformations of a Wedge of a Non-Linearly Elastic Material." Archive for Rational Mechanics and Analysis 147, no. 3 (August 1, 1999): 179–96. http://dx.doi.org/10.1007/s002050050148.

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35

Wang, Mingji, Kenneth M. Liechti, Vibha Srinivasan, John M. White, Peter J. Rossky, and Matthew T. Stone. "A Hybrid Continuum-Molecular Analysis of Interfacial Force Microscope Experiments on a Self-Assembled Monolayer." Journal of Applied Mechanics 73, no. 5 (November 24, 2004): 769–77. http://dx.doi.org/10.1115/1.1943435.

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Nanoindentation experiments were performed on a defect-free, molecular self-assembled monolayer of octadecyltrichlorosilane (OTS) on silicon using an interfacial force microscope (IFM). The IFM provided repeatable and elastic force profiles corresponding to the adhesive and compressive response of these 2.5nm thick monolayers. As a first step in the analysis of the force profiles, the OTS was assumed to be linearly elastic and isotropic, and adhesive interactions were accounted for via a cohesive zone model. However, the assumption of linearity gave rise to force profiles that did not match the measurements. As a result, the mechanical behavior of the OTS was extracted from molecular-dynamics simulations and represented as a hypoelastic material, which, when used in finite element analyses of the IFM experiments, was able to fully reproduce the force profiles. This suggests that the continuum representation of the mechanical and adhesive behavior of self-assembled monolayers may be directly obtained from molecular analyses.

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36

Lohar, H., A. Mitra, and S. Sahoo. "Free vibration analysis of axially functionally graded linearly taper beam on elastic foundation." IOP Conference Series: Materials Science and Engineering 149 (September 2016): 012130. http://dx.doi.org/10.1088/1757-899x/149/1/012130.

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37

Morris, Glenn, and Husam Omar. "Analysis of laterally loaded flat-plate structures." Canadian Journal of Civil Engineering 18, no. 1 (February 1, 1991): 109–17. http://dx.doi.org/10.1139/l91-013.

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Flat-plate reinforced concrete structures tend to behave nonlinearly, even at service load levels, when subjected to lateral loading. This is due mainly to the deformations that occur at the column-to-plate boundaries. Currently available structural analysis computer programs assume linearly elastic behaviour and thus underestimate lateral displacements. This paper describes an efficient, easy-to-use structural analysis procedure and computer program for predicting the nonlinear response of flat-plate structures subjected to lateral loading. The structure is assumed to be a three-dimensional frame comprised of linearly elastic columns, flat-plate floor panels and shear walls, and nonlinear "connections" between the columns and the flat-plate floors. Utilizing all available experimental data, standardized functions have been derived to predict the nonlinear moment–rotation behaviour of these plate-to-column connections. The functions have been incorporated into the structural analysis computer program. Examples are presented to illustrate the capabilities of the program, to compare results computed by it with published results, and to illustrate the effects of several geometric and material parameters on the behaviour of the structure. Key words: reinforced concrete, flat plate, structural analysis, nonlinear analysis, lateral load analysis.

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38

LE DRET, HERVÉ. "WELL-POSEDNESS FOR KOITER AND NAGHDI SHELLS WITH A G1-MIDSURFACE." Analysis and Applications 02, no. 04 (October 2004): 365–88. http://dx.doi.org/10.1142/s0219530504000412.

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We extend the notion of G1-join or visually C1 join between two surface patches, that is to say, a continuous join with continuous tangent plane. This notion is familiar in CAD, to the case of surfaces with minimal regularity with respect to linearly elastic shell models. We then prove the well-posedness of various shell models for surfaces defined via a collection of such patches.

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39

Piersanti, Paolo. "On the improved interior regularity of a boundary value problem modelling the displacement of a linearly elastic elliptic membrane shell subject to an obstacle." Discrete & Continuous Dynamical Systems 42, no. 2 (2022): 1011. http://dx.doi.org/10.3934/dcds.2021145.

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<p style='text-indent:20px;'>In this paper we show that the solution of an obstacle problem for linearly elastic elliptic membrane shells enjoys higher differentiability properties in the interior of the domain where it is defined.</p>

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40

He, Bo, and Chang Qing Sun. "Analysis on Functionally Graded Material Coating Interface Crack." Advanced Materials Research 602-604 (December 2012): 1596–99. http://dx.doi.org/10.4028/www.scientific.net/amr.602-604.1596.

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It is assumed that the physical parameters of functionally graded coating material accords with the variation of degree n polynomial, and based on this material model, the behavior of crack fracture on the interface of functionally graded coating is studied. The results show that when the functionally graded coating structure bears a tension load, stress intensity factors of mode I and mode II exist at the same time generally, and the intensity factor of mode I occupies a leading position all along. Besides, when the elastic modulus ratio of the base to the functionally graded coating top is 5 and the elastic modulus of functionally graded coating varies linearly, the stress intensity factor of interface crack is the smallest, and with the increasing of elastic modulus ratio, the optimal non-uniform parameter tends to be larger than 1.

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41

Madsen, Nels. "An Alternative Approach to the Symmetrical Top and Slender Member Analysis." Journal of Applied Mechanics 58, no. 2 (June 1, 1991): 593–94. http://dx.doi.org/10.1115/1.2897231.

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This Note considers the problem of a symmetrical top under the action of gravity, or analogously the problem of a long, slender, initially straight linearly elastic, circular cross-section member loaded only at its ends. A nonbody fixed coordinate system is used. The standard results are obtained without any explicit reference to a space-fixed coordinate system.

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42

KONDO, Masanori, and Kenji OGUNI. "A PROPOSAL OF NUMERICAL ANALYSIS METHOD FOR DYNAMIC CRACK PROPAGATION IN LINEARLY ELASTIC SOLIDS." Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) 68, no. 1 (2012): 51–66. http://dx.doi.org/10.2208/jscejam.68.51.

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43

Zhang, Lei, Jizeng Wang, and You-He Zhou. "Large deflection and post-buckling analysis of non-linearly elastic rods by wavelet method." International Journal of Non-Linear Mechanics 78 (January 2016): 45–52. http://dx.doi.org/10.1016/j.ijnonlinmec.2015.10.002.

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44

Taylor, J. E. "A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle)." Journal of Applied Mechanics 61, no. 4 (December 1, 1994): 914–18. http://dx.doi.org/10.1115/1.2901577.

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An extremum problem formulation is presented for the equilibrium mechanics of continuum systems made of a generalized form of elastic/stiffening material. Properties of the material are represented via a series composition of elastic/locking constituents. This construction provides a means to incorporate a general model for nonlinear composites of stiffening type into a convex problem statement for the global equilibrium analysis. The problem statement is expressed in mixed “stress and deformation” form. Narrower statements such as the classical minimum potential energy principle, and the earlier (Prager) model for elastic/locking material are imbedded within the general formulation. An extremum problem formulation in mixed form for linearly elastic structures is available as a special case as well.

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45

Pucci, Edvige, Giuseppe Saccomandi, and Luigi Vergori. "Linearly polarized waves of finite amplitude in pre-strained elastic materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (June 2019): 20180891. http://dx.doi.org/10.1098/rspa.2018.0891.

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We study the propagation of linearly polarized transverse waves in a pre-strained incompressible isotropic elastic solid. Both finite and small-but-finite amplitude waves are examined. Irrespective of the magnitude of the wave amplitude, these waves may propagate only if the (unit) normal to the plane spanned by the directions of propagation and polarization is a principal direction of the left Cauchy–Green deformation tensor associated with the pre-strained state. A rigorous asymptotic analysis of the equations governing the propagation of waves of small but finite amplitude reveals that the time scale over which the nonlinear effects become significant depends on the direction along which the wave travels. Moreover, we design theoretically an experimental procedure to determine the Landau constants of the fourth-order weakly nonlinear theory of elasticity.

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46

Keskinen, E., V.-T. Kuokkala, T. Vuoristo, and M. Martikainen. "Multi-body wave analysis of axially elastic rod systems." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221, no. 3 (September 1, 2007): 417–28. http://dx.doi.org/10.1243/14644193jmbd75.

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Axially elastic rods are basic machine elements in hydraulic hammers, pilers, and percussive drills. The problem to analyse the motion history of such mechanisms is a very complex one, because the rods are simultaneously in large-amplitude axial motion superimposed with a small-amplitude elastic wave motion. The wave motion experiences division to reflected and transmitted components at each rod-rod interface depending on the current boundary stiffness. The wave motion in each rod can be computed by finite elements or, alternatively, in space of semidefinite eigenfunctions. The feasibility of these methods in solving wave propagation problems in multi-rod systems with non-linearly behaving rod-rod interfaces has been investigated and evaluated. The object of the experimental case study is a classical Hopkinson split bar apparatus used in experimental analysis of material response to shock pulses. Another example representing a pile hammering system evaluates the computational performance of the proposed approaches in long-termsimulation of a complete work process.

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47

Banks, J. W., and B. Sjögreen. "A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction." Communications in Computational Physics 10, no. 2 (August 2011): 279–304. http://dx.doi.org/10.4208/cicp.060210.300910a.

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AbstractIn multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocity- and stress-continuity can be enforced in the discrete approximation. This paper performs a normal mode stability analysis of the linearized problem to investigate the stability of different numerical interface conditions for a model problem approximated by upwind type finite difference schemes. The analysis shows that depending on the ratio of densities between the solid and the fluid, some numerical interface conditions are stable up to the maximal CFL-limit, while other numerical interface conditions suffer from a severe reduction of the stable CFL-limit. The paper also presents a new interface condition, obtained as a simplified characteristic boundary condition, that is proved to not suffer from any reduction of the stable CFL-limit. Numerical experiments in one space dimension show that the new interface condition is stable also for computations with the non-linear Euler equations of compressible fluid flow coupled with a linearly elastic solid.

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48

MADUREIRA, ALEXANDRE L. "AN IMPROVED BIHARMONIC MODEL: INCORPORATING HIGHER-ORDER RESPONSES OF THE PLATE BENDING PHENOMENA." Analysis and Applications 02, no. 01 (January 2004): 87–99. http://dx.doi.org/10.1142/s021953050400028x.

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We modify the usual biharmonic model, still frequently used in the engineering community to model linearly elastic plates. In its traditional form, the biharmonic model diverges, in general, since it does not incorporate shear effects. Our changes make it convergent for all loads, under the usual assumption on how the loads depend on the thickness. The idea is to add "higher-order" terms that appear in the asymptotic expansion of the exact solution. The changes can be readily incorporated into engineering codes without degrading the computational performance.

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49

McDevitt, T. J., and J. G. Simmonds. "The Axisymmetric Deformation of Linearly and Nonlinearly Elastic Spinning Tubes Under End Thrusts and Torques." Journal of Applied Mechanics 65, no. 1 (March 1, 1998): 99–106. http://dx.doi.org/10.1115/1.2789053.

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We consider the steady-state deformations of elastic tubes spinning steadily and attached in various ways to rigid end plates to which end thrusts and torques are applied. We assume that the tubes are made of homogeneous linearly or nonlinearly anisotropic material and use Simmonds” (1996) simplified dynamic displacement-rotation equations for shells of revolution undergoing large-strain large-rotation axisymmetric bending and torsion. To exploit analytical methods, we confine attention to the nonlinear theory of membranes undergoing small or large strains and the theory of strongly anisotropic tubes suffering small strains. Of particular interest are the boundary layers that appear at each end of the tube, their membrane and bending components, and the penetration of these layers into the tube which, for certain anisotropic materials, may be considerably different from isotropic materials. Remarkably, we find that the behavior of a tube made of a linearly elastic, anisotropic material (having nine elastic parameters) can be described, to a first approximation, by just two combined parameters. The results of the present paper lay the necessary groundwork for a subsequent analysis of the whirling of spinning elastic tubes under end thrusts and torques.

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50

Jaric, Jovo, Dragoslav Kuzmanovic, and Zoran Golubovic. "On tensors of elasticity." Theoretical and Applied Mechanics 35, no. 1-3 (2008): 119–36. http://dx.doi.org/10.2298/tam0803119j.

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An objective of this paper is to reconcile the "symmetry" approach with the "symmetry groups" approach as these two different points of view presently coexist in the literature. Here we will be concerned exclusively with linearly elastic materials. The starting point for an analysis of the inherent symmetry of elastic materials is the notion of a symmetry transformation. Particularly, we paid attention to the compliance tensor for cubic and hexagonal crystals.

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