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1.
The crack propagation problem for linear elastic fracture mechanics has been studied by several authors exploiting its analogy with standard dissipative systems theory (see e.g. Nguyen in Appl Mech Rev 47, 1994, Stability and nonlinear solid mechanics. Wiley, New York, 2000; Mielke in Handbook of differential equations, evolutionary equations. Elsevier, Amsterdam, 2005; Bourdin et al. in The variational approach to fracture. Springer, Berlin, 2008). In a recent publication (Salvadori and Carini in Int J Solids Struct 48:1362–1369, 2011) minimum theorems were derived in terms of crack tip “quasi static velocity” for two-dimensional fracture mechanics. They were reminiscent of Ceradini’s theorem (Ceradini in Rendiconti Istituto Lombardo di Scienze e Lettere A99, 1965, Meccanica 1:77–82, 1966) in plasticity. Following the cornerstone work of Rice (1989) on weight function theories, Leblond et al. (Leblond in Int J Solids Struct 36:79–103, 1999; Leblond et al. in Int J Solids Struct 36:105–142, 1999) proposed asymptotic expansions for stress intensity factors in three dimensions—see also Lazarus (J Mech Phys Solids 59:121–144, 2011). As formerly in 2D, expansions can be given a Colonnetti’s decomposition (Colonnetti in Rend Accad Lincei 5, 1918, Quart Appl Math 7:353–362, 1950) interpretation. In view of the expression of the expansions proposed in Leblond (Int J Solids Struct 36:79–103, 1999), Leblond et al. (Int J Solids Struct 36:105–142, 1999) however, symmetry of Ceradini’s theorem operators was not evident and the extension of outcomes proposed in Salvadori and Carini (Int J Solids Struct 48:1362–1369, 2011) not straightforward. Following a different path of reasoning, minimum theorems have been finally derived.  相似文献   

2.
The numerical simulation of contact problems is still a delicate matter especially when large transformations are involved. In that case, relative large slidings can occur between contact surfaces and the discretization error induced by usual finite elements may not be satisfactory. In particular, usual elements lead to a facetization of the contact surface, meaning an unavoidable discontinuity of the normal vector to this surface. Uncertainty over the precision of the results, irregularity of the displacement of the contact nodes and even numerical oscillations of contact reaction force may result of such discontinuity. Among the existing methods for tackling such issue, one may consider mortar elements (Fischer and Wriggers, Comput Methods Appl Mech Eng 195:5020–5036, 2006; McDevitt and Laursen, Int J Numer Methods Eng 48:1525–1547, 2000; Puso and Laursen, Comput Methods Appl Mech Eng 93:601–629, 2004), smoothing of the contact surfaces with additional geometrical entity (B-splines or NURBS) (Belytschko et al., Int J Numer Methods Eng 55:101–125, 2002; Kikuchi, Penalty/finite element approximations of a class of unilateral contact problems. Penalty method and finite element method, ASME, New York, 1982; Legrand, Modèles de prediction de l’interaction rotor/stator dans un moteur d’avion Thèse de doctorat. PhD thesis, École Centrale de Nantes, Nantes, 2005; Muñoz, Comput Methods Appl Mech Eng 197:979–993, 2008; Wriggers and Krstulovic-Opara, J Appl Math Mech (ZAMM) 80:77–80, 2000) and, the use of isogeometric analysis (Temizer et al., Comput Methods Appl Mech Eng 200:1100–1112, 2011; Hughes et al., Comput Methods Appl Mech Eng 194:4135–4195, 2005; de Lorenzis et al., Int J Numer Meth Eng, in press, 2011). In the present paper, we focus on these last two methods which are combined with a finite element code using the bi-potential method for contact management (Feng et al., Comput Mech 36:375–383, 2005). A comparative study focusing on the pros and cons of each method regarding geometrical precision and numerical stability for contact solution is proposed. The scope of this study is limited to 2D contact problems for which we consider several types of finite elements. Test cases are given in order to illustrate this comparative study.  相似文献   

3.
Robert L. Bish 《Acta Mechanica》2012,223(11):2411-2423
The theory of plastic flow by extended slip (Acta Mech 223:655–668, 2012; Philos Mag A 91:3343–3357, 2011; Z Angew Math Mech 84:266–279, 2004; Q J Mech Appl Math 52:645–662, 1999) is applied to a problem of bi-axial strain: the transverse plastic deflection, by means of a flat-ended punch, of a clamped plate of mild-steel. Two new theorems concerned with the Mechanics of Plates are presented. It is shown that, if the static shear yield stress of the plate material remains independent of strain, then the load–deflection relation for the punch, in the case of quasi-static punching of a plate clamped along a closed arbitrary contour, obeys an exactly linear theoretical relation. This prediction is then confirmed by experiments carried out at quasi-static rates of loading with thin plates of hot-rolled mild-steel. It is demonstrated by experiment, in the case of concentric circular punch and clamp contours, that the load–deflection relation for the punch remains linear to within <1 % provided that the maximum principal strain within the free domain of the plate does not exceed the yield-point elongation strain of the mild-steel concerned.  相似文献   

4.
5.
A physically-based small strain curing model has been developed and discussed in our previous contribution (Hossain et al. in Comput Mech 43:769–779, 2009a) which was extended later for finite strain elasticity and viscoelasticity including shrinkage in Hossain et al. (Comput Mech 44(5):621–630, 2009b) and in Hossain et al. (Comput Mech 46(3):363–375, 2010), respectively. The previously proposed constitutive models for curing processes are based on the temporal evolution of the material parameters, namely the shear modulus and the relaxation time (in the case of viscoelasticity). In the current paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Part I of this work will deal with an isothermal viscoelastic formulation including shrinkage effects whereas the following Part II will give emphasis on the thermomechanical coupled approach. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers.  相似文献   

6.
This paper shows an integrated structural design optimization of a composite rotor-hydrofoil of a water current turbine by means the finite elements method (FEM), using a Serial/Parallel mixing theory (Rastellini et al. Comput. Struct. 86:879–896, 2008, Martinez et al., 2007, Martinez and Oller Arch. Comput. Methods. 16(4):357–397, 2009, Martinez et al. Compos. Part B Eng. 42(2011):134–144, 2010) coupled with a fluid-dynamic formulation and multi-objective optimization algorithm (Gen and Cheng 1997, Lee et al. Compos. Struct. 99:181–192, 2013, Lee et al. Compos. Struct. 94(3):1087–1096, 2012). The composite hydrofoil of the turbine rotor has been design using a reinforced laminate composites, taking into account the optimization of the carbon fiber orientation to obtain the maximum strength and lower rotational-inertia. Also, these results have been compared with a steel hydrofoil remarking the different performance on both structures. The mechanical and geometrical parameters involved in the design of this fiber-reinforced composite material are the fiber orientation, number of layers, stacking sequence and laminate thickness. Water pressure in the rotor of the turbine is obtained from a coupled fluid-dynamic simulation (CFD), whose detail can be found in the reference Oller et al. (2012). The main purpose of this paper is to achieve a very low inertia rotor minimizing the start-stop effect, because it is applied in axial water flow turbine currently in design by the authors, in which is important to take the maximum advantage of the kinetic energy. The FEM simulation codes are engineered by CIMNE (International Center for Numerical Method in Engineering, Barcelona, Spain), COMPack for the solids problem application, KRATOS for fluid dynamic application and RMOP for the structural optimization. To validate the procedure here presented, many turbine rotors made of composite materials are analyzed and three of them are compared with the steel one.  相似文献   

7.
The quantized vortex state appearing in the recently discovered new states in hcp 4He since their discovery (Kim and Chan, Nature, 427:225–227, 2004; Science, 305:1941, 2004) is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state (Anderson, Nat. Phys., 3:160–162, 2007; Phys. Rev. Lett., 100:215301, 2008; Penzev et al., Phys. Rev. Lett., 101:065301, 2008; Nemirovskii et al., arXiv:0907.0330, 2009) and its transition into the supersolid (SS) state (Shimizu et al., arXiv:0903.1326, 2009; Kubota et al., J. Low Temp. Phys., 158:572–577, 2010; J. Low Temp. Phys., 162:483–491, 2011). Its features are described. The historical explanations (Reatto and Chester, Phys. Rev., 155(1):88–100, 1967; Chester, Phys. Rev. A, 2(1):256–258, 1970; Andreev and Lifshitz, JETP Lett., 29:1107–1113, 1969; Leggett, Phys. Rev. Lett., 25(22), 1543–1546, 1970; Matsuda and Tsuneto, Prog. Theor. Phys., 46:411–436, 1970) for the SS state in quantum solids such as solid 4He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as vacancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high T c superconductors, HTSCs (Bednorz and Mueller, Z. Phys., 64:189, 1986), has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high T c s of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid 4He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.  相似文献   

8.
For a prime number \(p\) , Bergman (Israel J Math 18:257–277, 1974) established that \(\mathrm {End}(\mathbb {Z}_{p} \times \mathbb {Z}_{p^{2}})\) is a semilocal ring with \(p^{5}\) elements that cannot be embedded in matrices over any commutative ring. In an earlier paper Climent et al. (Appl Algebra Eng Commun Comput 22(2):91–108, 2011), the authors presented an efficient implementation of this ring, and introduced a key exchange protocol based on it. This protocol was cryptanalyzed by Kamal and Youssef (Appl Algebra Eng Commun Comput 23(3–4):143–149, 2012) using the invertibility of most elements in this ring. In this paper we introduce an extension of Bergman’s ring, in which only a negligible fraction of elements are invertible, and propose to consider a key exchange protocol over this ring.  相似文献   

9.
In this work, we consider as model problem an exterior 3D wave propagation Neumann problem reformulated in terms of a space–time hypersingular boundary integral equation with retarded potentials. This latter is set in the so-called energetic weak form, recently proposed in Aimi et al. (Int J Numer Methods Eng 80:1196–1240, 2009; CMES 58:185–219, 2010), regularized as in Frangi (Int J Numer Methods Eng 45:721–740, 1999) and then approximated by the Galerkin boundary element method. Details on the discretization phase and, in particular, on the computation of integrals, double in time and double in space, constituting the elements of the final linear system matrix are given and analyzed. Various numerical results and simulations are presented and discussed.  相似文献   

10.
Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a visco-elastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly visco-elastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969, Mech. Time-Depend. Mater. 1:209?C240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209?C240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored.  相似文献   

11.
The conventional forming limit curve (FLC) is significantly strain path-dependent and therefore is not valid for formability evaluation of sheet metal parts that undergo nonlinear loading paths during the forming process. The stress-based forming limit curve (SFLC) is path-independent for all but very large prestrains and is a promising tool for formability evaluation. The SFLC is an ideal failure criterion for virtual forming simulations but it cannot be easily used on the shop floor as there is no straightforward experimental method to measure stresses in stamped parts. This paper presents a theoretical basis for predicting the effective limit strain curve (ELSC) using the Marciniak and Kuczynski (MK) analysis (Int J Mech Sci 9:609–620, 1967, Int J Mech Sci 15:789–805, 1973). Since the in-plane strain components are sufficient to calculate the effective strain, the ELSC can easily be determined from strains measured in the stamping plant, and therefore it is a better alternative to the SFLC for formability evaluation. This model was validated using experimental data for AISI-1012 steel (Molaei 1999) and AA-2008-T4 aluminum alloys Graf and Hosford (Metall Trans 24A:2503–2512, 1993). Predicted results showed that, similar to SFLC, the ELSC remains practically unchanged for a significant range of prestrain values under various bilinear loading paths, but some strain-path dependence can be observed for significant magnitudes of the effective prestrain (ε e ?≥?0.37 for AISI-1012 steel and ε e ?≥?0.25 for AA-2008-T4 aluminum).  相似文献   

12.
20 years ago a new quantum state of matter was discovered and identified (Borovik-Romanov et al. in JETP Lett. 40:1033, 1984; 45:124, 1987; 47:478, 1988; Fomin in JETP Lett. 40:1037, 1984; Borovik-Romanov et al. in Sov. Phys. JETP 61:1199, 1985; Fomin in Sov. Phys. JETP 61:1207, 1985; Bunkov et al. in JETP Lett. 43:168, 1986). The observed dynamic quantum state of spin precession in superfluid 3He-B bears the properties of spin current superfluidity, Bose condensation of spin waves—magnons, off-diagonal long-range order and related phenomena of quantum coherence.  相似文献   

13.
In the Ref. (Lebedev and L’vov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0215-2), this issue, two of us (VVL and VSL) considered symmetry restriction on the interaction coefficients of Kelvin waves and demonstrated that linear in small wave vector asymptotic, obtained analytically, is not forbidden, as Kosik and Svistunov (KS) expect by naive reasoning. Here we discuss this problem in additional details and show that theoretical objections by KS, presented in Ref. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0242-z), this issue, are irrelevant and their recent numerical simulation, presented in Ref. (Kozik and Svistunov in arXiv:1007.4927v1, 2010) is hardly convincing. There is neither proof of locality nor any refutation of the possibility of linear asymptotic of interaction vertices in the KS texts, Refs. (Kozik and Svistunov in J. Low Temp. Phys. 161, 2010, doi:10.1007/s10909-010-0242-z; arXiv:1006.0506v1, 2010). Therefore we can state again that we have no reason to doubt in this asymptote, that results in the L’vov–Nazarenko energy spectrum of Kelvin waves.  相似文献   

14.
Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014) constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. In this paper, we consider two open problems involving the inverse APN function $f(x)=x^{q^m-2}$ and the Dobbertin APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$ . From the calculation of linear spans and the minimal polynomials of two sequences generated by these two classes of APN functions, the dimensions of the corresponding cyclic codes are determined and lower bounds on the minimum weight of these cyclic codes are presented. Actually, we present a framework for the minimal polynomial and linear span of the sequence $s^{\infty }$ defined by $s_t={\mathrm {Tr}}((1+\alpha ^t)^e)$ , where $\alpha $ is a primitive element in ${\mathrm {GF}}(q)$ . These techniques can also be applied to other open problems in Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014).  相似文献   

15.
We have reported the onset of the vortex fluid (VF) state in hcp solid 4He below an onset temperature T o (Penzev et al. in Phys. Rev. Lett. 101:065301, 2008). We have also shown the transition from the VF state into the supersolid (SS) state, which is characterized by a supersolid density and macroscopic coherence, below a transition (Kubota et al. in J. Low Temp. Phys. 158:572, 2010; Shimizu et al. in arXiv:0903.1326, 2009; Yagi et al. in J. Low Temp. Phys., QFS2010, 2011) at T c , as well as a critical velocity for the destruction of the SS state. Here we describe further confirming evidence of the phase transition into the SS state, namely, we report here some other observations than the hysteretic behavior. We find some other features which indicate a clear change of the properties in the hcp 4He below the same T c as hysteretic behavior, reported in Kubota et al. (J. Low Temp. Phys. 158:572, 2010), Shimizu et al. (arXiv:0903.1326, 2009), Yagi et al. (J. Low. Temp. Phys., QFS2010, 2011). It was discovered by detailed study of the torsional oscillator (TO) drive velocity V ac dependence of the nonlinear rotational susceptibility (NLRS) of the VF state. We discuss the features of the VF to SS transition. The large ratio between T o and T c may indicate large fluctuations of the system and it may give a basis for the vortex state (Fisher et al. in Phys. Rev. B 43(1):130, 1991) appearance in the hcp 4He, as seen in the new type of superconductors. We discuss a question related to the observation of the VF phase with specific dynamic features (Nemirovskii et al. in arXiv:0907.0330, 2009), coexisting with the SS phase and a possible new kind of phase transition coexisting with the SS phase and a possible new kind of phase transition for the VF to SS transition.  相似文献   

16.
Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, ${\overline{B}(\mathsf{\textstyle Z\kern-0.4em Z}[G])}$ , to a much smaller DGA-module hG. Such a contraction is called a homological model for G and is used as the input datum in the methods described in álvarez et?al. (J Symb Comput 44:558–570, 2009; 2012) for calculating a generating set for representative 2-cocycles and n-cocycles over G, respectively. These computations have led to the finding of new cocyclic Hadamard matrices (álvarez et al. in 2006).  相似文献   

17.
In this work a multi-axial yield/failure model for viscoelastic/plastic materials is applied, which was developed by Naghdi and Murch (in J.?Appl. Mech. 30:321?C328, 1963) and later extended and refined by Crochet (in J.?Appl. Mech. 33:327?C334, 1966), to predict long-term creep rupture of polymers. The criterion defines a function, which depends on time, the viscoelastic properties and applied stress, to establish an empirical law with creep yield (fracture). In this work a linear relationship is proposed, defined as a time-dependent failure criterion, which can be applied for extrapolation purposes. A comparative analysis using energy-based failure criteria is performed. It is proved, for the polymers considered in this study, that the proposed time-dependent failure criterion holds for long times. Experimental data are used to illustrate the applicability of this time-dependent failure criterion.  相似文献   

18.
A cohesive zone model (CZM) approach is applied to simulate mixed-mode I/III stable tearing crack growth events in specimens made of 6061-T6 aluminum alloy and GM 6208 steel. The materials are treated as elastic–plastic following the \(J_{2}\) flow theory of plasticity, and the triangular cohesive law is employed to describe the traction-separation relation in the cohesive zone ahead of crack front. A hybrid numerical/experimental approach is employed in simulations using 3D finite element method. For each material, CZM parameter values are chosen by matching simulation prediction with experimental measurement (Yan et al. in Int J Fract 144:297–321, 2009), of the crack extension-time curve for the \(30^{\circ }\) mixed-mode I/III stable tearing crack growth test. With the same sets of CZM parameter values, simulations are performed for the \(60^{\circ }\) loading cases. Good agreements are reached between simulation predictions of the crack extension-time curve and experimental results. The variations of CTOD with crack extension are calculated from CZM simulations under both \(30^{\circ }\) and \(60^{\circ }\) mixed-mode I/III conditions for the aluminum alloy and steel respectively. The predictions agree well with experimental measurements (Yan et al. in Int J Fract 144:297–321, 2009). The findings of the current study demonstrate the applicability of the CZM approach in mixed-mode I/III stable tearing simulations and reaffirm the connection between CTOD and CZM based simulation approaches shown previously for mixed-mode I/II crack growth events.  相似文献   

19.
Marcel Ausloos 《Scientometrics》2014,101(3):1565-1586
Each co-author (CA) of any scientist can be given a rank \((r)\) of importance according to the number \((J)\) of joint publications which the authors have together. In this paper, the Zipf–Mandelbrot–Pareto law, i.e. \( J \propto 1/(\nu +r)^{\zeta }\) is shown to reproduce the empirical relationship between \(J\) and \(r\) and shown to be preferable to a mere power law, \( J \propto 1/r^{\alpha } \) . The CA core value, i.e. the core number of CAs, is unaffected, of course. The demonstration is made on data for two authors, with a high number of joint publications, recently considered by Bougrine (Scientometrics, 98(2): 1047–1064, 2014) and for seven authors, distinguishing between their “journal” and “proceedings” publications as suggested by Miskiewicz (Physica A, 392(20), 5119–5131, 2013). The rank-size statistics is discussed and the \(\alpha \) and \(\zeta \) exponents are compared. The correlation coefficient is much improved ( \(\sim \) 0.99, instead of 0.92). There are marked deviations of such a co-authorship popularity law depending on sub-fields. On one hand, this suggests an interpretation of the parameter \(\nu \) . On the other hand, it suggests a novel model on the (likely time dependent) structural and publishing properties of research teams. Thus, one can propose a scenario for how a research team is formed and grows. This is based on a hierarchy utility concept, justifying the empirical Zipf–Mandelbrot–Pareto law, assuming a simple form for the CA publication/cost ratio, \(c_r = c_0\, log_2 (\nu +r)\) . In conclusion, such a law and model can suggest practical applications on measures of research teams. In Appendices, the frequency-size cumulative distribution function is discussed for two sub-fields, with other technicalities  相似文献   

20.
The KU Leuven pulsed magnet facility was established in the sixties by the late Prof. A. Van Itterbeek (Van Itterbeek et al., Appl. Sci. Res., 18:105, 1967, Van Itterbeek et al., Les Champs Magnétiques Intenses, vol. 379, 1966). During the period 1972–1997 the laboratory was directed by Prof. F. Herlach (Witters and Herlach, J. Phys. D, Appl. Phys., 16:255, 1983, Li and Herlach, Meas. Sci. Technol., 6:1035, 1995, Herlach et al., Physica B, 201:542, 1994) who continuously developed the facility further along two lines: improved pulsed-field-coil design and enhanced capabilities for experimentation. From 1998 on, the facility is lead by Prof. V.V. Moshchalkov, in close collaboration with Prof. E.F. Herlach and Prof. J. Vanacken. Recently, the laboratory has been completely renewed; its present configuration is based on the former installation of the High Field Magnet Laboratory at the Radboud University Nijmegen (the Netherlands) (Rosseel et al., IEEE Trans. Appl. Supercond., 16:1664, 2006), which was originally developed in collaboration with the KU Leuven spin-off company METIS (http://www.metis.be/).  相似文献   

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