Equivalent Continuum Research Articles

Hydro-mechanically coupled finite-element analysis of the stability of a fractured-rock slope using the equivalent continuum approach: a case study of planned reservoir banks in Blaubeuren, Germany

Construction works associated with the building of reservoirs in mountain areas can damage the stability of adjacent valley slopes. Seepage processes caused by the filling and drawdown operations of reservoirs also affect the stability of the reservoir banks over time. The presented study investigates the stability of a fractured-rock slope subjected to seepage forces in the lower basin of a planned pumped-storage hydropower (PSH) plant in Blaubeuren, Germany. The investigation uses a hydro-mechanically coupled finite-element analyses. For this purpose, an equivalent continuum model is developed by using a representative elementary volume (REV) approach. To determine the minimum required REV size, a large number of discrete fracture networks are generated using Monte Carlo simulations. These analyses give a REV size of 28 × 28 m, which is sufficient to represent the equivalent hydraulic and mechanical properties of the investigated fractured-rock mass. The hydro-mechanically coupled analyses performed using this REV size show that the reservoir operations in the examined PSH plant have negligible effect on the adjacent valley slope.

Unified nonlocal rational continuum models developed from discrete atomistic equations

In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type of enrichment can be useful in a wide range of mechanical problems such as localization of strain and damage in many quasibrittle structures, size effects in microscale elastoplasticity, and multiscale modeling of materials. A novel technique of transforming a discrete differential expression into an exact equivalent rational continuum derivative form is developed considering the Taylor’s series transformation of the continuous field variables and traveling wave type of solutions for both the discrete and continuum field variables. An exact equivalent continuum rod representation of the 1D harmonic lattice with the non-nearest neighbor interactions is developed considering the lattice details. Using similar enrichment technique in the variational framework, other useful higher-order equations, namely nonlocal rational Mindlin–Herrmann rod and nonlocal rational Timoshenko beam equations, are developed to explore their nonlocal properties in general. Some analytical and numerical studies on the high frequency dynamic behavior of these novel nonlocal rational continuum models are presented with their comparison with the atomistic solutions for the respective physical systems. These enriched rational continuum equations have crucial use in studying high-frequency dynamics of many nano-electro-mechanical sensors and devices, dynamics of phononic metamaterials, and wave propagation in composite structures. These new models can help to circumvent the biggest problem regarding size and time restrictions in many atomistic simulations.

King post truss as a motif for internal structure of (meta)material with controlled elastic properties.

One of the most interesting challenges in the modern theory of materials consists in the determination of those microstructures which produce, at the macro-level, a class of metamaterials whose elastic range is many orders of magnitude wider than the one exhibited by ‘standard’ materials. In dell’Isola et al. (2015 Zeitschrift für angewandte Mathematik und Physik 66, 3473–3498. (doi:10.1007/s00033-015-0556-4)), it was proved that, with a pantographic microstructure constituted by ‘long’ micro-beams it is possible to obtain metamaterials whose elastic range spans up to an elongation exceeding 30%. In this paper, we demonstrate that the same behaviour can be obtained by means of an internal microstructure based on a king post motif. This solution shows many advantages: it involves only microbeams; all constituting beams are undergoing only extension or compression; all internal constraints are terminal pivots. While the elastic deformation energy can be determined as easily as in the case of long-beam microstructure, the proposed design seems to have obvious remarkable advantages: it seems to be more damage resistant and therefore to be able to have a wider elastic range; it can be realized with the same three-dimensional printing technology; it seems to be less subject to compression buckling. The analysis which we present here includes: (i) the determination of Hencky-type discrete models for king post trusses, (ii) the application of an effective integration scheme to a class of relevant deformation tests for the proposed metamaterial and (iii) the numerical determination of an equivalent second gradient continuum model. The numerical tools which we have developed and which are presented here can be readily used to develop an extensive measurement campaign for the proposed metamaterial.

Non-destructive experimentation: Dynamic identification of multi-leaf masonry walls damaged and consolidated

Abstract The dynamic monitoring of multi-leaf masonry wall is here proposed. The results of non-destructive tests carried out in this work are a first part of a wider testing campaign aimed at verifying the structural performance of masonry walls. Multi-leaf masonry walls constitute the composite construction typology most widely adopted in historic buildings. This aspect, together with the intrinsic structural complexity, heterogeneity and irregularity, directs the present research towards a topic not yet sufficiently investigated by the scientific community. In this paper, the case of multi-leaf masonry wall has been investigated, and with the aim of reproducing historical buildings structural elements, three different typologies of multi-leaf masonry walls have been considered: (i) full infill, (ii) damaged infill, (iii) consolidated infill. Several masonry specimens of the above-described typologies have been built and tested in lab. The dynamic parameters, such as frequencies, modal shapes and damping ratios have been identified through the output-only procedure and the data were processed through the Least Square Complex Frequency (LSFC) estimator; the analysis of results allowed to evaluate the structural integrity, the efficacious of consolidating intervention and the potential performance mechanisms of different complex multi-leaf masonry walls. Experimental results are compared with numerical Finite Elements models. Composite multi-leaf masonry is modeled as an equivalent continuum obtained through a full 3D homogenization procedure. The mechanical properties of component materials have been obtained in lab by tests and then used to model the masonry at the micro-scale in order to derive the mechanical properties to be adopted at macro-scale. A parametric natural frequencies analysis is performed in order to calibrate the model by the comparison whit the experimental measures.

Continuum model of two-dimensional crystal lattice of metamaterials

ABSTRACTThe continuum models of two-dimensional crystal lattice of metamaterial are investigated in this paper. The equivalent classical continuum requires the introduction of frequency-dependent mass density that becomes negative or infinite near the resonance frequency. In order to avoid the frequency-dependent mass density and make the dispersive characteristic of the elastic waves propagating in the equivalent continuum approximating that of lattice wave in two-dimensional crystal lattice of metamaterial, three kinds of continuum models, namely, the multiple displacements continuum model, the strain gradient continuum model and the nonlocal strain gradient continuum model, are investigated. It is found that the nonlocal gradient continuum model may better represent the dispersive relation and the bandgap characteristics of the metamaterial by the appropriate selection of nonlocal parameters.

Diameter-dependent elastic properties of carbon nanotube-polymer composites: Emergence of size effects from atomistic-scale simulations

We propose a computational procedure to assess size effects in nonfunctionalized single-walled carbon nanotube (CNT)-polymer composites. The procedure upscales results obtained with atomistic simulations on a composite unit cell with one CNT to an equivalent continuum composite model with a large number of CNTs. Molecular dynamics simulations demonstrate the formation of an ordered layer of polymer matrix surrounding the nanotube. This layer, known as the interphase, plays a central role in the overall mechanical response of the composite. Due to poor load transfer from the matrix to the CNT, the reinforcement effect attributed to the CNT is negligible; hence the interphase is regarded as the only reinforcement phase in the composite. Consequently, the mechanical properties of the interface and the CNT are not derived since their contribution to the elastic response of the composite is negligible. To derive the elastic properties of the interphase, we employ an intermediate continuum micromechanical model consisting of only the polymer matrix and a three-dimensional fiber representing the interphase. The Young's modulus and Poisson's ratio of the equivalent fiber, and therefore of the interphase, are identified through an optimization procedure based on the comparison between results from atomistic simulations and those obtained from an isogeometric analysis of the intermediate micromechanical model. Finally, the embedded reinforcement method is employed to determine the macroscopic elastic properties of a representative volume element of a composite with various fiber volume fractions and distributions. We then investigate the role of the CNT diameter on the elastic response of a CNT-polymer composite; our simulations predict a size effect on the composite elastic properties, clearly related to the interphase volume fraction.

A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. We compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1×1×1km3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. We identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.

Buckling analyses of double-shell octagonal lattice truss composite structures

To reveal the compression failure modes of one-dimensional hierarchical double-shell octagonal lattice truss composite structures (DLTCSs), finite element modeling and equivalent continuum models were developed. DLTCS has three typical failure modes: (a) fracture of the strut, (b) global buckling, and (c) local buckling. Failure mode maps were constructed. It is found that column of long enough length will collapse at global buckling. When the column length decreases, the failure mode will turn to local buckling and strut fracture successively. Bay length greatly influences the buckling mode. Longer bay length could change the buckling mode from global buckling to local buckling. Compared with single-shell lattice truss composite structure, DLTCS has advantage in load carrying when the column fails at strut fracture or global buckling, while local buckling tolerance of DLTCS is smaller.

An enhanced equivalent continuum model for layered rock mass incorporating bedding structure and stress dependence

Layered rock masses exhibit significant anisotropy in both the deformability and strength. Properties of this rock mass are largely affected by its bedding structure and also by the stress state change. For the purpose of characterizing these salient features using the equivalent continuum concept, an enhanced model is proposed in this paper based on the ubiquitous-joint model. In the enhanced model, the intact bedded rock is assumed to behave as a transversely isotropic elastic body. A modified anisotropic strength criterion is adopted to describe the direction dependence of the strength of intact bedded rock. In addition, stress-sensitive parameters are utilized for both the intact rock and bedding plane, among which the dilation angle and strength parameters of intact rock are influenced by confining pressure and loading history, whereas the stiffnesses of bedding planes are closely related to the current normal stress. The effect of layer thickness on the mechanical behavior of rock mass is reflected by continuously updating the global stiffness matrix after failure of bedding plane, and by conditions for conducting bedding plane related calculations determined by the relative scales between element size and layer thickness. Preliminary validation of this model is conducted by comparing with the closed-form solutions and with laboratory tests. Generally good agreements can be achieved between numerical simulations and theoretical/experimental results, which indicate that applicability of the enhanced model on underground engineering issues related to layered rock mass is promising.

A plate model for multilayer graphene sheets and its finite element implementation via corotational formulation

An equivalent continuum model for multilayer graphene sheets (MLGSs) and its plate model are developed to analyze the deformation behavior of MLGSs. Hyperelastic material models are introduced for the MLGS continuum model by examining the atomistic structures of MLGSs and obtaining their mechanical properties by means of molecular statics simulations. The MLGS plate model, a structural model for MLGSs, is developed by applying kinematics assumptions to the MLGS continuum model subjected to infinitesimal deformation. Finite element methods (FEM) with the corotational formulation are adopted to analyze the mechanical behavior of MLGSs under small-strain deformation and large rotation conditions. The MLGS plate element passes several basic numerical tests, including patch tests, eigenvalue analyses, and geometrically nonlinear benchmark problems. Finally, the deflections of a plane-strain cantilever and spherical indentations are analyzed by the proposed MLGS plate element and molecular dynamics (MD) simulations. These results show that the MLGS plate element properly represents the deformation behaviors of MLGSs from the atomic scale to the macroscopic continuum scale.

An experimental and numerical study on radon transport from UMT-contaminated sand to a house basement under variable weather conditions

Numerical modelling is necessary in order to better understand transient phenomena of radon transport from radium-contaminated soils to a house basement where high radon levels were observed. The present work aims to develop a robust and simplified subsurface numerical model which can simulate radon transport at the soil-basement foundation interface under variable weather conditions around a house. The equivalent continuum modelling (ECM) approach has been used assuming an equivalent porosity and permeability of the basement foundation cracked concrete materials. This approach has been applied for simulating two-dimensional (2D) soil-gas and radon-entry into a house basement built on sand contaminated by uranium mill tailings (UMT) considering the presence of an aquifer with water-table, rainfall, evapotranspiration, atmospheric air pressure, and house under-pressurization.Sensitivity analysis of the model foundation parameters, performed at steady-state, showed that the numerical model predictions at transient conditions were in a good agreement with measurements of the radon-entry-rate through the basement foundation and radon concentration in the basement. The optimized parameters are physically sound and consistent with the observations and literature data.

Finite element simulation of mechanical properties of graphene sheets

Graphene is the material for the twenty first century applications. In this paper, the elastic properties of monolayer and double layer Graphene sheets, typically less than 10nm in size are investigated through linear finite element simulations. The effect of aspect ratio, sizes and chirality of the Graphene sheet on the Young’s modulus, Shear modulus and Poisson’s ratio are studied. By using structural mechanics approach combining atomistic and equivalent continuum techniques, the Young’s modulus, shear modulus and the Poisson ratio were found and they slightly increase with the aspect ratio but decrease with the size of the Graphene sheet. These simulated properties compliment the mechanical properties of Graphene found in literature.

Factors controlling the permeability distribution in fault vein zones surrounding granitic intrusions (Ore Mountains/Germany)

AbstractAn outstanding legacy data set has been compiled from underground excavations mostly prospected and mined by the former Soviet (German) Stock Company Wismut describing the hydrology of faulted basement rocks in the Ore Mountains (SE Germany). It consists of more than 5000 detailed descriptions of groundwater inflows to about 660 km of tunnels and 57 km of drillings measured during or shortly after excavation. Inflow measurements (recorded between 1E−8 and 4E−2 m3/s) have been converted to fracture transmissivities using a simplified analytical solution. Discarding site specific effects, the median log transmissivity decreases from 1E−7 to 1E−10 m2/s within the studied depth interval of 0–2000 meters below ground surface (mbgs), and the spacing of conductive fracture increases from 0.1 to 2500 m. This general trend is overprinted at three mining sites by a clear reversal of fracture transmissivity which correlates with contact metamorphic aureoles around Variscan granite intrusions (327–295 Ma). We hypothesize that this transmissivity increase is caused by processes accompanying granite intrusion and contact metamorphism. The thickness of these hydraulically active aureoles is greater in lower‐grade metamorphic schist than in higher‐grade metamorphic gneisses. Rock mass equivalent continuum conductivities have been estimated by arithmetic averaging of fracture and matrix transmissivities over 100 m intervals and have been converted to permeabilities. The median equivalent continuum permeability decreases with depth according to log(k) = − 1.7 * log(z) − 17.3 (k in m2 and increasing depth z in kilometer being positive). Matrix conductivity controls the bulk conductivity below about 1000 mbgs and is less sensitive to the occurrence of contact metamorphic aureoles.

Micromechanical modeling of thermal expansion coefficients for unidirectional glass fiber-reinforced polyimide composites containing silica nanoparticles

The coefficients of thermal expansion (CTEs) of unidirectional glass fiber-reinforced polyimide composites containing silica nanoparticles are investigated. To this end, a three-dimensional unit cell-based micromechanical model together with an individual representative volume element (RVE) with c×r×h sub-cells is proposed. The interphase region between silica nanoparticle and polyimide matrix is considered as an equivalent solid continuum. Comparisons are made between the results of present model with those of available cylinder model and experiment. The results reveal that with adding silica nanoparticles to glass fiber-reinforced polyimide composites, the transverse CTE of composite decreases, while its longitudinal CTE increases. The effects of fiber volume fraction and aspect ratio, interphase thickness and material properties, silica nanoparticle volume fraction and diameter on the thermal expansion behavior of silica nanoparticle-glass fiber-reinforced polyimide composites are studied. The obtained results could be useful to guide the design of composites with optimal CTEs.

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet–Bloch approach. From the resulting eigenproblem derived by the Euler–Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre–Hadamard ellipticity conditions requiring real values for the wave velocity.

Bending analyses of FG-CNTRC plates using the modified mesh-free radial point interpolation method based on the higher-order shear deformation theory

This study presents nonlinear bending analyses of functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates using the modified mesh-free radial point interpolation method (RPIM). The nonlinear bending formulations of the FG-CNTRC plates are derived from the modified RPIM which employs a new radial basis function able to construct the shape functions without the need for introducing supporting fixing coefficients based on the higher-order shear deformation plate theory. Single-walled carbon nanotubes (SWCNTs) are selected as the reinforcement and the effective material properties of the FG-CNTRC plates are evaluated by an equivalent continuum model based on the rule of mixture. The simulated results by the modified RPIM are compared with the other numerical solutions to verify the effectiveness and the accuracy of the developed mesh-free method. Detailed parametric studies are then performed to explore the effects that the plate width-to-thickness ratio, aspect ratio, load type, boundary condition and initial deflection have on the nonlinear flexural responses of the CNTRC plates, and the results for uniformly distributed (UD) CNTRC plate are provided for comparison. Results demonstrate that the modified mesh-free RPIM can effectively predict the nonlinear bending behavior of the CNTRC plates.

History matching and uncertainty quantification of discrete fracture network models in fractured reservoirs

Fractured reservoirs are highly heterogeneous and can be characterized by the probability distributions of fracture properties in a discrete fracture network model. The relationship between production performance and the fracture parameters is vastly nonlinear, rendering the process of adjusting model parameters to match both the static geological and dynamic production data challenging. This creates a need for a comprehensive history matching workflow for fractured reservoirs, which considers different local as well as global fracture parameters and leads to multiple equally-probable realizations of the discrete fracture network model parameters for uncertainty quantification.This paper presents an integrated approach for the history matching of fractured reservoirs. This new methodology includes generating multiple discrete fracture models, upscaling them for numerical multiphase flow simulation, and updating the fracture properties using dynamic flow responses such as continuous rate and pressure measurements. Available geological and tectonic information such as well-logs, seismic, and structural maps are incorporated into commercially available DFN modeling and simulation software to infer the probability distributions of relevant fracture parameters (including aperture, length, connectivity, and intensity) and to generate multiple discrete fracture network model realizations. The fracture models are further upscaled into an equivalent continuum dual-porosity model in the software using either analytical approaches or dynamic methods. The upscaled models are subjected to the flow simulation, and their production performances are compared to the true recorded responses. An automated history matching algorithm is implemented to reduce the uncertainties of the fracture properties. Components of vectors representing the principal flow directions and average fracture orientations are obtained by means of eigenvector decomposition of the permeability tensor and are optimized in the algorithm. In addition, both global fracture intensity and the local grid based intensity, which highly affect the fluid flow pattern and rate in different regions of the reservoir, are adjusted.A case study with various fracture sets is presented. The initial realizations were generated by means of Monte Carlo simulations, using the observed fractures at the well locations. Fracture intensity, orientation, and conductivity of different fracture sets were the uncertain parameters in our studies. Using the proposed methodology, parameters of different fracture sets were satisfactorily updated. Implementation of this automated history matching approach resulted in multiple equally probable discrete fracture network models and their upscaled flow simulation models that honor the geological information, and at the same time they match the dynamic production history.

Mapping local deformation behavior in single cell metal lattice structures

The deformation behavior of metal lattice structures is extremely complex and challenging to predict, especially since strain is not uniformly distributed throughout the structure. Understanding and predicting the failure behavior for these types of light-weighting structures is of great interest due to the excellent scaling of stiffness- and strength-to weight ratios they display. Therefore, there is a need to perform simplified experiments that probe unit cell mechanisms. This study reports on high resolution mapping of the heterogeneous structural response of single unit cells to the macro-scale loading condition. Two types of structures, known to show different stress-strain responses, were evaluated using synchrotron radiation micro-tomography while performing in-situ uniaxial compression tests to capture the local micro-strain deformation. These structures included the octet-truss, a stretch-dominated lattice, and the rhombic-dodecahedron, a bend-dominated lattice. The tomographic analysis showed that the stretch- and bend-dominated lattices exhibit different failure mechanisms and that the defects built into the structure cause a heterogeneous localized deformation response. Also shown here is a change in failure mode for stretch-dominated lattices, where there appears to be a transition from buckling to plastic yielding for samples with a relative density between 10 and 20%. The experimental results were also used to inform computational studies designed to predict the mesoscale deformation behavior of lattice structures. Here an equivalent continuum model and a finite element model were used to predict both local strain fields and mechanical behavior of lattices with different topologies.

欠陥導入によるナノ炭素材料の構造最適設計法

Because of their superior mechanical, structural, and electronic properties, carbon nanomaterials (CNs) (e.g. graphene sheets and carbon nanotubes) are supposed to be base materials for nanoelectromechanical systems (NEMS). In the present work, we propose a structural optimization method of carbon nanomaterials by introducing topological defects, which consists of the molecular mechanics method, the free-form optimization method, the Phase-Field-Crystal (PFC) method, Voronoi tessellation, and molecular dynamics (MD) simulation. The C-C bonds of CNs are simulated as equivalent continuum beams by a combination of molecular and continuum mechanics, so the atomic structures of CNs can be treated as frame structures. We adopt the free-form optimization method for frames to determine the optimal shapes of CNs in stiffness maximization problem. For obtaining the stable atomic structures of the optimal shapes of CNs, topological defects are introduced in the optimal shapes of CNs using a combination of PFC method, Voronoi tessellation, and MD simulation. The numerical results show that the compliance of CNs can be significantly reduced according to the structural optimization method, which is helpful for designing CNs components in NEMS.

The effect of carbon nanotubes agglomeration on vibrational response of thick functionally graded sandwich plates

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of twoparameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.