• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.613-630
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• 1996

The homogenization method is used to develop a beam element in space for thermo-mechanical analysis of unidirectional composites. Local stress and temperature field in the microscale are described using the function of homogenization. The global (macroscopic) behaviour of the structure is supposed to be that of a beam. Beam-type kinematical hypotheses (including independent shear rotations) are hence applied and superposed on the microdescription. A macroscopic stiffness matrix for such a beam element is then developed which contains the microscale properties of the single cell of periodicity. The presented model enables us to analyse without too much computational effort complicated composite structures such as e.g. toroidal coils of a fusion reactor. We need only a FE mesh sufficiently fine for a correct description of the local geometry of a single cell and a few of the newly developed elements for the description of the global behaviour. An unsmearing procedure gives the stress and temperature field in the different materials of a single cell.

• Structural Engineering and Mechanics
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• v.85 no.1
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• pp.105-118
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• 2023

The present work is an attempt to develop a simple and accurate finite element formulation for the assessment of thermal shock/thermally induced vibrations in pretwisted and tapered functionally graded material thin (FGM) blades obtained from Voigt and local representative volume elements (LRVE) homogenization models, based on neutral surface approach. The neutral surface of the FGM blade does not coincide with its mid-surface. A finite element model (FEM) is developed using first-order shear deformation theory (FSDT) and the FGM turbine blade is modelled according to the shallow shell theory. The top and the bottom layers of the FGM blade are made of pure ceramic and pure metal, respectively and temperature-dependent material properties are functionally graded in the thickness direction, the position of the neutral surface also depends on the temperature. The material properties are estimated according to two different homogenization models viz., Voigt or LRVE. The top layer of the FGM blade is subjected to high temperature and the bottom surface is either thermally insulated or kept at room temperature. The solution of the nonlinear profile of the temperature in the thickness direction is obtained from the Fourier law of heat conduction in the unsteady state. The results obtained from the present FEM are compared with the benchmark examples. Next, the effect of angle of twist, intensity of thermal shock, variable chord and span and volume fraction index on the transient response due to thermal shock obtained from the two homogenization models viz., Voigt and LRVE scheme is investigated. It is shown that there can be a significant difference in the transient response calculated by the two homogenization models for a particular set of material and geometric parameters.

• Advances in aircraft and spacecraft science
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• v.9 no.3
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• pp.217-242
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• 2022

This paper proposes a novel time-domain homogenization model combining the viscoelastic constitutive law with Eshelby's inclusion theory-based micromechanics model to predict the mechanical behavior of the particle reinforced composite material. The proposed model is intuitive and straightforward capable of predicting composites' viscoelastic behavior in the time domain. The isotropization technique for non-uniform stress-strain fields and incremental Mori-Tanaka schemes for high volume fraction are adopted in this study. Effects of the imperfectly bonded interphase layer on the viscoelastic behavior on the dynamic mechanical behavior are also investigated. The proposed model is verified by the direct numerical simulation and DMA (dynamic mechanical analysis) experimental results. The proposed model is useful for multiscale analysis of viscoelastic composite materials, and it can also be extended to predict the nonlinear viscoelastic response of composite materials.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.65-80
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• 2020

This paper presents a theoretical investigation on the response of the thermo-mechanical bending of FG plate on variable elastic foundation. A quasi-3D higher shear deformation theory is used that contains undetermined integral forms and involves only four unknowns to derive. The FG plates are supposed simply supported with temperature-dependent material properties and subjected to nonlinear temperature rise. Various homogenization models are used to estimate the effective material properties such as temperature-dependent thermoelastic properties. Equations of motion are derived from the principle of virtual displacements and Navier's solution is used to solve the problem of simply supported plates. Numerical results for deflections and stresses of FG plate with temperature-dependent material properties are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of FG thick plates.

• Proceedings of the Korean Geotechical Society Conference
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• 2001.11a
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• pp.72-84
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• 2001

In order to utilize mass of oyster shells for a partial substitute material for reclamation, we investigate the shear characteristics of dredged sluge mixed with oyster shells. the apparent modulus of elasticity of the this mixture are obtained from the triaxial compression tests and is utilized to characterize the apparent modulus of elastic of the oyster shells by carrying out some numerical analysis based upon the homogenization theory. We got the conclusion by a series of experiment, 1) It is verified that modulus of elasticity of dredged clay is improved by mixing with oyster shells. 2) The homogenization method for deducing apparent modulus of elasticity of oyster shells, which can consider micro-structure of mixed soil, is introduced. The elastic modulus is affected from the skeleton structure of oyster shell. The effect of 49kPa is bigger than that of 98kPa.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.701-711
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• 2018

Herein, the thermo-magneto-elastic wave dispersion answers of functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler-Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.713-722
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• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.873-884
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• 1999

On the basis of the semi-linear material of John invoking the theory of homogenization for heterogeneous media and the theory of invariants for isotropic scalar functions an energy function is built for a transversely-isotropic medium in finite elastic deformation. The ponyting Effect for material in simple shear is reviewed for this case of transversal isotropy. It is shown that this effect is apprehended by the constructed energy function.

• The Journal of Engineering Geology
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• v.16 no.3 s.49
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• pp.227-233
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• 2006

Bedrock is inhomogeneous for its genetically diverse origins and geological conditions when it forms, and especially, conglomerates and core-stones are one of these typical composite geo-materials composed of weak matrixes and strong pebbles. Mechanical properties of these composite bedrocks, like a conglomerate, generally vary depending on the mechanical properties and distributions of pebbles and the matrix. Therefore, regarding the consequence of understanding mechanical property of bedrocks in the designing slopes, tunnels, and other engineering facilities, empirical rock classification methods generally applied in the mechanical property modeling may not be suitable and rather, we may need some other classification methods, or tests more specific for these inhomogeneous composite bedrocks. This study includes a series of analyses to see elastic behaviors and modulus of composite geo-materials using homogenization theory. Forty nine case models were made for the elastic analysis with considering 5 factors such as gravel content, gravel size, strength of matrix, sorting and dip angle. The results analyzed are applicable to calculate elastic modulus of composite geo-materials as conglomerates and core-stones.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.105-114
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• 2018

In this paper, the computer simulations are carried out by using the peridynamic theory model with various conditions including quasi-static loads, dynamic loads and crack propagation, branching crack pattern and isotropic materials, orthotropic materials. Three examples, a plate with a hole under quasi-static loading, a plate with a pre-existing crack under dynamic loading and a lamina with a pre-existing crack under quasi-static loading are analyzed by computational simulations. In order to simulate the quasi-static load, an adaptive dynamic relaxation technique is used. In the orthotropic material analysis, a homogenization method is used considering the strain energy density ratio between the classical continuum mechanics and the peridynamic. As a result, crack propagation and branching cracks are observed successfully and the direction and initiation of the crack are also captured within the peridynamic modeling. In case of applying peridynamic used homogenization method to a relatively complicated orthotropic material, it is also verified by comparing with experimental results.