• Structural Engineering and Mechanics
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• 제73권2호
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• pp.191-207
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• 2020

This study aims at investigating the size-dependent free vibration of porous nanoplates when exposed to hygrothermal environment and rested on Kerr foundation. Based on the modified power-law model, material properties of porous functionally graded (FG) nanoplates are supposed to change continuously along the thickness direction. The generalized nonlocal strain gradient elasticity theory incorporating three scale factors (i.e. lower- and higher-order nonlocal parameters, strain gradient length scale parameter), is employed to expand the assumption of second shear deformation theory (SSDT) for considering the small size effect on plates. The governing equations are obtained based on Hamilton's principle and then the equations are solved using an analytical method. The elastic Kerr foundation, as a highly effected foundation type, is adopted to capture the foundation effects. Three different patterns of porosity (namely, even, uneven and logarithmic-uneven porosities) are also considered to fill some gaps of porosity impact. A comparative study is given by using various structural models to show the effect of material composition, porosity distribution, temperature and moisture differences, size dependency and elastic Kerr foundation on the size-dependent free vibration of porous nanoplates. Results show a significant change in higher-order frequencies due to small scale parameters, which could be due to the size effect mechanisms. Furthermore, Porosities inside of the material properties often present a stiffness softening effect on the vibration frequency of FG nanoplates.

• Structural Engineering and Mechanics
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• 제40권2호
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Structural Engineering and Mechanics
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• 제75권1호
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• pp.109-122
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• 2020

An asymptotic local plane strain elasticity theory is reformulated for the static analysis of a simply-supported, multiple graphene sheet system (MGSS) in cylindrical bending and resting on an elastic medium. The dimension of the MGSS in the y direction is considered to be much greater than those in the x and z directions, such that all the field variables are considered to be independent of the y coordinate. Eringen's nonlocal constitutive relations are used to account for the small length scale effects in the formulation examining the static behavior of the MGSS. The interaction between the MGSS and its surrounding foundation is modelled as a Winkler foundation with the parameter k_w, and the interaction between adjacent graphene sheets (GSs) is considered using another Winkler model with the parameter c_w. A parametric study with regard to some effects on the static behavior of the MGSS resting on an elastic medium is undertaken, such as the aspect ratio, the number of the GSs, the stiffness of the medium between the adjacent layers and that of the surrounding medium of the MGSS, and the nonlocal parameter.

• Advances in aircraft and spacecraft science
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• 제2권3호
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• pp.275-302
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• 2015

Theoretical and numerical assessments of approximate evaluations and simplified analyses of piezoelectric structures transverse shear modal effective electromechanical coupling coefficient (EMCC) are presented. Therefore, the latter is first introduced theoretically and its approximate evaluations are reviewed; then, three-dimensional (3D) and simplified two-dimensional (2D) plane-strain (PStrain) and plane-stress (PStress) piezoelectric constitutive behaviors of electroded shear piezoceramic patches are derived and corresponding expected short-circuit (SC) and open-circuit (OC) frequencies and resulting EMCC are discussed; next, using a piezoceramic shear sandwich beam cantilever typical benchmark, a 3D finite element (FE) assessment of different evaluation techniques of the shear modal effective EMCC is conducted, including the equipotential (EP) constraints effect; finally, 2D PStrain and PStress FE modal analyses under SC and OC electric conditions, are conducted and corresponding results (SC/OC frequencies and resulting effective EMCC) are compared to 3D ones. It is found that: (i) physical EP constraints reduce drastically the shear modal effective EMCC; (ii) PStress and PStrain results depend strongly on the filling foam stiffness, rendering inadequate the use of popular equivalent single layer models for the transverse shear-mode sandwich configuration; (iii) in contrary to results of piezoelectric shunted damping and energy harvesting popular single-degree-of-freedom-based models, transverse shear modal effective EMCC values are very small in particular for the first mode which is the common target of these applications.

• 한국지진공학회논문집
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• 제25권5호
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• pp.191-199
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• 2021

In seismic design, hollow section concrete columns offer advantages by reducing the weight and seismic mass compared to concrete section RC bridge columns. However, the flexure-shear behavior and spirals strain of hollow section concrete columns are not well-understood. Octagonal RC bridge columns of a small-scale model were tested under cyclic lateral load with constant axial load. The volumetric ratio of the transverse spiral hoop of all specimens is 0.00206. The test results showed that the structural performance of the hollow specimen, such as the initial crack pattern, initial stiffness, and diagonal crack pattern, was comparable to that of the solid specimen. However, the lateral strength and ultimate displacement of the hollow specimen noticeably decreased after the drift ratio of 3%. The columns showed flexure-shear failure at the final stage. Analytical and experimental investigations are presented in this study to understand a correlation confinement steel ratio with neutral axis and a correlation between the strain of spirals and the shear resistance capacity of steel in hollow and solid section concrete columns. Furthermore, shear strength components (V_c, V_s·, V_p) and concrete stress were investigated.

• 대한토목학회논문집
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• 제14권3호
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• pp.543-552
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• 1994

본 연구는 공중낙하법으로 만든 공기건조 상태의 일본의 표준사인 풍포사(豊浦砂)(Toyoura sand)와 영국의 표준사인 Silver Leighton Buzzard sand 공시체를 배수상태에서 평면 변형율 압축시험을 실시하여, 구속압이 모래의 변형 강도특성에 미치는 영향을 조사하였다. 축방향 변위와 수평방향의 변위는 변형율수준(strain level) $10^{-6}$에서 파괴상태까지를 연속적으로 구할 수 있는 장치를 사용하여 정도 높게 측정함으로써 미소변형에서 파괴상태까지의 응력 변형율 특성을 상세히 연구하였다. 그 결과, 극저구속압에서는 구속압이 작아져도 내부마찰각 ${\sigma}^{\prime}{_{max}}=arcsin\{({\sigma}{_1}^{\prime}-{\sigma}{_3}^{\prime})/({\sigma}{_1}^{\prime}+{\sigma}{_3}^{\prime})\}_{max}$가 급격히 크게 되지는 않아, Bolton의 경험식을 사용할 시는 어느 정도 구속압이 클 때만 적용 가능하다는 것을 알았다. 또, 모래의 강성률은 근사적으로 구속압의 m승에 비례하는데(G or $E{\propto}{\sigma}{_3}^{{\prime}m}$), 이때 m은 변형율수준 $10^{-4}$이하에서는 약 0.4 정도이고 변형율=$10^{-1}$에서는 $m{\fallingdotseq}0.9$ 정도이었다. 이러한 경향은 모래의 종류, 혹은 시험종류에 따라 거의 변화하지 않음을 알았다. 이것은 구속압이 작을수록 강성률의 변형율수준 의존성, 응력수준 의존성이 크게 되는 것과 대응한다. 끝으로, Rowe의 응력-다이러턴시 관계는 미소 변형율수준($10^{-4}$ 이하)에서 파괴까지 거의 직선적으로 성립하고, 구속압의 영향을 거의 받지 않는다는 것을 알았다.

• Geomechanics and Engineering
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• 제24권2호
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• pp.193-203
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• 2021

The time-history finite element analysis is usually used to evaluate the seismic response of shallow foundations. However, the literature lacks studies on the influence of the soil constitutive model complexity on the seismic response of shallow foundations. This study, thus, aims to fill this gap by investigating the seismic response of shallow foundation resting on dry silica sand using the linear elastic (LE) model, elastic-perfectly-plastic (EPP) model, and hardening soil with small strain stiffness (HS small) model. These models have been used because it is intended to compare the results of a soil constitutive model that accurately captures the seismic response of the soil-structure interaction problems (which is the HS small model) with simpler models (the LE and EPP models) that are routinely used by practitioners in geotechnical designs. The results showed that the LE model produces a very small seismic settlement value which is approximately equal to zero. The EPP model predicts a seismic settlement higher than that produced using the HS small model for earthquakes with a peak ground acceleration (PGA) lower than 0.25 g for a relative density of 45% and 0.40 g for a relative density of 70%. However, the HS small model predicts a seismic settlement higher than the EPP model beyond the aforementioned PGA values with the difference between both models increases as the PGA rises. The results also showed that the LE and EPP models predict similar trend and magnitude of the acceleration-time relationship directly below the foundation, which was different than that predicted using the HS small model. The results reported in this paper provide a useful benchmark for future numerical studies on the response of shallow foundations subjected to seismic shake.

• Earthquakes and Structures
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• 제13권5호
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• pp.485-496
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• 2017

The behavior of 8 steel reinforced high-strength concrete (SRHSC) columns, which comprised of four identical columns with cross-shaped steel and other four identical columns with square steel tube, was investigated experimentally under cyclic uniaxial and biaxial loading independently. The influence of steel configuration and loading path on the global behavior of SRHSC columns in terms of failure process, hysteretic characteristics, stiffness degradation and ductility were investigated and discussed, as well as stress level of the longitudinal and transverse reinforcing bars and steel. The research results indicate that with a same steel ratio deformation capacity of steel reinforced concrete columns with a square steel tube is better than the one with a cross-shaped steel. Loading path affects hysteretic characteristics of the specimens significantly. Under asymmetrical loading path, hysteretic characteristics of the specimens are also asymmetry. Compared with specimens under unidirectional loading, specimens subjected to bidirectional loading have poor carrying capacity, fast stiffness degradation, small yielding displacement, poor ductility and small ultimate failure drift. It also demonstrates that loading paths affect the deformation capacity or deformation performance significantly. Longitudinal reinforcement yielding occurs before the peak load is attained, while steel yielding occurs at the peak load. During later displacement loading, strain of longitudinal and transverse reinforcing bars and steel of specimens under biaxial loading increased faster than those of specimens subjected to unidirectional loading. Therefore, the bidirectional loading path has great influence on the seismic performance such as carrying capacity and deformation performance, which should be paid more attentions in structure design.

• Geomechanics and Engineering
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• 제34권2호
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• pp.115-124
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• 2023

By conducting three-dimensional simulation with consideration of small-strain characteristics of soil stiffness, the effects of excavation geometry and tunnel cover to diameter ratio on deformation mechanisms of an existing tunnel located either at a side of basement or directly underneath the basement were systematically studied. Field measurements were used to verify the numerical model and model parameters. For basement excavated at a side of an existing tunnel, the maximum settlement and horizontal displacement of the tunnel are always observed at the tunnel springline closer to basement and tunnel crown, respectively, regardless of basement geometry. By increasing basement length and width by five times, the maximum movements of tunnel located at the side of basement and directly underneath the basement increase by 450% and 186%, respectively. Obviously, tunnel movements are more sensitive to basement length rather than basement width. For basement excavated at a side of an existing tunnel, tunnel movements at basement centerline become stable when basement length reaches 10 H_e (i.e., final excavation depth). Moreover, tunnel heaves due to overlying basement excavation become stable when the normalized basement length (L/H_e) is larger than 8.0. As tunnel cover to diameter ratio varies from 2.5 to 3.0, the maximum heave and tensile strain of tunnel due to overlying basement excavation decrease by up to 41.0% and 44.5%, respectively. If basement length is less than 8 H_e, the assumption of plane strain condition of basement-tunnel interaction grossly overestimates tunnel movements, and ignores tensile strain of tunnel along its longitudinal direction. Thus, three-dimensional numerical analyses are required to obtain a reasonable estimation of tunnel responses due to adjacent and overlying basement excavations in clay.

• Geomechanics and Engineering
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• 제35권4호
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• pp.449-464
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• 2023

Advanced nonlinear effective stress constitutive models are started to be frequently used in one-dimensional (1D) and two-dimensional (2D) site response analysis for assessment of porewater generation and liquefaction potential in soft soil deposits. The emphasis of this research is on the assessment of the implementation of this category of models at the element stage. Initially, the performance of a coupled porewater pressure (PWP) and constitutive models were evaluated employing a catalogue of 40 unidirectional cyclic simple shear tests with a variety of relative densities between 35% and 80% and effective vertical stresses between 40 and 80 kPa. The authors evaluated three coupled constitutive models (PDMY02, PM4SAND and PDMY03) using cyclic direct simple shear tests and for decide input parameters used in the model, procedures are recommended. The ability of the coupled model to capture dilation as strength is valuable because the studied models reasonably capture the cyclic performance noted in the experiments and should be utilized to conduct effective stress-based 1D and 2D site response analysis. Sandy soils may become softer and liquefy during earthquakes as a result of pore-water pressure (PWP) development, which may have an impact on seismic design and site response. The tested constitutive models are mathematically coupled with a cyclic strain-based PWP generation model and can capture small-strain stiffness and large-strain shear strength. Results show that there are minor discrepancies between measured and computed excess PWP ratios, indicating that the tested constitutive models provide reasonable estimations of PWP increase during cyclic shear (r_u) and the banana shape is reproduced in a proper way indicating that dilation and shear- strain behavior is well captured by the models.