• Computers and Concrete
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• 제22권6호
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• pp.539-550
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• 2018

Concrete is highly non-linear material which is originating from the transition zone in the form of micro-cracks, governs material response under various loadings. In this paper, the constitutive models published by many researchers have been used to generate novel stiffness parameters and constitutive curves for concrete. Following such linear material formulations, where the energy is conservative during the curvature, and a nonlinear contribution to the concrete has been made and investigated. In which, nonlinear concrete elastic modulus modeling has been developed that is capable-of representing concrete elasticity for grades ranging from 10 to 140 MPa. Thus, covering the grades range of concrete up to the ultra-high strength concrete, and replacing many concrete models that are valid for narrow ranges of concrete strength grades. This has been followed by the introduction of the nonlinear Hooke's law for the concrete material through the replacement of the Young constant modulus with the nonlinear modulus. In addition, the concept of concrete elasticity index (${\varphi}$) has been proposed and this factor has been introduced to account for the degradation of concrete stiffness in compression under increased loading as well as the multi-stages micro-cracking behavior of concrete under uniaxial compression. Finally, a sub-routine artificial neural network model has been developed to capture the concrete behavior that has been introduced to facilitate the prediction of concrete properties under increased loading.

• Structural Engineering and Mechanics
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• 제22권2호
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• pp.197-222
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• 2006

In this paper, the non-linear time-dependent closed-form, discrete and combined solutions for the post-elastic response of a geometrically and physically non-linear suspended cable to a uniformly distributed load considering the creep effects, are presented. The time-dependent closed-form method for the particularly straightforward determination of a vertical uniformly distributed load applied over the entire span of a cable and the accompanying deflection at time t corresponding to the elastic limit and/or to the elastic region, post-elastic and failure range of a suspended cable is described. The actual stress-strain properties of steel cables as well as creep of cables and their rheological characteristics are considered. In this solution, applying the Irvine's theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. The results obtained by the closed-form solution, i.e., a load corresponding to the elastic limit, post-elastic and failure range at time t, enable the direct use in the discrete non-linear time-dependent post-elastic analysis of a suspended cable. This initial value of load is necessary for the non-linear time-dependent elastic and post-elastic discrete analysis, concerning incremental and iterative solution strategies with tangent modulus concept. At each time step, the suspended cable is analyzed under the applied load and imposed deformations originated due to creep. This combined time-dependent approach, based on the closed-form solution and on the FEM, allows a prediction of the required load that occurs in the post-elastic region. The application of the described methods and derived equations is illustrated by numerical examples.

• Geotechnical Engineering
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• 제4권3호
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• pp.27-34
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• 1988

Soils behave non-linearly at high strain. This study investigated the non-linear behavior of silty sands (Mixture of Ottawa Sand and Quartz Powder) by resonant column tests. The results were ·compared with Ramberg-Osgood's non-linear equation. From the tests, it was shown that the change of shear modulus and damping ratio was more sharp at low fine content, high void ratio and low confining pressure. It was also found that famberg-Osgood parameter, R was approximately 2.0, however the range of C varied from 200 to 3200.

• Proceedings of the Korean Geotechical Society Conference
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• 한국지반공학회 2002년도 봄 학술발표회 논문집
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• pp.101-110
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• 2002

This article summarises the traditional method of soil-structure interaction based on the modulus of subgrade reaction and shows its weakness. In order to avoid these weakness, a new soil-structure interaction model is proposed. This model considers the soil as a set of connected springs which enables interaction between springs. Its use is as simple as the traditional model but allows to define the soil properties independently from the structural properties and the loading conditions. Thus, the definition of the modulus of subgrade reaction is unnecessary as each component is defined by its own modulii (Young's modulus and shear modulus). The non-linear soil behaviour for the shear stress versus distortion is also incorporated in the model. This feature allows to pinpoint the arching effect in the ground and shows how the stresses concentrate on stiff materials. Based on these principles, three dimensional program has been developed in order to solve the difficult problem of soil improvement by inclusions (stiff or soft). Also the possibility to take into account a flexible mat and/or a subgrade layer has been implemented. Equations used in the model are developed and a parametric study of the necessary data used in the program is presented. In particular, the Westergaard modulus notion and the arching effect are analysed.

• Journal of the Korean GEO-environmental Society
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• 제19권12호
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• pp.47-58
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• 2018

Duncan & Chang(1970) proposed the Duncan-Chang model that a linear relation of transformed stress-strain plots was reconstituted from a nonlinear relation of stress-strain curve of triaxial compression test using hyperbolic theory so as to estimate an initial tangent modulus and ultimate deviator stress for the soil specimen. Although the transformed stress-strain plots show a linear relationship theoretically, they actually show a nonlinearity at both low and high values of strain of the test. This phenomenon indicates that the stress-strain curve is not a complete form of a hyperbola. So, if linear regression analyses for the transformed stress-strain plot are performed over a full range of strain of a test, error in the estimation of their linear equations is unavoidable depending on ranges of strain with non-linearity. In order to reduce such an error, a modified regression analysis method is proposed in this study, in which linear regression analyses for transformed stress-strain plots are performed over the entire range of strain except the range the non-linearity is shown around starting and ending of the test, and then the initial tangent modulus and ultimate deviator stresses are calculated. Isotropically consolidated-drained triaxial compression tests were performed on compacted weathered soil with a modified Proctor density to obtain their model parameters. The modified regression analyses for transformed stress-strain plots were performed and analyzed results are compared with results estimated by 2 points method (Duncan et al., 1980). As a result of analyses, initial tangent moduli are about 4.0% higher and ultimate deviator stresses are about 2.9% lower than those values estimated by Duncan's 2 points method.

• Structural Engineering and Mechanics
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• 제12권6호
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• pp.657-668
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• 2001

Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

• Computers and Concrete
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• 제21권1호
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• pp.11-20
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• 2018

The possibilities of non-linear analysis of reinforced-concrete structures are under development. In particular, current research areas include structural analysis with the application of advanced computational and material models. The submitted article aims to evaluate the possibilities of the determination of material properties, involving the tensile strength of concrete, fracture energy and the modulus of elasticity. To evaluate the recommendations for concrete, volume computational models are employed on a comprehensive series of tests. The article particularly deals with the issue of the specific properties of fracture-plastic material models. This information is often unavailable. The determination of material properties is based on the recommendations of Model Code 1990, Model Code 2010 and specialized literature. For numerical modelling, the experiments with the so called "classic" concrete beams executed by Bresler and Scordelis were selected. It is also based on the series of experiments executed by Vecchio. The experiments involve a large number of reinforcement, cross-section and span variants, which subsequently enabled a wider verification and discussion of the usability of the non-linear analysis and constitutive concrete model selected.

• Tunnel and Underground Space
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• 제21권6호
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• pp.480-493
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• 2011

Dynamic rock property is one of most important parameters in design of earthquake-resistant structures. In this study, free-free resonant column test has been conducted to obtain dynamic Young's modulus, dynamic shear modulus, and damping ratio among dynamic properties with granite specimen of Chungnam Yeongi area. The dynamic properties obtained from this test were compared with the physical properties from static rock tests, and their relationship has been analyzed. From our study, it has been concluded that the dynamic Young's modulus and the dynamic shear modulus are linearly proportional to the elastic wave velocity. And also the damping ratio has been identified to be in non-linear inverse proportion to the elastic wave velocity.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제31권7호
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• pp.808-815
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• 2007

The optical performance of the mirror fur satellite camera is highly dependent on the adhesive properties between the mirror and its support. Therefore, in order to design a mirror with high optical performance, the mechanical properties of adhesives should be well defined. In this research, the mechanical properties of three kinds of space adhesives are studied. In case of the materials which show nearly incompressible behavior such as space adhesives, it is important to measure shear modulus which governs deviatoric stress components. Also the experiment should be performed in circumstances similar to real manufacturing process of mirror, because extra factors such as size effects, the adhesion effects of primer and reactions between adhesive and primer affect the properties of adhesive regions. In this research shear moduli of the adhesives are determined by using a single lap adhesively bonded joint. For the shear tests, several temperatures have been selected from $-20^{\circ}C$ to $55^{\circ}C$ which is operating temperature range of the adhesive. In the case of linear behavior materials, shear moduli are calculated through a linear curve fitting. Shear stress-strain relation is obtained by using an exponential curve fitting for material which shows non-linear behavior. The shear modulus of each adhesive is expressed as a function of temperature. Characteristics and adaptability of the adhesives are discussed regarding their temperature sensitivity.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• 제35권2호
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• pp.101-106
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• 2007

The optical performance of the mirror for satellite camera is highly dependent on the adhesive properties between the mirror and its support. Therefore, in order to design a mirror with high optical performance, the mechanical properties of adhesives should be well defined. In this paper, the mechanical properties of three kinds of space adhesives are studied. Elastic moduli of the adhesives are determined by tensile tests. Stress-strain relation is obtained by using exponential curve fitting for the adhesive which shows non-linear behavior. In case of the linear behavior material, elastic modulus is calculated through linear curve fitting. For the tensile tests, several points have been selected in the operating temperature range of the adhesive. The elastic modulus of each adhesive is expressed as a function of temperature. Characteristics of the adhesives are discussed regarding their temperature sensitivity.