• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.4
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• pp.415-422
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• 2016

When shock acceleration is applied to a mechanical system, it may cause malfunctioning and damage to the system. Hence, to prevent these problems when developing a gimbal structure system for observation reconnaissance, the MIL-STD-810G shock standard must be satisfied as a design specification. Rubber vibration isolators are generally assembled on the base of the system in order to reduce the shock transferred from the aircraft. It is difficult to analyze the transient behavior of the system accurately, because rubber has a nonlinear load-deformation curve. To treat the nonlinear characteristic of the rubber, bilinear approximation was introduced. Using this assumption, transient responses of the system under base shock acceleration were calculated by the finite element method. In addition, experiments with a true prototype were performed using the same conditions as the analytical model. Compared with experimental data, the proposed numerical method is useful for the transient analysis of gimbal structure systems, including rubber vibration isolators with nonlinear stiffness and damping.

• Korea-Australia Rheology Journal
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• v.21 no.4
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• pp.203-211
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• 2009

In flows with deformation rates larger than the inverse Rouse time of the polymer chain, chains are stretched and their confining tubes become increasingly anisotropic. The pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic and limit chain stretch. In the Molecular Stress Function (MSF) model, chain stretch is balanced by an interchain pressure term, which is inverse proportional to the $3^{rd}$ power of the tube diameter and is characterized by a tube diameter relaxation time. We show that the tube diameter relaxation time is equal to 3 times the Rouse time in the limit of small chain stretch. At larger deformations, we argue that chain stretch is balanced by two restoring tensions with weights of 1/3 in the longitudinal direction of the tube (due to a linear spring force) and 2/3 in the lateral direction (due to the nonlinear interchain pressure), both of which are characterized by the Rouse time. This approach is shown to be in quantitative agreement with transient and steady-state elongational viscosity data of two monodisperse polystyrene melts without using any nonlinear parameter, i.e. solely based on the linear-viscoelastic characterization of the melts. The same approach is extended to model experimental data of four styrene-butadiene random copolymer melts in shear flow. Thus for monodisperse linear polymer melts, for the first time a constitutive equation is presented which allows quantitative modeling of nonlinear extension and shear rheology on the basis of linear-viscoelastic data alone.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.1
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• pp.57-69
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• 1990

The static nonlinear analysis of offshore pipeline is carried out by the finite element method. The governing equilibrium equation are derived by the principle of minimum potential energy and the modified Newton-Raphson procedure is used to solve the system of nonlinear algebraic equation. Geometrically nonlinear beam elements and spring elements are utilized to model the pipeline, stinger, pipe supports and seabed simultaneously. The beam element developed can be used to model redundant structures. It provides for both the torsional deformation and elongation of pipeline, and permits the use of different physical properties in each principal direction. The validity of this method is investigated by comparing the results with these obtained by other methods.

• Steel and Composite Structures
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• v.27 no.6
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• pp.717-725
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• 2018

One of the most important design criteria in military tunnels and armoured doors is to resist the blast loads with minimum structural weight. This can be achieved by using steel sandwich panels. In this paper, the nonlinear behaviour of steel sandwich panels, with different core materials: (1) Hollow (no core material); (2) Rigid Polyurethane Foam (RPF); and (3) Vulcanized Rubber (VR) under free air blast loads, was investigated using detailed 3D nonlinear finite element models in Ansys Autodyn. The accuracy of the finite element model proposed was verified using available experimental test data of a similar steel sandwich panel tested. The results show the developed finite element model can be reliably used to simulate the nonlinear behaviour of the steel sandwich panels under free air blast loads. The verified finite element model was used to examine the different parameters of the steel sandwich panel with different core materials. The result shows that the sandwich panel with RPF core material is more efficient than the VR sandwich panel followed by the Hollow sandwich panels. The average maximum displacement of RPF sandwich panel under different ranges of TNT charge (1 kg to 10 kg at a standoff distance of 1 m) is 49% and 53% less than the VR and Hollow sandwich panels, respectively. Detailed empirical design equations were provided to quantify the maximum deformation of the steel sandwich panels with different core materials and core thickness under a different range of blast loads. The developed equations can be used as a guide for engineer to design steel sandwich panels with RPF and VR core material under a different range of free air blast loads.

• Journal of the Korea institute for structural maintenance and inspection
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• v.22 no.6
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• pp.130-137
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• 2018

Many constitutive models for concrete have been developed to predict the nonlinear behavior of concrete members considerably. The constitutive model for reinforcing bar that include the tension stiffening effect due to the bond characteristics between steel bars and concrete is being studied but the bilinear model is generally used. It was found that the buckling of the longitudinal reinforcing bars is controlled the nonlinear behavior of hybrid precast concrete panel, which is being developed for core wall. In this study, the constitutive models that can consider the embedding and buckling effects of reinforcing bar are investigated and a new model combing these constitutive models is proposed. In order to verify the proposed model, the analysis results are compared with experimental results of the concrete wall and hybrid precast concrete panel. The analysis of embedding-effect-only modeling predicted that the deformation increases continually without the decrease in the load carrying capacity. However, the analysis results of proposed model showed good agreement with some experimental results, thus verifying the proposed computational model.

• Steel and Composite Structures
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• v.51 no.4
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• pp.391-406
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• 2024

The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

• International Journal of Highway Engineering
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• v.11 no.1
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• pp.165-175
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• 2009

With the current move towards adopting mechanistic-empirical concepts in the design of pavement structures, state-of-the-art mechanistic analysis methodologies are needed to determine accurate pavement responses, such as stress, strain, and deformation. Previous laboratory studies of pavement foundation geomaterials, i.e., unbound granular materials used in base/subbase layers and fine-grained soils of a prepared subgrade, have shown that the resilient responses followed by nonlinear, stress-dependent behavior under repeated wheel loading. This nonlinear behavior is commonly characterized by stress-dependent resilient modulus material models that need to be incorporated into finite element (FE) based mechanistic pavement analysis methods to predict more realistically predict pavement responses for a mechanistic pavement analysis. Developed user material subroutine using aforementioned resilient model with nonlinear solution technique and convergence scheme with proven performance were successfully employed in general-purpose FE program, ABAQUS. This numerical analysis was investigated in predicted critical responses and domain selection with specific mesh generation was implemented to evaluate better prediction of pavement responses. Results obtained from both axisymmetric and three-dimensional (3D) nonlinear FE analyses were compared and remarkable findings were described for nonlinear FE analysis. The UMAT subroutine performance was also validated with the instrumented full scale pavement test section study results from the Federal Aviation Administration's National Airport Pavement Test Facility (FAA's NAPTF).

• Journal of Theoretical and Applied Mechanics
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• v.3 no.1
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• pp.45-65
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• 2002

A constitutive model on oorthotropic thermo-elasto-viscoplasticity for fiber-reinforced composite materials Is illustrated, and their thermomechanical responses are predicted with the fully-coupled finite element formulation. The unmixing-mixing scheme can be adopted with the multipartite matrix method as the constitutive model. Basic assumptions based upon the composite micromechanics are postulated, and the strain components of thermal expansion due to temperature change are included In the formulation. Also. more than two sets of mechanical variables, which represent the deformation states of multipartite matrix can be introduced arbitrarily. In particular, the unmixing-mixing scheme can be used with any well-known isotropic viscoplastic theory of the matrix material. The scheme unnecessitates the complex processes for developing an orthotropic viscoplastic theory. The governing equations based on fully-coupled thermomechanics are derived with constitutive arrangement by the unmixing-mixing concept. By considering some auxiliary conditions, the Initial-boundary value problem Is completely set up. As a tool of numerical analyses, the finite element method Is used with isoparametric Interpolation fer the displacement and the temperature fields. The equation of mutton and the energy conservation equation are spatially discretized, and then the time marching techniques such as the Newmark method and the Crank-Nicolson technique are applied. To solve the ultimate nonlinear simultaneous equations, a successive iteration algorithm is constructed with subincrementing technique. As a numerical study, a series of analyses are performed with the main focus on the thermomechanical coupling effect in composite materials. The progress of viscoplastic deformation, the stress-strain relation, and the temperature History are careful1y examined when composite laminates are subjected to repeated cyclic loading.

• Advances in nano research
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• v.9 no.3
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• pp.211-220
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• 2020

This paper investigates the effect of linear and non-linear distribution of carbon nanotube volume fraction in the FG-CNTRC beams on the critical buckling by using higher-order shear deformation theories. Here, the material properties of the CNTRC beams are assumed to be graded in the thickness direction according to a new exponential power law distribution in terms of the carbon nanotube volume fractions. The single-walled carbon nanotube is aligned and distributed in the polymeric matrix with different patterns of reinforcement; the material properties of the CNTRC beams are described by using the rule of mixture. The governing equations are derived through using Hamilton's principle. The Navier solution method is used under the specified boundary conditions for simply supported CNTRC beams. The mathematical models provided in this work are numerically validated by comparison with some available results. New results of critical buckling with the non-linear distribution of CNT volume fraction in different patterns are presented and discussed in detail, and compared with the linear distribution. Several aspects of beam types, CNT volume fraction, exponent degree (n), aspect ratio, etc., are taken into this investigation. It is revealed that the influences of non-linearity distribution in the beam play an important role to improve the mechanical properties, especially in buckling behavior. The results show that the X-Beam configuration is the strongest among all different types of CNTRC beams in supporting the buckling loads.