• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.461-472
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• 2005

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) approach. Several aspects that turned out to be crucial for the presented approach are discussed. The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist. In this paper the performance of several solvers is investigated regarding their suitability for the application to the usually highly stiff DAE. The substructures are connected with each other by nonlinear algebraic constraint equations. Further, partial derivatives of the constraints are required, which often leads to extensive algebraic trans-formations. Handcoding of analytically determined derivatives is compared to an approach utilizing algorithmic differentiation.

• Coupled systems mechanics
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• v.12 no.6
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• pp.519-530
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• 2023

This paper presents a mathematical model suitable for the calculation of laminated glass, i.e. glass plates combined with an interlayer material. The model is based on a beam differential equation for each glass plate and a separate differential equation for the slip in the interlayer. In addition to slip, the model takes into account prestressing force in the interlayer. It is possible to combine the two contributions arbitrarily, which is important because the glass sheet fabrication process changes the stiffness of the interlayer in ways that are not easily predictable and could introduce prestressing of varying magnitude. The model is suitable for reformulation into an inverse procedure for calculation of the relevant parameters. Model consisting of a system of differential-algebraic equations, proved too stiff for cases with the thin interlayer. This novel approach covers the full range of possible stiffnesses of layered glass sheets, i.e., from zero to infinite stiffness of the interlayer. The comparison of numerical and experimental results contributes to the validation of the model.

• Earthquakes and Structures
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• v.14 no.4
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• pp.285-295
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• 2018

In this study, the effect of local site conditions (site class and site amplifications) and structural variability are investigated on fragility functions of typical building structures. The study area is chosen as Eastern Turkey. The fragility functions are developed using site-specific uniform hazard spectrum (UHS). The site-specific UHS is obtained based on simulated ground motions. The implementation of ground motion simulation into seismic hazard assessment has the advantage of investigating detailed local site effects. The typical residential buildings in Erzincan are represented by equivalent single degree of freedom systems (ESDOFs). Predictive equations are accomplished for structural seismic demands of ESDOFs to derive fragility functions in a straightforward manner. To study the sensitivity of fragility curves to site class, two sites on soft and stiff soil are taken into account. Two alternative site amplification functions known as generic and theoretical site amplifications are examined for these two sites. The reinforced concrete frames located on soft soil display larger fragilities than those on stiff soil. Theoretical site amplification mostly leads to larger fragilities than generic site amplification more evidently for reinforced concrete buildings. Additionally, structural variability of ESDOFs is generally observed to increase the fragility especially for rigid structural models.

• Proceedings of the Korean Geotechical Society Conference
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• 2002.03a
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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 Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.22 no.1
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• pp.1-7
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• 2024

In this research, a detailed analysis of the decay heat contributions of both actinides and non-actinides (fission fragments) from spent nuclear fuel (SNF) was made after 50 GWd·tHM^-1 burnup of fresh uranium fuel with 4.5% enrichment lasted for 1,350 days. The calculations were made for a long storage period of 300 years divided into four sections 1, 10, 100, and 300 years so that we could study the decay heat and physical disposal ratios of radioactive waste in medium- and long-term storage periods. Fresh fuel burnup calculations were made using the code MCNP, while isotopic content and then decay heat were calculated using the built-in stiff equation solver in the MATLAB code. It is noted that only around 12 isotopes contribute more than 90% of the decay heat at all times. It is also noted that the contribution of actinides persists and is the dominant ether despite decreasing decay heat, while the effect of fission products decreases at a very rapid rate after about 40 years of storage.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.4
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• pp.337-344
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• 2014

While implicit integration methods such as Newton's method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newton's method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newton's method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.

• Bulletin of the Korean Chemical Society
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• v.20 no.1
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• pp.35-41
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• 1999

Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.

• 한국전산유체공학회:학술대회논문집
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• 2008.03b
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• pp.216-217
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• 2008

In recent years, scientific community has found renewed interest in hypersonic flight research. These hypersonic vehicles undergo severe aero-thermal environment during their flight regimes. During reentry and hypersonic flight of these vehicles through atmosphere real gas effects come into play. The analysis of such hypersonic flows is critical for proper aero-thermal design of these vehicles. The numerical simulation of hypersonic real gas flows is a very challenging task. The present work emphasizes numerical simulation of hypersonic flows with thermal non-equilibrium. Hyperbolic system of equations with stiff relaxation method are identified in recent literature as a novel method of predicting long time behaviour of systems such as gas at high temperature. In present work, Energy Relaxation Method (ERM) has been considered to simulate the real gas flows. Navier-Stokes equations A numerical scheme Advection Upstream Splitting Method (AUSM) has been selected. Navier-Stokes solver along with relaxation method has been used for the simulation of real flow over a circular cylinder. Pressure distribution and heat flux over the surface of cylinder has been compared with experiment results of Hannemann. Present heat flux results over the cylinder compared well with experiment. Thus, real gas effects in hypersonic flows can be modeled through energy relaxation method.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.107-128
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• 2018

Thermo-mechanical vibration of sandwich beams with a stiff core and face sheets made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) is investigated within the framework of Timoshenko beam theory. The material properties of FG-CNTRC are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture and are considered to be temperature dependent. The governing equations and boundary conditions are derived by using Hamilton's principle and are solved using an efficient semi-analytical technique of the differential transform method (DTM). Comparison between the results of the present work and those available in literature shows the accuracy of this method. A parametric study is conducted to study the effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, and various boundary conditions on free vibration behavior of sandwich beams with FG-CNTRC face sheets. It is explicitly shown that the vibration characteristics of the curved nanosize beams are significantly influenced by the surface density effects.

• Coupled systems mechanics
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• v.6 no.2
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• pp.207-227
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• 2017

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.