• Journal of Korean Society of Steel Construction
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• v.9 no.3 s.32
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• pp.401-419
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• 1997

In this paper the kinematics of damage for finite strain, elasto-plastic deformation is introduced using the fourth-order damage effect tensor through the concept of the effective stress within the framework of continuum damage mechanics. In the absence of the kinematic description of damage deformation leads one to adopt one of the following two different hypotheses for the small deformation problems. One uses either the hypothesis of strain equivalence or the hypotheses of energy equivalence in order to characterize the damage of the material. The proposed approach in this work provides a general description of kinematics of damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain equivalence approaches. In this work, the damage is described kinematically in both the elastic domain and plastic domain using the fourth order damage effect tensor which is a function of the second-order damage tensor. The damage effect tensor is explicitly characterized in terms of a kinematic measurure of damage through a second-order damage tensor. Two kinds of second-order damage tensor representations are used in this work with respect to two reference configurations.

• CELLMED
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• v.5 no.2
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• pp.9.1-9.14
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• 2015

The so-called "Needham's Grand Question" (NGQ) can be formulated as why modern science was developed in Europe despite the earlier successes of science and technology in ancient China. Numerous answers have been proposed. In this review, it will be pointed out that traditional Chinese natural philosophy (TCNP) and traditional Chinese medicine (TCM) are in fact dealing with problems of highly complex dynamical systems of Nature and human beings. Due to the lack of mathematical machinery in dealing with such complex phenomena, a holistic approach was taken by ancient Chinese instead. It was very successful for the first eighteen centuries. In the recent three centuries, however, the reductionist and mechanistic viewpoints of Western natural philosophy, sciences, and medicine have been prevalent all over the world up to now. The main obstacle in preventing the advancement of TCM, TCNP and its sciences is actually the lacking of proper mathematical tools in dealing with complex dynamical systems. Fortunately, the tools are now available and a "chaotic wave theory of fractal continuum" has been proposed recently. To give the theory an operational meaning, three basic laws of TCNP are outlined. These three laws of wave/field interactions contrast readily with those of Newton's particle collisions. Via the proposed three laws, TCM, TCNP and its sciences can be unified under the same principles. Finally, an answer to NGQ can be accurately given. It is hoped that this review will help promoting a genuine understanding of natural philosophy, sciences, and medicine in an ecumenical way.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.511-521
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• 2002

A simple numerical modelling technique is proposed for estimating the shear stress distribution in beams of framed tube structures with multiple internal tubes. The structures arc analysed using a continuum approach in which each tube is individually modelled by a tube beam that accounts for the flexural and shear deformations, as well as the shear lag effects. The numerical analysis of shear stress is based on the mathematical analogy in conjunction with the elastic theory By simplifying assumptions regarding the form of strain distributions in external and internal tubes, the shear stress distributions are expressed in terms of a series of lineal functions of the second moments of area of the structures and the corresponding geometric and material properties, as well as the applied loads. Previous studies for axial stresses and shear lag phenomenon are further developed lot the numerical analysis of shear stresses in the tubes. The simplicity and accuracy of the proposed method are demonstrated through the solutions of throe numerical examples.

• Steel and Composite Structures
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• v.34 no.2
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• pp.261-277
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• 2020

The main objective of this research paper is to consider vibration analysis of vacancy defected graphene sheet as a nonisotropic structure via molecular dynamic and continuum approaches. The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defected graphene sheets. Molecular dynamic simulations have been performed to estimate the mechanical properties of graphene as a nonisotropic structure with single- and double- vacancy defects using open source well-known software i.e., large-scale atomic/molecular massively parallel simulator (LAMMPS). The interactions between the carbon atoms are modelled using Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. An isogeometric analysis (IGA) based upon non-uniform rational B-spline (NURBS) is employed for approximation of single-layered graphene sheets deflection field and the governing equations are derived using nonlocal elasticity theory. The dependence of small-scale effects, chirality and different defect types on vibrational characteristic of graphene sheets is investigated in this comprehensive research work. In addition, numerical results are validated and compared with those achieved using other analysis, where an excellent agreement is found. The interesting results indicate that increasing the number of missing atoms can lead to decrease the natural frequencies of graphene sheets. It is seen that the degree of the detrimental effects differ with defect type. The Young's and shear modulus of the graphene with SV defects are much smaller than graphene with DV defects. It is also observed that Single Vacancy (SV) clusters cause more reduction in the natural frequencies of SLGS than Double Vacancy (DV) clusters. The effectiveness and the accuracy of the present IGA approach have been demonstrated and it is shown that the IGA is efficient, robust and accurate in terms of nanoplate problems.

• Structural Engineering and Mechanics
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• v.49 no.1
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• pp.95-110
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• 2014

The study deals with physical modeling of space frame-pile foundation and soil system using finite element models. The superstructure frame is analyzed using complete three-dimensional finite element method where the component of the frame such as slab, beam and columns are descretized using 20 node isoparametric continuum elements. Initially, the frame is analyzed assuming the fixed column bases. Later the pile foundation is worked out separately wherein the simplified models of finite elements such as beam and plate element are used for pile and pile cap, respectively. The non-linear behaviour of soil mass is incorporated by idealizing the soil as non-linear springs using p-y curve along the lines similar to that by Georgiadis et al. (1992). For analysis of pile foundation, the non-linearity of soil via p-y curve approach is incorporated using the incremental approach. The interaction analysis is conducted for the parametric study. The non-linearity of soil is further incorporated using iterative approach, i.e., secant modulus approach, in the interaction analysis. The effect the various parameters of the pile foundation such as spacing in a group and configuration of the pile group is evaluated on the response of superstructure owing to non-linearity of the soil. The response included the displacement at the top of the frame and bending moment in columns. The non-linearity of soil increases the top displacement in the range of 7.8%-16.7%. However, its effect is found very marginal on the absolute maximum moment in columns. The hogging moment decreases by 0.005% while sagging moment increases by 0.02%.

• Structural Engineering and Mechanics
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• v.33 no.1
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• pp.95-107
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• 2009

A method for vibration analysis of asymmetric shear wall and Thin walled open section structures is presented in this paper. The whole structure is idealized as an equivalent bending-warping torsion beam in this method. The governing differential equations of equivalent bending-warping torsion beam are formulated using continuum approach and posed in the form of simple storey transfer matrix. By using the storey transfer matrices and point transfer matrices which consider the inertial forces, system transfer matrix is obtained. Natural frequencies can be calculated by applying the boundary conditions. The structural properties of building may change in the proposed method. A numerical example has been solved at the end of study by a program written in MATLAB to verify the presented method. The results of this example display the agreement between the proposed method and the other valid method given in literature.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.299-312
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• 2012

Stiffened coupled shear walls (SCSW) are under axial load resulting from their weight and this axial load affects the behavior of walls because of their excessive height. In this paper, based on the continuum approach, the optimal position of the stiffening beam on the stiffened coupled shear walls is investigated considering the effect of uniformly distributed axial loads. Moreover, the effect of the height of stiffened coupled shear walls on the optimal position of the stiffening beam has been studied with and without considering the axial force effect. A computer program has been developed in MATLAB and numerical examples have been solved to demonstrate the reliability of this method. The effects of the various flexural rigidities of the stiffening beam on the internal forces and the lateral deflection of the structure considering axial force effect have also been investigated.

• Advances in concrete construction
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• v.9 no.3
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• pp.301-312
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• 2020

This research deals with the study of the orthotropic vibrational features of single-walled carbon nanotubes according to Kelvin's model and to check the accuracy of the models, the results have been compared with earlier modeling/simulations. Obtaining rough approximations of the natural frequencies of CNTs using continuum equations are still a common procedure, even at high harmonics. The effects of different physical and material parameters on the fundamental frequencies are investigated for zigzag and chiral single-walled carbon nanotubes invoking Kelvin's theory. By using nonlocal Kelvin's model, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes (SWCNTs) have been calculated. The influence of frequencies with nonlocal parameters and bending rigidity are investigated in detail for these tubes. Computer software MATLAB is utilized for the frequencies of SWCNTs and current results shows a good stability with comparison of other studies.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.595-608
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• 2018

This paper deals with the lateral - torsional motion of bridges provided with external cables acting as dampers under the action of horizontal dynamic loads or of walking human crowd loads. A three dimensional analysis is performed for the solution of the bridge models. The theoretical formulation is based on a continuum approach, which has been widely used in the literature to analyze bridges. The resulting equations of the uncoupled motion are solved using the Laplace Transformation, while the case of the coupled motion is solved through the use of the potential energy. Finally, characteristic examples are presented and useful results are obtained.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.3
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• pp.256-264
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• 2004

The granular flow has been numerically studied by using DEM(Discrete Element Method). The eve교 particle is checked if it collides neighbor particles, and the next motion of the particle is predicted. The computing time has been drastically reduced by improving the collision check against neighboring particles. The comparison of the present method with ail experiment for the vibrating floor problem shows the good accuracy. The broken tower problem has been calculated to show the good comparison with the other computational result. This DEM(Discrete Element Method) can be a useful tool for constructing the constitute equation of the continuum approach of the granular flow.