• Structural Engineering and Mechanics
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• v.12 no.5
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• pp.507-526
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• 2001

In standard finite element algorithms, the local stability conditions are not accounted for in the formulation of the tangent stiffness matrix. As a result, the loss of the local stability is not adequately related to the onset of the global instability. The phenomenon typically arises with material-type localizations, such as shear bands and plastic hinges. This paper addresses the problem in the context of the planar, finite-strain, rate-independent, materially non-linear beam theory, although the proposed technology is in principle not limited to beam structures. A weak formulation of Reissner's finite-strain beam theory is first presented, where the pseudocurvature of the deformed axis is the only unknown function. We further derive the local stability conditions for the large deformation case, and suggest various possible combinations of the interpolation and numerical integration schemes that trigger the simultaneous loss of the local and global instabilities of a statically determined beam. For practical applications, we advice on a procedure that uses a special numerical integration rule, where interpolation nodes and integration points are equal in number, but not in locations, except for the point of the local instability, where the interpolation node and the integration point coalesce. Provided that the point of instability is an end-point of the beam-a condition often met in engineering practice-the procedure simplifies substantially; one of such algorithms uses the combination of the Lagrangian interpolation and Lobatto's integration. The present paper uses the Galerkin finite element discretization, but a conceptually similar technology could be extended to other discretization methods.

• Journal of Ocean Engineering and Technology
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• v.32 no.6
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• pp.466-473
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• 2018

This paper presents an estimation method for the static configuration of a steel lazy wave riser (SLWR) using the dynamic relaxation method applied to estimate the configuration of structures with strong geometric non-linearity. The lumped mass model is introduced to reflect the flexible structural characteristics of the riser. In the lumped mass model, the tensions, shear forces, buoyancy, self-weights, and seabed reaction forces at nodal points are considered in order to find the static configuration of the SLWR. The dynamic relaxation method using a viscous damping formulation is applied to the static configuration analysis. Fictitious masses are defined at nodal points using the sum of the largest direct stiffness values of nodal points to ensure the numerical stability. Various case studies were performed according to the bending stiffness and size of the buoyancy module using the dynamic relaxation method. OrcaFlex was employed to validate the accuracy of the developed numerical method.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.451-462
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• 2023

Lumped Damage Mechanics (LDM) is a theory proposed in the late eighties, which assumes that structural collapse may be analyzed as a two-phase phenomenon. In the first (pre-localization) stage, energy dissipation is a continuous process and it may be modelled by means of the classic versions of the theory of plasticity or Continuum Damage Mechanics (CDM). The second, post-localization, phase can be modelled assuming that energy dissipation is lumped in zones of zero volume: inelastic hinges, hinge lines or localization surfaces. This paper proposes a new LDM formulation for cracking in concrete structures in tension. It also describes its numerical implementation in conventional finite element programs. The results of three numerical simulations of experimental tests reported in the literature are presented. They correspond to plain and fiber-reinforced concrete specimens. A fourth simulation describes also the experimental results of a new test using the digital image correlation technique. These numerical simulations are also compared with the ones obtained using conventional Cohesive Fracture Mechanics (CFM). It is then shown that LDM conserves the advantages of both, CDM and CFM, while overcoming their drawbacks.

• Geomechanics and Engineering
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• v.7 no.6
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• pp.613-631
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• 2014

To complement the method of field-scale seismic ground motion simulations by buried blast techniques, the application and evaluation of the capability of a numerical modeling platform to simulate buried explosion-induced ground motion at a real soil site is presented in this paper. Upon a layout of the experimental setup at a level site wherein multiple charges that were buried over a large-diameter circle and detonated in a planned sequence, the formulation of a numerical model of the soil and the explosives using the finite element code LS-DYNA is developed for the evaluation of the resulting ground motion and surface subsidence. With a compact elastoplastic cap model calibrated for the loess soils on the basis of the site and laboratory test program, numerical solutions are obtained by explicit time integration for various dynamic aspects and their relation with the field blast experiment. Quantitative comparison of the computed ground acceleration time histories at different locations and induced spatial subsidence on the surface afterwards is given for further engineering insights in regard to the capabilities and limitations of both the numerical and experimental approaches.

• Wind and Structures
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• v.1 no.4
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• pp.337-349
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• 1998

A numerical and experimental study was performed for the wind flow field in one area, comprising a group of several pavilions separated by passageways, of the EXPO '98 - a World Exposition (Lisbon, Portugal). The focus of this study is the characterization of the flow field to assess pedestrian comfort. The predictions were obtained employing the Reynolds averaged Navier-Stokes equations with the turbulence effects dealt with the ${\kappa}-{\varepsilon}$ RNG model. The discretization of the differential equations was accomplished with the control volume formulation in a Cartesian coordinate system, and an advanced segregated procedure was used to achieve the link between continuity and momentum equations. The evaluation of the overall numerical model was performed by comparing its predictions against experimental data for a square cylinder placed in a channel. The predicted values, for the practical geometry studied, are in a good agreement with the experimental data, showing the performance and the reliability of the ${\kappa}-{\varepsilon}$ RNG model and suggesting that the numerical simulation is a reliable methodology to provide the required information.

• Journal of Korean Society of Steel Construction
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• v.20 no.3
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• pp.409-419
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• 2008

A co-rotational quasi-conforming formulation of four- node stress resultant shell elements using Ivanov-Ilyushin yield criteria are presented for the nonlinear analysis of plate and shell structure. The formulation of the geometrical stiffness is defined by the full definition of the Green strain tensor and it is efficient for analyzing stability problems of moderately thick plates and shells as it incorporates the bending moment and transverse shear resultant force. As a result of the explicit integration of the tangent stiffness matrix, this formulation is computationally very efficient in incremental nonlinear analysis. This formulation also integrates the elasto-plastic material behaviour using Ivanov Ilyushin yield condition with isotropic strain hardening and its asocia ted flow rules. The Ivanov Ilyushin plasticity, which avoids multi-layer integration, is computationally efficient in large-scale modeling of elasto-plastic shell structures. The numerical examples herein illustrate a satisfactory concordance with test ed and published references.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.29-38
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• 1990

A totally, new approach of Lagrangian formulation named 'Pseudo Lagrangian Formulation(PLF)' for large deformation analysis of continue and structures by the finite of element method has been presented, and the efficiency and accuracy of nonlinear analysis beam element formulated by PLF has been discussed by solving several numerical examples. In PLF, the deformation of a body is maeasured by assigning a nonphysical 'Pseudo' configuration as reference. The Lagrangian deformation and the finite element mapping of the traditonal Lagrangian approaches are then carried out directly at the same time, The result of numerical tests shows superior performance of PLF to the traditional Lagrangian methods, Applications of PLF to small and finite deformation problems indicate that PLF not only serves as an alternative but has certain implementational advantages over total or updated Lagrangian formulations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.3
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• pp.255-263
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• 2017

This paper presents a beam element capable of conducting material and geometric nonlinear analysis for applications requiring the ultimate behavioral analysis of structures with composite cross-sections. The element formulation is based on co-rotational kinematics to simulate geometrically nonlinear behaviors, and it uses the fiber section method to calculate the stiffness and internal forces of the element. The proposed element was implemented using an in-house numerical program in which an arc-length method was adopted to trace severe nonlinear responses(such as snap-through or snapback), as well as ductile behavior after the peak load. To verify the proposed method of element formulation and the accuracy of the program that was used to employ the element, several numerical studies were conducted and the results from these numerical models were compared with those of three-dimensional continuum models and previous studies, to demonstrate the accuracy and computational efficiency of the element. Additionally, by evaluating an example case of a frame structure with a composite member, the effects of differences between composite material properties such as the elastic modulus ratio and strength ratio were analyzed. It was found that increasing the elastic modulus of the external layer of a composite cross-section caused quasi-brittle behavior, while similar responses of the composite structure to those of homogeneous and linear materials were shown to increase the yield strength of the external layer.

• Journal of Soil and Groundwater Environment
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• v.20 no.2
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• pp.10-21
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• 2015

The present study introduces a novel numerical approach for solving dispersion dominated problems with Cauchy boundary condition in an Eulerian-Lagrangian scheme. The study reveals the incapability of traditional Neuman approach to address the dispersion dominated problems with Cauchy boundary condition, even though it can produce reliable solution in the advection dominated regime. Also, the proposed numerical approach is applied to a real field problem of radioactive contaminant migration from radioactive waste repository which is a major current waste management issue. The performance of the proposed numerical approach is evaluated by comparing the results with numerical solutions of traditional FDM (Finite Difference Method), Neuman approach, and the analytical solution. The results show that the proposed numerical approach yields better and reliable solution for dispersion dominated regime, specifically for Peclet Numbers of less than 0.1. The proposed numerical approach is validated by applying to a real field problem of radioactive contaminant migration from radioactive waste repository of varying Peclet Number from 0.003 to 34.5. The numerical results of Neuman approach overestimates the concentration value with an order of 100 than the proposed approach during the assessment of radioactive contaminant transport from nuclear waste repository. The overestimation of concentration value could be due to the assumption that dispersion is negligible. Also our application problem confirms the existence of real field situation with advection dominated condition and dispersion dominated condition simultaneously as well as the significance or advantage of the proposed approach in the real field problem.