• Steel and Composite Structures
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• v.48 no.1
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.5
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• pp.577-588
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• 2011

This paper provides a novel extended Moving Least Squares(MLS) difference method for the potential problem with weak and strong discontinuities. The conventional MLS difference method is enhanced with jump functions such as step function, wedge function and scissors function to model discontinuities in the solution and the derivative fields. When discretizing the governing equations, additional unknowns are not yielded because the jump functions are decided from the known interface condition. The Poisson type PDE's are discretized by the difference equations constructed on nodes. The system of equations built up by assembling the difference equations are directly solved, which is very efficient. Numerical examples show the excellence of the proposed numerical method. The method is expected to be applied to various discontinuity related problems such as crack problem, moving boundary problem and interaction problems.

• Computational Structural Engineering
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• v.31 no.3
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• pp.23-30
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• 2018

• Computers and Concrete
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• v.5 no.4
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• pp.401-416
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• 2008

The paper presents a methodology to model three-dimensional reinforced concrete members by means of embedded discontinuity elements based on the Continuum Strong Discontinuous Approach (CSDA). Mixture theory concepts are used to model reinforced concrete as a 3D composite material constituted of concrete with long fibers (rebars) bundles oriented in different directions embedded in it. The effects of the rebars are modeled by phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel action. The paper presents the constitutive models assumed for the components and the compatibility conditions chosen to constitute the composite. Numerical analyses of existing experimental reinforced concrete members are presented, illustrating the applicability of the proposed methodology.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.4
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• pp.283-288
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• 2017

A spot welded joint is modeled using 3-D finite elements with embedded strong discontinuities. The spot weld is represented by a special cohesive law on the embedded discontinuity surface, instead of meshing its geometry. This strategy naturally eliminates the need of adaptive FEM meshes fitting the local geometry of the spot weld. Mesh independent solutions are guaranteed by explicitly modeling the detailed shape of the spot weld, which is in contrast with the exiting approach using point constraints for the spot weld.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.10a
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• pp.285-289
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• 2005

The Cenozoic Era consists of two period , the Tertiary and the Quaternary Period. Weak rock types may include areas containing: 1) poorly cemented or uncemented sediments, 2) highly weathered rock, or 3) fault lines. Especially this paper deal with poorly cemented or uncemented sedimentary rocks in slope. Mechanical weathering is caused by physical processes such as absorption and release of water, and changes in temperature and stress at or near the exposed rock surface. It results in the opening of discontinuities, the formation of new discontinuities by rock fracture, the opening of grain boundaries, and the fracture or cleavage of individual mineral grains. Decomposition causes some silicate minerals such as feldspars to change to clay minerals. There was a strong negative correlation between water absorption and important engineering properties such as strength and durability.

• Computers and Concrete
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• v.1 no.1
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• pp.61-76
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• 2004

The paper is devoted to present the Continuum Strong Discontinuity Approach (CSDA) and to examine its capabilities for modeling cracking of concrete. After introducing the main ingredients of the CSDA, an isotropic continuum damage model, which distinguishes tension and compression states, is used to implicitly induce a projected traction separation-law that rules the cracking phenomena. Criteria for onset and propagation of material failure and specific finite elements with embedded discontinuities are also briefly sketched. Finally, some representative numerical simulations of cracking, in plain and reinforced concrete specimens, using the CSDA are presented.

• Geomechanics and Engineering
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• v.13 no.4
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• pp.535-570
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• 2017

There are only few cases where cause and location of failure of a rock structure are limited to a single discontinuity. Usually several discontinuities of limited size interact and eventually form a combined shear plane where failure takes place. So, besides the discontinuities, the regions between adjacent discontinuities, which consist of strong rock and are called material or rock bridges, are of utmost importance for the shear strength of the compound failure plane. Shear behaviour of persistent and non-persistent joint are different from each other. Shear strength of rock mass containing non-persistent joints is highly affected by mechanical behavior and geometrical configuration of non-persistent joints located in a rock mass. Therefore investigation is essential to study the fundamental failures occurring in a rock bridge, for assessing anticipated and actual performances of the structures built on or in rock masses. The purpose of this review paper is to present techniques, progresses and the likely future development directions in experimental testing of non-persistent joint failure behaviour. Experimental results showed that the presence of rock bridges in not fully persistent natural discontinuity sets is a significant factor affecting the stability of rock structures. Compared with intact rocks, jointed rock masses are usually weaker, more deformable and highly anisotropic, depending upon the mechanical properties of each joint and the explicit joint positions. The joint spacing, joint persistency, number of rock joint, angle of rock joint, length of rock bridge, angle of rock bridge, normal load, scale effect and material mixture have important effect on the failure mechanism of a rock bridge.

• Journal of computational fluids engineering
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• v.12 no.1
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• pp.60-67
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• 2007

In this paper, the dispersion controlled dissipative (DCD) scheme is reviewed and then extended to simulate chemically reacting gas flows in multicomponent mixtures in the presence of strong shock waves. Furthermore, the properties of the reactive DCD (DCD-R) scheme are discussed, followed by several applications. The DCD scheme has been shown to have the following features: high accuracy and robustness for reacting gas flows in the presence of strong shock waves and contact discontinuities, and algorithmic simplicity.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.11-19
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• 2001

An adaptive nonlinear artificial dissipation model is presented for performing aeroacoustic computations by the high-order and high-resolution numerical schemes based on the central finite differences. An effective formalism of it is devised by combining a selective background smoothing term and a well-established nonlinear shock-capturing term which is for the temporal accuracy as well as the numerical stability. A conservative form of the selective background smoothing term is presented to keep accurate phase speeds of the propagating nonlinear waves. The nonlinear shock-capturing term that has been modeled by the second-order derivative term is combined with it to improve the resolution of discontinuities and stabilize the strong nonlinear waves. It is shown that the improved artificial dissipation model with an adaptive control constant which is independent of problem types reproduces the correct profiles and speeds of nonlinear waves, suppresses numerical oscillations near discontinuity and avoids unnecessary damping on the smooth linear acoustic waves. The feasibility and performance of the adaptive nonlinear artificial dissipation model are investigated by the applications to actual computational aeroacoustics problems.