• Structural Engineering and Mechanics
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• v.4 no.1
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• pp.25-35
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• 1996

This paper describes a continuum variational formulation for design optimization of nonlinear structures in the elastic-plastic domain, where unloading and reloading of the structures are allowed to occur. The Total Lagrangian procedure is used for the description of the structural deformation. The direct differentiation approach is used to derive the sensitivities of the various structural response measures with respect to the design parameters. Since the material goes into the inelastic range and unloading and reloading of the structure are allowed to occur, the structural response is path dependent and an additional step is needed to integrate the constitutive equations. It can be shown, consequently, that design sensitivity analysis is also path-dependent. The theory has been discretized by the finite element technique and implemented in a structural analysis code. Mathematical programming approach is used for the optimization process. Numerical applications on trusses are performed, where cross-sectional areas and nodal point coordinates are treated as design variables. Optimal designs have been obtained and compared by using two different strategies: a two level strategy where the levels are defined accordingly the type of design variables, cross sectional areas or node coordinates, and optimizing simultaneously with respect to both types of design variables.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.3
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• pp.540-544
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• 1998

Compliance calibration method is frequently used to determine $G_IC$ from the DCB composite specimen. However, the method requires at least 4 to 5 fracture test (loading-unloading) records. In this study, $G_IC$ of unidirectional graphite/epoxy DCB composites was determined from the elastic work factor approach which uses a single fracture test record. In order to inspect the validity of the elastic work factor approach, $G_IC$ determined from the elastic work factor approach was compared to that of determined from the compliance calibration method. It was shown that $G_IC$ determined from the elastic work factor approach was comparable to that determined from the compliance calibration method. That is, the elastic work factor approach can be used to determine $G_IC$ of unidirectional graphite/epoxy DCB specimen from a single fracture record.

• Structural Engineering and Mechanics
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• v.77 no.2
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• pp.179-196
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• 2021

Experimental investigations on the seismic behaviors of the PVC-FRP Confined Reinforced Concrete (PFCRC) columns under low cyclic loading are carried out and two variable parameters including CFRP strips spacing and axial compression ratio are considered. The PFCRC column finally fails by bending and is characterized by the crushing of concrete and yielding of the longitudinal reinforcement, and the column with a high axial compression ratio is also accompanied by the cracking of the PVC tube and the fracture of CFRP strips. The hysteretic curves and skeleton curves of the columns are obtained from the experimental data. With the increase of axial compression ratio, the stiffness degradation rate accelerates and the ductility decreases. With the decrease of CFRP strips spacing, the unloading sections of the skeleton curves become steep and the ductility reduces significantly. On the basis of fiber model method, a numerical analysis approach for predicting the skeleton curves of the PFCRC columns is developed. Additionally, a simplified skeleton curve including the elastic stage, strengthening stage and unloading stage is suggested depending on the geometric drawing method. Moreover, the loading and unloading rules of the PFCRC columns are revealed by analyzing the features of the skeleton curves. The quantitative expressions that are used to predict the unloading stiffness of the specimens in each stage are proposed. Eventually, an analytical model for the PFCRC columns under low cyclic loading is established and it agrees well with test data.

• Transactions of Materials Processing
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• v.22 no.8
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• pp.470-476
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• 2013

The aim of the current study was to predict shape recovery behavior of Ni-Ti shape memory alloy (SMA) wire after loading-unloading and after wire drawing. The superelasticity of SMA was analyzed by a hyper-elastic model for the Mullins effect using ABAQUS. Firstly, tensile tests and loading-unloading tests of the Ni-Ti SMA wire with a diameter 1.0 mm were performed using an MTS servo-hydraulic tester. The parameters for the Mullins effect were computed by ABAQUS based on curve-fitting of the loading-unloading test data. The proposed FE-model predicted the shape recovery of Ni-Ti SMA after wire drawing. Finally, the effectiveness of the model was verified by drawing experiments. The wire drawing experiments using the Ni-Ti SMA were conducted on a drawing machine(1ton, 50mm/s). In order to evaluate the shape recovery of Ni-Ti SMA, the drawn wires are annealed for 30min at $450^{\circ}C$.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.10a
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• pp.167-170
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• 2003

Thermal elastic-plastic analysis was performed to assess the initial residual stress distribution of welded joints considering temperature dependent material properties. The test model was the idealized boxing fillet specimen, frequently appeared in the joints of longitudinal and transverse members of ship structure. Residual stress relaxations due to external loads were analyzed by subsequent elastic-plastic analysis considering loading and unloading steps, and the characteristics of residual stress relaxations were discussed with the levels of external loads. Additionally, to define the fatigue life of crack initiation and propagation, the S-N data for each crack length were appraised.

• Proceedings of the Korea Concrete Institute Conference
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• 1995.10a
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• pp.178-182
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• 1995

Strain localization is important phenomenon since it governs the total behavior or ultimate loads in various kinds of engineering problems. Establishment of an analysis method for strain localization phenomena is also of great concern for expansion of fracture mechanics of concrete. Inside zone of localization, a decrese in stress is accompanied by an increse in strain; outside the strain decreses. All deformation localization phenomenon cannot be predicted by both the classical stress-strain formulation and the linear elastic fracture mechanics. In this paper, a simple one dimensional model including localized deformation zone is studied under compressive and tensile loading. When the model is loaded. localization is assumed to occur uniformly in a finite region and material outside the localization zone is modelled as elastic unloading occurs. Size effects of effective elastic moduli under compression and tension in localization zone are examined.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.469-483
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• 2014

In an indentation approach, the smooth rigid spherical ball penetrated into a deformable flat is considered for the study based on contact mechanics approach. The elastic-plastic frictionless spherical indentation analysis has been under taken in the finite element analysis using "ABAQUS" and experimental study. The spherical indentation has been studied for the materials like steel, aluminium, copper and brass with an identical spherical indenter for diverse indentation depths. The springback analysis is executed for studying the actual indentation depth after the indenter is unloaded. In the springback simulation, the material recovers its elastic deformation after the indenter is unloaded. The residual diameter and depth of an indentation for various materials are measured and compared with simulation results. It shows a good agreement between the simulation and an experimental studies.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1757-1760
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• 2005

This paper is concerned with spring back after sheet forming of bulk amorphous alloys in the super cooled liquid state. The temperature-dependence and strain-rate dependence of Newtonian/non-Newtonian viscosities as well as the stress overshoot/undershoot behavior of amorphous alloys are reflected in the thermo-mechanical Finite Element simulations. Hemispherical deep drawing operations are simulated for various forming conditions such as punch velocity, die corner radius, friction, blank holder force, clearance and initial forming temperature. Here, spring back by an instantaneous elastic unloading was followed by thermal deformation during cooling and two modes of spring backs are examined in detail. It could be concluded that the superior sheet formability of an amorphous alloy can be obtained by taking the proper forming conditions for loading/unloading.

• Transactions of Materials Processing
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• v.14 no.9 s.81
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• pp.751-755
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• 2005

This paper is concerned with spring back after sheet forming of bulk amorphous alloys in the super cooled liquid state. The temperature-dependence and strain-rate dependence of Newtonian/non-Newtonian viscosities as well as the stress overshoot/undershoot behavior of amorphous alloys are reflected in the thermo-mechanical Finite Element simulations. Hemispherical deep drawing operations are simulated for various forming conditions such as punch velocity, die comer radius, friction, blank holder force, clearance and initial funning temperature. Here, spring back by an instantaneous elastic unloading was followed by thermal deformation during cooling, and two modes of spring back are examined in detail. It could be concluded that the superior sheet formability of an amorphous alloy can be obtained by taking the proper forming conditions for loading/unloading.

• Transactions of Materials Processing
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• v.22 no.4
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• pp.216-222
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• 2013

Solid polymers exhibit rate-dependent deformation behavior such as nonlinear strain rate sensitivity and stress relaxation like metallic materials. Despite the different microstructures of polymeric and metallic materials, they have common properties with respect to inelastic deformation. Unlike most metallic materials, solid polymers and shape memory alloys (SMAs) exhibit highly nonlinear stress-strain behavior upon unloading. The present work employs the viscoplasticity theory [K. Ho, 2011, Trans. Mater. Process. 20, 350-356] developed for the pseudoelastic behavior of SMAs, which is based on unified state variable theory for the rate-dependent inelastic deformation behavior of typical metallic materials, to depict the curved unloading behavior of polyphenylene oxide (PPO). The constitutive equations are characterized by the evolution laws of two state variables that are related to the elastic modulus and the back stress. The simulation results are compared with the experimental data obtained by Krempl and Khan [2003, Int. J. Plasticity 19, 1069-1095].