• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.1-16
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• 2001

This paper discusses the elastic stability of unbraced frames under non-proportional loading based on the concept of storey-based buckling. Unlike the case of proportional loading, in which the load pattern is predefined, load patterns for non-proportional loading are unknown, and there may be various load patterns that will correspond to different critical buckling loads of the frame. The problem of determining elastic critical loads of unbraced frames under non-proportional loading is expressed as the minimization and maximization problem with subject to stability constraints and is solved by a linear programming method. The minimum and maximum loads represent the lower and upper bounds of critical loads for unbraced frames and provide realistic estimation of stability capacities of the frame under extreme load cases. The proposed approach of evaluating the stability of unbraced frames under non-proportional loading has taken into account the variability of magnitudes and patterns of loads, therefore, it is recommended for the design practice.

• Steel and Composite Structures
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• v.47 no.2
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• pp.289-296
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• 2023

The failure of a thin-walled tube was studied in this paper based on three failure models. Both proportional and non-proportional loading paths were applied. Proportional loading consisted of combined tension-torsion. Cyclic non-proportional loading was also applied. It was a circular out-of-phase axial-shear stress loading path. The third loading path was a combination of a constant internal pressure and a bending moment. The failure models under study were equivalent plastic strain, modified Mohr-Coulomb (Bai-Wierzbicki) and Tearing parameter models. The elasto-plastic analysis was conducted using J2 criterion and nonlinear kinematic hardening. The return mapping algorithm was employed to numerically solve the plastic flow relations. The effects of the hydrostatic stress on the plastic flow and the stress triaxiality parameter on the failure were discussed. Each failure model under study was utilized to predict failure. The failure loads obtained from each model were compared with each other. The equivalent plastic strain model was independent from the stress triaxiality parameter, and it predicted the highest failure load in the bending problem. The modified Mohr-Coulomb failure model predicted the lowest failure load for the range of the stress triaxiality parameter and Lode's angle.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.1
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• pp.104-111
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• 1997

Accounting for the additional damages come out from non-proportional loading path effect, material damage according to crystal structure dependence was studied. Microscopic observations of damaged material by SEM(Scanning Electron Microscope) showed crystal structure dependence. Biaxial in-phase loaded specimens showed the slips of same direction, which pararell each other, but biaxial 90.deg. out-of-phase loaded specimens showed multiply crossed slips. S. H. Doong and D. F. Socie reported that wavy/planar or planar slip material showed the increase in the cyclic hardening level during non-proportional cycling. From these results, the additional hardening and non-proportional loading effects were related with slip mechanism, and the slip mechanism was related with crystal structure. In the present study, a damage mechanism which accounts for the non-proportional loading effect from crystal structure dependence was considered and applied to A17075-T651.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1352-1361
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• 2000

We obtain a micromechanics-based Helmholtz free energy and then in the framework of irreversible thermodynamics, a kinetic relation, a martensitic nucleation criterion and the reorientation criterion of martensitic variants are obtained. These relations are valid for a three-dimensional proportional and non-proportional loadings and for a combination of mechanical and thermal loading. From the simulated pseudoelastic stress-strain relation of a single crystal with loading rate effect, polycrystalline behavior in case of proportional and non-proportional loading is predicted by a homogenization method. The obtained results are compared quantitatively with experimental results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.77-84
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• 2003

In this paper, the refined plastic-hinge analysis accounting for the effect of strain reversal caused by non-proportional loading is developed. This analysis accounts for material and geometric nonlinearities of the structural system and its component members. Moreover, the problem, conventional refined plastic-hinge analyses have underestimated the strength of structures subjected to non-proportional loading, is overcome. The modified stiffness degradation model approximating the effect of strain reversal is discussed in detail. The proposed analysis is verified by the comparison of the finite element analysis. A case study shows that the effect of strain reversal is a very crucial element to be considered in second-order plastic-hinge analysis. The proposed analysis is shown to be an efficient, reliable tool ready to be implemented into design practice.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.549-553
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• 2007

Moving parts of the rotating and reciprocating mechanism are the most important components of the diesel engines and require very high reliability in their design. Especially the crankshaft, the key component of running gear (powertrain), is subject to complicated loadings such as bending, shear and torsion coming from firing pressure, inertia forces and torsional vibration of crankshaft system. Intrinsically they show different cyclic patterns of loading in both direction and magnitude, and thus ordinary approach of proportional loading is less valid to analyze the dynamic structural behavior of crankshaft. In this paper, new fatigue analysis method is introduced to analyze and design the crankshaft of a medium-speed diesel engine in order to consider the non-proportional multi-axial loads realistically as well as to present the general fatigue analysis approach for an engine crankshaft.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.12
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• pp.2056-2061
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• 2001

Non-proportional loading tests of Nylon 66 at room temperature exhibit path dependent behavior and plasticity-relaxation interactions. The uniaxial formulation of the viscoplasticity theory based on overstress (VBO), which has been used to reproduce the nonlinear strain rate sensitivity, relaxation, significant recovery and cyclic softening behaviors of Nylon 66, is extended to three-dimensions to predict the response in strain-controlled, comer-path tests. VBO consists of a flow law that is easily written for either the stress or the strain as the independent variable. The flow law depends on the overstress, the difference between the stress and the equilibrium stress that is a state variable in VBO. The evolution law of the equilibrium stress in turn contains two additional state variables, the kinematic stress and the isotropic stress. The simulations show that the constitutive model is competent at modeling the deformation behavior of Nylon 66 and other solid polymers.

• Journal of Ocean Engineering and Technology
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• v.31 no.4
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• pp.288-298
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• 2017

A study of the damage evolution laws for ductile materials was carried out to predict the ductile fracture behavior of a marine structural steel (EH36). We conducted proportional and non-proportional stress tests in the experiments. The existing 3-D fracture strain surface was newly calibrated using two fracture parameters: the average stress triaxiality and average normalized load angle taken from the proportional tests. Linear and non-linear damage evolution models were taken into account in this study. A damage exponent of 3.0 for the non-linear damage model was determined based on a simple optimization technique, for which proportional and non-proportional stress tests were simultaneously used. We verified the validity of the three fracture models: the newly calibrated fracture strain model, linear damage evolution model, and non-linear damage evolution model for the tensile tests of the asymmetric notch specimens. Because the stress evolution pattern for the verification tests remained at mode I in terms of the linear elastic fracture mechanics, the three models did not show significant differences in their fracture initiation predictions.

• Proceedings of the KSR Conference
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• 2000.05a
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• pp.250-257
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• 2000

A Helmholtz free energy for a martensitic transformation of a single crystalline shape-memory alloy is obtained by a micromechanical approach, 24 variants of the single crystal are taken into account. In the framework of irreversible thermodynamics, a kinetic relation, a martensitic nucleation criterion and the reorientation criterion of martensitic variants are obtained. These relations are valid for a three-dimensional proportional or non-proportional mechanical loading or a combination of mechanical and thermal loading. Reorientation behavior of a single crystalline shape-memory alloy CuZnAl is simulated. When a tensile load is applied to a thermally-induced martensite, 24 self-accommodated martensitic variants are reoriented to the most favorable variant. In the following unloading, the most favorable variant in the tensile load is reoriented to the most favorable variant in this loading condition.

• Journal of the Korea Concrete Institute
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• v.15 no.3
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• pp.433-442
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• 2003

This paper presents a hypoplastic model for three-dimensional analysis of concrete structures under monotonic, cyclic, proportional and non-proportional loading. The constitutive model is based on the concept of equivalent uniaxial strains that allows the assumed orthotropic model to be described via three equivalent uniaxial stress-strain curves. The characteristics of these curves are obtained from the ultimate strength surface in the principal stress space based on the Willam-Warnke curve. A cap model is added to consider loading along or near the hydrostatic axis. The equivalent uniaxial curve is based on the Popovics and Saenz models. The post-peak behavior is adjusted to account for the effects of confinement and to describe the change in response from brittle to ductile as the lateral confinement increases. Correlation studies with available experimental tests are presented to demonstrate the model performance. Tests with monotonic loading on specimens under constant lateral confinement are considered first, followed by biaxial and triaxial tests with cyclic loads. The triaxial test example considers non-proportional loading.