• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• Structural Engineering and Mechanics
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• v.13 no.1
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• pp.35-52
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• 2002

It was shown in the previous study (Lee and Bertero 1993) that incremental collapse can lead to the exhaustion of the plastic rotation capacity at critical regions in a structure when subjected to the number of load cycles and load intensities as expected during maximum credible earthquakes and that this type of collapse can be predicted using the shakedown analysis technique. In this study, a minimum-weight design methodology, which takes into account not only the prevention of this incremental collapse but also the requirements of the serviceability limit states, is proposed by using the shakedown analysis technique and a nonlinear programming algorithm (gradient projection method).

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.1
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• pp.60-66
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• 1999

This study is to develop design sensitivity analysis method based on continuum theory for the actual buckling load of vehicle passenger compartment with respect to sizing design variables. For nonlinear structural analysis, both geometric and material nonlinear effects are considered. The total Lagrangian formulation for incremental equilibrium analysis and one-point linear eigenvalue problem for buckling analysis are utilized. Numerical methods are presented to evaluate design sensitivity expressions, using structural analysis results from FEM code. Optical design of vehicle passenger compartment with buckling constraint solved using Gradient projection method.

• Journal of Welding and Joining
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• v.16 no.2
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• pp.111-121
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• 1998

It is well recognized that a excessive temperature gradient from the junction of head to skirt in axial direction in a hot pressure vessel can cause unpredicted high thermal stress at the junction and/or in axial direction of a skirt. this thermal stress resulting from axial thermal gradient may be a major cause of unsoundness of structural integrity. In case of cyclic operation of hot pressure vessels, the thermal stress becomes one of the primary design consideration because of the possibility of fracture as a result of cyclic thermal fatigue and progressively incremental plastic deformation. To perform thermal stress analysis of the junction and cylindrical skirt of a vessel, or, at least, to inspect quantitatively the magnitude and effect of thermal stress, the temperature profile of the vessel and skirt must be known. This paper demonstrated the temperature distribution and thermal stress analysis for the junction of skirt to head using F.E. analysis. Effect of air pocket in crotch space was quantitatively investigated to minimize the temperature gradient causing the thermal stress in axial direction. Effect of the skirt height on thermal stresses was also studied. Analysis results were compared with theoretical formulas to verify th applicability to the strength calculation in design field.

• Steel and Composite Structures
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• v.42 no.1
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• pp.23-32
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• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.9
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• pp.1041-1050
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• 2011

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.775-789
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• 2012

This paper focuses on post-buckling analysis of functionally graded Timoshenko beam subjected to thermal loading by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. As far as the authors know, there is no study on the post-buckling analysis of functionally graded Timoshenko beams under thermal loading considering full geometric non-linearity investigated by using finite element method. The convergence studies are made and the obtained results are compared with the published results. In the study, with the effects of material gradient property and thermal load, the relationships between deflections, end constraint forces, thermal buckling configuration and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• v.17 no.2
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• pp.245-266
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• 2004

Incremental launching method is one of the highly competitive techniques for construction of concrete bridges. It avoids costly and time consuming form work and centralizes all construction activities in a small casting yard, thus saving in cost and time against conventional bridge construction. From the quality point of view, it eliminates the uncertainty of monolithic behaviour by allowing high repetitiveness and industrial environment. But, from analysis and design point of view, the most characteristic aspect of incrementally launched bridges is that, it has to absorb the stresses associated with the temporary supports that are gradually taken on by the deck during its launch. So, it is necessary to analyse the structure for each step of launching which is a tedious and time consuming process. Effect of support settlements or temperature variation makes the problem more complex. By using transfer matrix method, this problem can be handled efficiently with minimal computational effort. This paper gives insight into method of analysis, formulation for optimization of the structural system, effect of support settlement and temperature gradient, during construction, on the stress state of incrementally launched bridges.

• Steel and Composite Structures
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• v.15 no.5
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• pp.481-505
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• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1632-1642
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• 1992

When a blind hole of small diameter is drilled in the field of residual stress, strain relieved around the hole is function of magnitude of stress, patterns of stress distribution and hole geometry of diameter and depth. Relieved strain coefficients can be calculated from FEM analysis of relieved strain and actual stress. These relieved strain coefficients make it possible to measure residual stress which vary along the depth in the subsurface of stressed material. In this study, the calibration tests of residual stress measurement are carried out by drilling a hole incrementally on the cantilever or on the tensile test bar. Residual stresses can be determined from measured strains around a shallow hole by application of power series method. For the sake of reliable measurement of residual stress, much efforts should be done to measure relieved strains and hole depth more accurately comparing with conventional procedures of gage subject to the external load. Otherwise linear equations converting strains into stresses may yield erratic residual stresses because of ill-conditions of linear equations. With accurate measurements of relieved strains, residual stress even if varying along the depth can be measured. It is also possible to measure residual stress in the thin film of material by drilling a shallow hole.