• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.20 no.1
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• pp.30-36
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• 1984

It is well known that the application of linear elastic fracture mechanics is inadequate to solve the large deformation fracture failures which occurr in ductile manner because of the large scale yielding due to the severe stress concentration in the region adjacent to the crack tip. The authors have been evolved a fracture model, the crack plane equilibrium model, for this kinds of elastic-plastic fracture problems in the previous report. In this report, the crack plane equilibrium model was compared with the Irwin's plastic zone corrected linear elastic fracture mechanics through theoretical comparisons and experimental results to examine the validity of the crack plane equilibrium model as an available tool for nonlinear fracture analysis. Through this study, the main results were reached as follows; Irwin's plastic zone corrected linear elastic fracture mechanics could be applicable only for small scale yielding problems as expected while the crack plane equilibrium model valid as a fracture model for large deformation fracture failure. However, the followings should be considered for the more precise evaluations of CPE model; 1) It is necessary to test more specimens which contain small cracks in the range of 2a/W<0.1. 2) It is important to detect the crack initiation point during the fracture test for determining an accurate fracture load. 3) Effects of specimen thickness in the fracture process zone should be examined.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.6
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• pp.792-801
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• 2000

The problem of phase change from liquid to solid in the inviscid plane-stagnation flow is theoretically investigated. The solution at the initial stage of freezing is obtained by expanding it in powers of time, and the final equilibrium state is determined from the steady-state governing equations. The transient solution is dependent on the three dimensionless parameters, but the equilibrium state is determined by one parameter of (temperature ratio/conductivity ratio). The effect of the fluid flow on the growth rate of the solid in the pure conduction problem can be clearly seen from the solution of the initial stage and the final equilibrium state. The characteristics of the transient heat transfer at the surface of the solid and the liquid side of the solid-liquid interface for all the dimensionless parameters are elucidated.

• Steel and Composite Structures
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• v.30 no.6
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.

• Steel and Composite Structures
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• v.24 no.5
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.6
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• pp.843-849
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• 2010

This paper presents definition of symmetry of a ship section where three symmetries are proposed: material, geometric, and load symmetries. Precise terminologies of centroid, moment plane, and neutral axis plane are also defined. It is suggested that force vector equilibrium as well as force equilibrium are necessary condition to determine new position of neutral axis due to translational and rotational mobility. It is also stated that new reference datum of ENMP(elastic neutral moment plane), PNMP(fully plastic moment plane), ENAP(elastic neutral axis plane), and INAP(inelastic neutral moment plane) are required to define asymmetric section properties such as second moment of area, elastic section modulus, yield moment, fully plastic moment, and ultimate moment. Since collision-induced damage and flooding-induced biaxial bending moment produce typical asymmetry of section, the section properties are calculated for a typical VLCC. Geometry asymmetry is determined from ABS and DNV rules and two moment planes of 0/30 degs are assumed for load asymmetry. It is proved that the property reduction ratios directly calculated from second moment of area are usually larger than area reduction ratio. Reduction ratio of ultimate moment capacity shows almost linearly proportional to area reduction ratio. Mobility of elastic and inelastic neutral axis planes is visually provided.

• Proceedings of the ESK Conference
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• 1992.10a
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• pp.46-53
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• 1992

Finger movements in the sagittal plane mainly consist of flexion and extension about the metacarpophalangeal(MCP) and proximal interphalangeal(PIP) joints. A kinematic finger model was developed with the assumption of constant tendon moment arms. Equations of static equilibrium were derived for the finger model using the principle of virtual work. Equations of static equilibrium for the finger model were indeterminate since only three equations were available for five unknown variables(forces). The number of variables was reduced based on information on muscular activities in finger movements. Then the amounts of forces which muscles exerted to maintain static equilibrium against external loads were computed from the equilibrium equations. The muscular forces were expressed mathematically as functions of finger positions, tendon moment arms, lengths of phalanges, and the magnitude and direction of external load. The external finger strength were computed using the equations of muscular forces and anatomical data. Experiments were performed to measure finger strengths. Measurements were taken in combinations of four finger positions and four directions of force exertions. Validation of the finger models and of procedure to estimate finger strengths was done by comparing the results of computations and experiments. Significang differences were found between the predicted and measured finger strengths. However, the trends of finger strengths with respect to finger positions were similar inboth the predicted and measured. These findings indicate that the finger model and the procedure to predict finger strengths were correctly developed.

• Geomechanics and Engineering
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• v.22 no.6
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• pp.553-564
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• 2020

In this study, a simple numerical approach for a circular tunnel opening in strain-softening surrounding rock is proposed considering out-of-plane stress and seepage force based on Biot's effective stress principle. The plastic region of strain-softening surrounding rock was divided into a finite number of concentric rings, of which the thickness was determined by the internal equilibrium equation. The increments of stress and strain for each ring, starting from the elastic-plastic interface, were obtained by successively incorporating the effect of out-of-plane stress and Biot's effective stress principle. The initial value of the outmost ring was determined using equilibrium and compatibility equations. Based on the Mohr-Coulomb (M-C) and generalized Hoek-Brown (H-B) failure criteria, the stress-increment approach for solving stress, displacement, and plastic radius was improved by considering the effects of Biot's effective stress principle and the nonlinear degradation of strength and deformation parameters in plastic zone incorporating out-of-plane stress. The correctness of the proposed approach is validated by numerical simulation.

• The Journal of Engineering Geology
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• v.10 no.3
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• pp.205-216
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• 2000

An unstable natural slope located at Icheon-Ri, Dasa-Eup, Dalseong-Kun which has been severely cracked during heavy rain fall in September, 1998, was investigated and analysed for remedial measures. Various geological data were obtained by performing a surface geological survey, a ground penetrating radar(GPR) exploration, four geotechnical borings with field and laboratory tests, and the precipitation records were also reviewed. Based on the these data, the probable sliding plane was determined as a bedding plane with dip angle of 20 to 25 degrees between sandstone and shale layers at depth of 6 to 8 meters. By performing back analyses with the limit equilibrium method, the friction angle and cohesion of the sliding plane were determined as 18$^{\circ}$ and 0, respectively. Based on these results, a series of stability analyses such as stereo-graphic projection method, limiting equilibrium method and numerical method were carried out. The remedial measures for the unstable slope were selected based on the results of the limit equilibrium analyses by considering various conditions expected at the site. Ground grouting or anchoring method with proper surface drainage systems could be employed for the long term safety of the slope.

• Proceedings of the Korean Geotechical Society Conference
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• 2002.03a
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• pp.643-650
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• 2002

The large planar failure has occurred in a rock cut slope of highway construction site in Boeun. This area is considered as unstable since the discontinuities whose orientations are similar to the orientation of the failure plane, are observed in many areas. Therefore, several analysis techniques such as SMR, stereographic analysis, limit equilibrium, numerical analysis, which are commonly used in rock slope stability analysis, are adopted in this area. In order to analyze the stress redistribution and nonlinear displacement caused by cut, which are not obtained in limit equilibrium method, the UDEC and shear strength reduction technique were used in this study Then the factors of safety evaluated by shear strength reduction technique and limit equilibrium were compared. In addition, the factor of safety under fully saturated slope condition was calculated and subsequently, the effect of the reinforcement was evaluated.