• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.215-219
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• 2003

Buckling and post-buckling Analysis of Ludwick type and modified Ludwick type elastic materials was carried out. Because the constitutive equation, or stress-strain relationship is different from that of linear elastic one, a new governing equation was derived and solved by $4^{th}$ order Runge-Kutta method. Considered as a special case of combined loading, the buckling under both point and distributed load was selected and researched. The final solution takes distinguished behavior whether the constitutive relation is chosen to be modified or non-modified Ludwick type as well as linear or non-linear. We also derived strain energy function for non-linear elastic constitutive relationship. By doing so, we calculated the criterion function which estimates the stability of the equilibrium solutions and determines critical buckling load for non-linear cases. We applied this theory to the constitutive relationship of fabric, which also is the non-linear equation between the applied moment and curvature. This results has both technical and mathematical significance.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.61-72
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• 2012

The paper is on contact analysis of a spherical ball with a deformable flat, considering the effect of tangent modulus on the contact parameters of a non-adhesive frictionless elastic-plastic contact. The contact analysis of this model has been carried out using analysis software Ansys and Abaqus. The contact parameters such as area of contact between two consecutive steps, volume of bulged material are evaluated from the formulated equations. The effect of the tangent modulus is considered for determining these parameters. The tangent modulus are accounted between 0.1E and 0.5E of materials E/Y value greater than 500 and less than 1750. Result shows that upto an optimal tangent modulus values the elastic core push up to the free surface in the flat. The simulation is also carried out in Abaqus and result provide evidence for the volume of bulged material in the contact region move up and flow into the free surface of the flat from the contact edge between the ball and flat. The strain energy of the whole model is varied between 20 to 40 percentage of the stipulated time for analysis.

• Journal of the Korea Society of Computer and Information
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• v.28 no.9
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• pp.73-79
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• 2023

This paper describes a level of detail (LOD) based bending spring structure and damping technique that can reliably represent strain-based dynamics (SBD) on a triangular mesh. SBD models elastic energy using strain instead of energy based on the edge length of a triangular mesh. However, when a large external force occurs, the process of calculating the elastic energy based on edges results in a degenerate triangle, which stretches in the wrong direction because it calculates an unstable strain. In this paper, we introduce an LOD-based bending spring generation and energy calculation method that can efficiently handle this problem. As a result, the technique proposed in this paper can reliably and efficiently handle SBD based on bending springs, which can provide a stable representation of cloth simulation.

• Steel and Composite Structures
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• v.45 no.3
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• pp.437-454
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• 2022

Elliptic-braced simple resisting frame as a new lateral bracing system installed in the middle bay of frame in building facades has been recently introduced. This system not only creates a problem for opening space from the architectural viewpoint but also improves the structural behavior. Despite the researches on the seismic performance of lateral bracing systems, there are few studies performed on the effect of the stiffness parameters on the elastic story drift and calculation of period in simple braced steel frames. To overcome this shortcoming, in this paper, for the first time, an analytical solution is presented for calculating elastic lateral stiffness in a simple steel frame equipped with elliptic brace subjected to lateral load. In addition, for the first time, in this study, a precise formulation has been developed to evaluate the elastic stiffness variation in a steel frame equipped with a two-dimensional single-story single-span elliptic brace using strain energy and Castigliano's theorem. Thus, all the effective factors, including axial and shear loads as well as bending moments of elliptic brace could be considered. At the end of the analysis, the lateral stiffness can be calculated by an improved and innovative relation through the energy method based on the geometrical properties of the employed sections and specification of the used material. Also, an equivalent element of an elliptic brace was presented for the ease of modeling and use in linear designs. Application of the proposed relation have been verified through a variety of examples in OpenSees software. Based on the results, the error percentage between the elastic stiffness derived from the developed equations and the numerical analyses of finite element models was very low and negligible.

• Elastomers and Composites
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• v.42 no.3
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• pp.168-176
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• 2007

When the rubber vulcanizates reinforced with carbon black or silica are subjected to cyclic loading from its virgin state, the stress required on reloading is less than that on the initial loading. This stress softening phenomenon is referred to as the Mullins effect. The strain energy function of rubber vulcanizates was investigated using theory of pseudo-elasticity incorporated damage parameter that Ogden and Roxburgh have proposed to describe the damage-induced stress softening effect in rubber-like solids. The quasi-static cyclic loading test was performed using the NR-SBR vulcanizates reinforced with carbon black, and then the effect of a damage parameter to stress-strain curve in reloading and subsequent reloading paths was studied. The strain energy function of the rubber vulcanizates with a different filler content was also evaluated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1357-1365
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• 2009

In this study, we enhance the numerical approach of Lee et al.$^{(1)}$ to spherical indentation technique for property evaluation of hyper-elastic rubber. We first determine the friction coefficient between rubber and indenter in a practical viewpoint. We perform finite element numerical simulations for deeper indentation depth. An optimal data acquisition spot is selected, which features sufficiently large strain energy density and negligible frictional effect. We then improve two normalized functions mapping an indentation load vs. deflection curve into a strain energy density vs. first invariant curve, the latter of which in turn gives the Yeoh-model constants. The enhanced spherical indentation approach produces the rubber material properties with an average error of less than 3%.

• Advances in aircraft and spacecraft science
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• v.2 no.1
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• pp.57-76
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• 2015

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

• Magazine of the Korea Concrete Institute
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• v.4 no.1
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• pp.81-87
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• 1992

In this thesis, the fatigue tests were performed on a series of SFRC(steel fiber reinforced concrete) to investigate the fatigue behavior of SFRC varying with the steel fiber contents and the steel fiber aspect ratios. The three point loading system is used in the fatigue tests. In tl1ese tests, relations between the repeated loading cycles and the mid-span deflections, number of repeated loadmg cycles when specimen was fractured were observed. On this basis, the mid-span deflections, the elastic strain energy and inelastic strain energy of SFRC were studied. A S - N curve \vas drawn to present the fatigue strength of SFRC beam. From che test results, by increasing the steel fiber content the energy lost on the permanent deformation decreases and the energy spent on crack growth increases. But in case of SFRC with the same steel fiber content the higher the steel fiber aspect ratio is, the less the elastic strain energy is. According to S - N curve drawn by the regression analysis on the fatugue test results, the fatigue strength with 2,000,000 repeated loading cycles in SFRC with the steel fiber content is 1.0% shows about 70% on the first crack static flexural strength.

• Structural Engineering and Mechanics
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• v.10 no.6
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• pp.589-601
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• 2000

A simplified analysis procedure utilizing the strut-tie modeling technique is developed to take a close look into the post-elastic deformation capacity of beam-column connections in ductile reinforced concrete frame structures. Particular emphasis is given to the effect of concrete strength decay and quantity and arrangement of joint shear steel. For this a fan-shaped crack pattern is postulated through the joints. A series of hypothetical rigid nodes are assumed through which struts, ties and boundaries are connected to each other. The equilibrium consideration enables all forces in struts, ties and boundaries to be related through the nodes. The boundary condition surrounding the joints is obtained by the mechanism analysis of the frame structures. In order to avoid a complexity from the indeterminacy of the truss model, it is assumed that all shear steel yielded. It is noted from the previous research that the capacity of struts is limited by the principal tensile strain of the joint panel for which the strain of the transverse diagonal is taken. The post-yield deformation of joint steel is taken to be the only source of the joint shear deformation beyond the elastic range. Both deformations are related by the energy consideration. The analysis is then performed by iteration for a given shear strain. The analysis results indicate that concentrating most of the joint steel near the center of the joint along with higher strength concrete may enhance the post-elastic joint performance.

• Geomechanics and Engineering
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• v.24 no.2
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• pp.179-191
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• 2021

In this study, the strength and failure mechanism of red sandstones with combined defects were investigated by uniaxial compression tests on red sandstones with different crack angles using two-dimensional particle flow code numerical software, and their mechanical parameters and failure process were studied and analyzed. The results showed that the mechanical characteristics such as peak strength, peak strain, and elastic modulus of the samples with prefabricated combined defects were significantly inferior than those of the intact samples. With increasing crack angle from 15° to 60°, the weakening area of cracks increased, elastic modulus, peak strength, and peak strain gradually reduced, the total number of cracks increased, and more strain energy was released. In addition, the samples underwent initial brittle failure to plastic failure stage, and the failure form was more significant, leading to peeling phenomenon. However, with increasing crack angle from 75° to 90°, the crack-hole combination shared the stress concentration at the tip of the crack-crack combination, resulted in a gradual increase in elastic modulus, peak strain and peak strength, but a decrease in the number of total cracks, the release of strain energy reduced, the plastic failure state weakened, and the spalling phenomenon slowed down. On this basis, the samples with 30° and 45° crack-crack combination were selected for further experimental investigation. Through comparative analysis between the experimental and simulation results, the failure strength and final failure mode with cracks propagation of samples were found to be relatively similar.