• Structural Engineering and Mechanics
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• v.24 no.2
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• pp.227-245
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• 2006

The performance of a three dimensional non-linear finite element model for hyperelastic material considering the effect of compressibility is studied by analyzing rubber blocks under different modes of deformation. It includes simple tension, pure shear, simple shear, pure bending and a mixed mode combining compression, shear and bending. The compressibility of the hyperelastic material is represented in the strain energy function. The nonlinear formulation is based on updated Lagrangian (UL) technique. The displacement model is implemented with a twenty node brick element having u, ${\nu}$ and w as the degrees of freedom at each node. The results obtained by the present numerical model are compared with the analytical solutions available for the basic modes of deformation where the agreement between the results is found to be satisfactory. In this context some new results are generated for future references since the number of available results on the present problem is not sufficient enough.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.253-256
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• 2011

본 논문에서는 표면효과와 비선형 탄성효과를 고려한 FCC 나노박막의 순차적 멀티스케일 해석 모델을 제시한다. 표면에서의 구성방정식은 표면응력과 표면탄성계수를 이용하여 선형으로 표시되며, 표면효과를 나타내기 위한 표면물성들은 EAM 포텐셜을 이용한 원자적 계산 방법으로 계산된다. 두께가 얇은 나노박막은 표면응력으로 인하여 면내 방향으로 수축 또는 인장의 변형이 발생하게 된다. 나노박막의 평형상태에서의 변형율은 두께가 얇은 박막의 경우 재료가 선형 탄성 영역을 벗어나는 값을 가지는 경우가 많으므로 나노박막의 해석시 벌크 영역의 비선형 탄성 효과를 고려해야 한다. 이러한 비선형 탄성 효과를 고려하기 위해 본 연구에서는 FCC 구조를 가지는 금속의 비선형 탄성 모델을 제시하고, EAM 포텐셜로 계산된 응력과 탄성 계수를 이용하여 매칭 기법을 통하여 비선형 탄성 모델의 계수들을 결정한다. 또한 Cauchy-Born Rule 모델과 분자동역학 전산모사를 통하여 본 연구에서 제안된 비선형 탄성 모델에 대한 검증을 수행한다.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.1107-1124
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• 2016

Consistent finite strain Plate constitutive relations are derived based on a hyperelastic formulation for an isotropic material. Plate equilibrium equations under finite strain are derived following a static kinematic approach. Three Euler angles and four shear angles, based on Timoshenko beam theory, represent the kinematics of the deformations in the plate cross section. The Green deformation tensor has been expressed in term of a deformation tensor associated with the deformation and stretches of an embedded plate element. Buckling formulation includes the in-plane axial deformation prior to buckling and transverse as well as in-plane shear deformations. Numerical results for a simply supported thick plate under uni-axial compression force are presented.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1076-1086
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• 2003

The effect of a rubber mould on densification behavior of aluminum alloy powder was investigated under cold isostatic compaction. A thickness of rubber mould and friction effect between die wall and rubber mould were also studied. The hyperelastic constitutive equation based on the Ogden strain energy potential was employed to analyze deformation of rubber. The elastoplastic constitutive equation of Shima and Oyane and that of Lee on densification were implemented into a finite element program (ABAQUS) to simulate densification of metal powder for cold isostatic pressing and rubber isostatic pressing. Finite element results were compared with experimental data for densification and deformation of aluminum alloy powder under isostatic compaction.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.5
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• pp.584-590
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• 2012

The structural and functional disorder of a detrusor induces a bladder hypertrophy and degenerates a bladder muscle gradually by preventing normal urination. Thus, the thickness of the bladder wall has been increased in proportion to the degree of bladder outlet obstruction. In this study, the mechanical characteristics of the detrusor is analyzed for the physical properties and the thickness changes of the bladder muscle using a mathematically analytic method. In order to obtain the mechanical property of the bladder muscle, the tensile test of porcine bladder tissue is performed because its property is similar to that of human. The result of tensile test is applied to the mathematically model as Mooney Rivlin coefficients which represent the hyperelastic material. The model of the bladder is defined as the spherical shape with the initial volume of 50ml. The principal stress and strain according to the thickness are analyzed. Also, computer simulations for three types of the material property for the model of the bladder are performed based on the fact that the stiffness of the bladder is weakened as the progress of the benign prostatic hyperplasia. As a result, the principal stress is 341kPa at the initial thickness of 2.2mm, and is 249kPa at 6.5mm. As the bladder wall thickness increases, the principal stress decreases. The principal stress and strain decrease as the stiffness of the bladder decreases under the same thinkness.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.330-342
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• 1998

The effect of rubber mold on densification behavior of pure iron powder was investigated under cold isostatic pressing. The thickness effect of rubber mold was also studied. The elastoplastic constitutive equation based on the yield function of Shima and Oyane was implemented into the finite element program(ABAQUS) to predict compaction responses of metal powder under cold isostatic pressing. The hyperelastic constitutive equation based on Moony-Rivlin and Ogden strain energy potentials was also employed to analyze deformation of rubber mold. The coefficients of the strain energy potentials were obtained from tension and volumetric compression data of rubber. Finite element results were compared with experimental data for densification of pure iron powder under cold isostatic pressing.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.425-430
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• 2003

The material properties of rubber was determined by the experiments of uniaxial tension, uniaxial compression, planer tension, equi-biaxial tension and volumetric compression. In compression test, it is difficult to obtain the pure state of compression stress and strain due to friction force between the specimen and compression platen. In this study, the stress and strain data from the equi-biaxial tension test were converted to compression stress and strain and compared to a perfect state of simple compression data when friction was zero. The compression test device with the tapered platen was proposed to overcome the effect of friction. It was turned out that the relationship of the stress and strain using the tapered platen was in close agreement with the pure compressive state.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.45 no.9
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• pp.784-793
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• 2017

A two-axis gimbal-type X-band antenna mounted on an observation satellite can efficiently transmit high-capacity image data to a ground station regardless of both the satellite position and the orbital motion. However, this X-band antenna induces unnecessary micro-jitter which can degrade the image quality of the high-resolution observation satellite. Therefore, to achieve the high-resolution image quality from the observation satellite, micro-jitters have been required to be isolated. In this study, to resolve aforementioned drawback, we proposed blade gear using a shape memory alloy (SMA) applied to azimuth stage of X-band antenna. To investigate the rotational basic characteristics of the proposed SMA blade gear, we performed rotational static loading test. Futhermore, to evaluate the cycle to failure of the gear, accelerated life test was conducted. The temperature test was conducted to confirm rotational basic characteristics at various temperature conditions. To verify the isolation performance for micro-jitter, we performed micro-jitter measurement test.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.6
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• pp.848-859
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• 2004

Mechanical testing methods to determine the material constants for large deformation nonlinear finite element analysis were demonstrated for natural rubber. Uniaxial tension, uniaxial compression, equi-biaxial tension and pure shear tests of rubber specimens are performed to achieve the stress-strain curves. The stress-strain curves are obtained after between 5 and 10 cycles to consider the Mullins effect. Mooney and Ogden strain-energy density functions, which are typical form of the hyperelastic material, are determined and compared with each other. The material constants using only uniaxial tension data are about 20% higher than those obtained by any other test data set. The experimental equations of shear elastic modulus on the hardness and maximum strain are presented using multiple regression method. Large deformation finite element analysis of automotive transmission mount using different material constants is performed and the load-displacement curves are compared with experiments. The selection of material constant in large deformation finite element analysis depend on the strain level of component in service.