• Computers and Concrete
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• v.25 no.4
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• pp.311-325
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• 2020

In this research work, the hygrothermal and mechanical buckling responses of simply supported FG sandwich plate seated on Winkler-Pasternak elastic foundation are investigated using a novel shear deformation theory. The current model take into consideration the shear deformation effects and ensures the zero shear stresses on the free surfaces of the FG-sandwich plate without requiring the correction factors "Ks". The material properties of the faces sheets of the FG-sandwich plate are assumed varies as power law function "P-FGM" and the core is isotropic (purely ceramic). From the virtual work principle, the stability equations are deduced and resolved via Navier model. The hygrothermal effects are considered varies as a nonlinear, linear and uniform distribution across the thickness of the FG-sandwich plate. To check and confirm the accuracy of the current model, a several comparison has been made with other models found in the literature. The effects the temperature, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio and the inhomogeneity parameter on the critical buckling of FG sandwich plates are also investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.1 s.232
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• pp.30-37
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• 2005

There is few research about contact problem for a rigid surface with an arbitrary shape in SPH. The variational equation based on the virtual work principle is derived and its solution is obtained by the penalty method. It is proposed a new method that can determine the parameters for a penetration and a penetration rate used in the penalty method. The reproducing condition is adopted to correct the deficiency of kernel on the boundary. In order to calculate a penetration of particles, after checking boundary particles for deformable body, boundary normal vectors were determined on the rigid surface. Numerical simulations for models which have rigid surface with an arbitrary shape were conducted to validate the proposed method in 2D Cartesian and cylindrical coordinate. The results of those analysis represent that the contact algorithm proposed in this study works properly.

• Structural Engineering and Mechanics
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• v.84 no.5
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• pp.685-697
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• 2022

Nanotechnology has become one of the interesting technique used in material science and engineering. However, it is low used in civil engineering structures. The purpose of the present study is to investigate the static behavior of concrete plates reinforced with silica-nanoparticles. Due to agglomeration effect of silica-nanoparticles in concrete, Voigt's model is used for obtaining the equivalent nano-composite properties. Furthermore, the plate is simulated mathematically with higher order shear deformation theory. For a large use of this study, the concrete plate is assumed resting on a Pasternak elastic foundation, including a shear layer, and Winkler spring interconnected with a Kerr foundation. Using the principle of virtual work, the equilibrium equations are derived and by the mean of Hamilton's principle the energy equations are obtained. Finally, based on Navier's technique, closed-form solutions of simply supported plates have been obtained. Numerical results are presented considering the effect of different parameters such as volume percent of SiO₂ nanoparticles, mechanical loads, geometrical parameters, soil medium, on the static behavior of the plate. The most findings of this work indicate that the use of an optimum amount of SiO₂ nanoparticles on concretes increases better mechanical behavior. In addition, the elastic foundation has a significant impact on the bending of concrete slabs.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.379-385
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• 1983

Many papers have shown limit loads of v-notched tension specimens in plane stress by the elastic-plastic finite element method. But they are always higher than the theoretical maximum loads. The present approach tries to find the reasons and formulates correction factor applicable to any notch shape using virtual work principle with triangular elements. The corrected limit loads are in good agreement with theoretical upper bound solutions and they are little influenced by mesh size and specimen length, which make the computing time save.

• Journal of the korean Society of Automotive Engineers
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• v.12 no.2
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• pp.29-42
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• 1990

Three dimensional frame structures with such nonlinearities as large displacements, medium rotations, plastic hinges and local defects are efficiently analyzed by introducing the nonlinear rotational spring. Formulations are based on the incremental updated Lagrangian descriptions and the virtual work principle, Axial displacement and twisted angle in beam elements are interpolated linearly, while bending displacements are approximated by the Hermite polynomials. The modified are length method is used as a solution method. The moment-angle of rotation relationship obtained analytically or experimentally can be easily incorporated into the solution procedure. Several examples tested show that the present method can be used efficiently in analyzing nonlinear frame structures with plastic hinges or local defect.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.10
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• pp.193-202
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• 1998

본 논문에서는 비선형 고체역학 이론에 대하여 특히 시간에 무관한 변형을 하는 초탄성 및 탄소성고체물질의 비선형 변형이론에 대하여 철저한 분석을 수행하였다 특히 비선형 변형의 해석방범론에 대하여 특별한 관심을 가지고 분석하였다. 비선형 변형해석 방법론으로 널리 논의되고 있는 증분뉴튼랩슨 방법에 대하여 수정된 개념을 제시하여 비선형 변형 해석의 정 확성을 향상시켰다.

• Ocean Systems Engineering
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• v.10 no.1
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• pp.67-86
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• 2020

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

• Smart Structures and Systems
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• v.25 no.2
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• pp.197-218
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• 2020

In this work, thermomechanical flexural analysis of functionally graded material sandwich plates with P-FGM face sheets and E-FGM and symmetric S-FGM core is performed by employing a nth-order shear deformation theory. A novel type of S-FGM sandwich plates, namely, both P-FGM face sheets and a symmetric S-FGM hard core are considered. By employing only four unknown variables, the governing equations are obtained based on the principle of virtual work and then Navier method is used to solve these equations. Analytical solutions are deduced to compute the stresses and deflections of simply supported S-FGM sandwich plates. The effects of volume fraction variation, geometrical parameters and thermal load on thermomechanical flexural behavior of the symmetric FGM sandwich plates are investigated.

• Steel and Composite Structures
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• v.32 no.5
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• pp.611-632
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• 2019

In this work, a four-variable refined plate model is applied to study the thermomechanical bending of two kinds of functionally graded material (FGM) sandwich plates. The sandwich core of one kind is isotropic with the FGM face sheets whereas in the second kind, the sandwich core is FGM with the isotropic and homogeneous face sheets. By considering only four unknown variables, the governing equations are written based on the principle of virtual work and then Navier method is employed to solve these equations. Deflections and stresses of two kinds of FGM sandwich structures are analyzed and discussed. The validity and efficiency of the proposed model is checked by comparing it with various available solutions in the literature. The effects of volume fraction distribution, geometric ratio and thermal load on thermomechanical bending properties of FGM sandwich plate are investigated in detail.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.725-734
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• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.