• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.2
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• pp.149-156
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• 2011

In this paper, a methodology is proposed to improve the stress prediction of plates via Saint Venant's principle. According to Saint Venant's principle, the stress resultants can be used to describe linear elastic problems. Many engineering problems have been analyzed by Euler-Bernoulli beam(E-B) and/or Kirchhoff-Love(K-L) plate models. These models are asymptotically correct, and therefore, their accuracy is mathematically guaranteed for thin plates or slender beams. By post-processing their solutions, one can improve the stresses and displacements via Saint Venant's principle. The improved in-plane and out-of-plane displacements are obtained by adding the perturbed deflection and integrating the transverse shear strains. The perturbed deflection is calculated by applying the equivalence of stress resultants before and after post-processing(or Saint Venant's principle). Accuracy and efficiency of the proposed methodology is verified by comparing the solutions obtained with the elasticity solutions for orthotropic beams.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.4
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• pp.381-387
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• 2016

In this paper, the methodology applied to the improvement of stress analyses is extended to free vibration and buckling analyses. The essence of the methodology is the Saint-Venant's principle that is applicable to beam and plate models. The principle allows one to dimensionally reduce three-dimensional elasticity problems. Thus the methodology can be employed to vibration and buckling as well as stress analysis. First, the principle is briefly revisited, and then the formations of classical beam theories are presented. To improve the predictions, the perturbed terms (unknowns) are introduced together with the warping functions that are calculated by stress equilibrium equations. The unknowns are then calculated by applying the equivalence of stress resultants (i.e., Saint-Venant's principle). As numerical examples, cantilever and simply supported beams are analytically solved. The results obtained are compared with those of the classical beam theories. It is shown that the methodology can be used to improve the predictions without introducing shear correction factors.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.4
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• pp.451-455
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• 2012

Asymptotic analysis is a powerful tool for the mathematically rigorous design and analysis of anisotropic beam structures. However, it has a limitation in that the asymptotic approach requires asymptotically correct boundary conditions for higher-order solutions, which are often needed for beams weak in shear. A method utilizing Saint-Venant's principle was proposed in a previous work to improve the stress state of isotropic beams and plates. In this paper, such a method is generalized for anisotropic beams, so that one does not need to consider the asymptotically correct boundary conditions for higher-order solutions. Consequently, solving the recursive system equations is not necessary, which makes the method very efficient in terms of accuracy and computational effort.

• Structural Engineering and Mechanics
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• v.84 no.3
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• pp.423-435
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• 2022

In this article, we present torsion-bending analysis of a composite FGM beam with an open section, according to the advanced and refined theory of 1D / 3D beams based on the 3D Saint-Venant's solution and taking into account the edge effects. The (initially one-dimensional) model contains a set of three-dimensional (3D) displacement modes of the cross section, reflecting its 3D mechanical behaviour. The modes are taken into account depending on the mechanical characteristics and the geometrical form of the cross-section of the composite FGM beam. The model considered is implemented on the CSB (Cross-Section and Beam Analysis) software package. It is based on the RBT/SV theory (Refined Beam Theory on Saint-Venant principle) of FGM beams. The mechanical and physical characteristics of the FGM beam continuously vary, depending on a power-law distribution, across the thickness of the beam. We compare the numerical results obtained by the three-beam theories, namely: The Classical Beam Theory of Saint-Venant (Classical Beam Theory CBT), the theory of refined beams (Refined Beam Theory RBT), and the theory of refined beams, using the higher (high) modes of distortion of the cross-section (Refined Beam Theory using distorted modes RBTd). The results obtained confirm a clear difference between those obtained by the three models at the level of the supports. Further from the support, the results of RBT and RBTd are of the same order, whereas those of CBT remains far from those of higher-order theories. The 3D stresses, strains and displacements, obtained by the present study, reflect the 3D behaviour of FGM beams well, despite the initially 1D nature of the problem. A validation example also shows a very good agreement of the proposed models with other models (classical or higher-order beam theory) and Carrera Unified Formulation 1D-beam model with Lagrange Expansion functions (CUF-LE).

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1153-1170
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• 2011

In this paper, spatial decay estimates for the time dependent compressible viscous isentropic flow in a semi-infinite three dimensional pipe are derived. An upper bound for the total energy in terms of the initial boundary data is obtained as well. The results established in this paper may be viewed as a version of Saint-Venant's principle in transient compressible Navier-Stokes flow.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.3
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• pp.229-235
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• 2016

In this paper, a methodology, which is able to predict the thermal stresses accurately yet efficiently, is presented for beam structures via Saint-Venant's principle. In general, higher-order beam theories have been known to be effective for the prediction of thermal stresses. In contrast to this, we propose the method to predict the thermal stresses of beam structures by post-processing the classical beam theory via Saint-Venant's principle. The approach includes an out-of-plane warping displacement to account for the through-the-thickness thermal deformation. With this, one can accurately recover the thermal stresses as compared to the elasticity solutions. In fact, they are identical for the beams made of isotropic materials. The effect of out-of-plane warping is also investigated, it turns out that the effect is negligible in mechanical stress analysis but not in thermal stress analysis.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1999.06a
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• pp.20-29
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• 1999

The stress field in the body by tangential loading of a rectangular patch on a semi-infinite solid has been solved analytically using Boussinesque's potential function. Its validity was proved by saint-venant's principle in remote region of the and in the vicinity of the surface with superposition of point loads.

• KSTLE International Journal
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• v.2 no.1
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• pp.29-34
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• 2001

The stress field in a body caused by the tangential loading of a rectangular patch on a semi-infinite solid has been solved analytically using a potential function. The validity of the results of this study was preyed by Saint-Venant's principle in the remote region and by the superposition of point loads in the vicinity of the surface.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.651-662
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• 2014

The main goal of this study is to extend the domain of influence result to cover the micropolar thermoelastic diffusion. So, we prove that for a finite time t>0 the displacement field $u_i$, the microrotation vector ${\varphi}_i$, the temperature ${\theta}$ and the chemical potential P generate no disturbance outside a bounded domain $B_t$.

• Tribology and Lubricants
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• v.18 no.3
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• pp.194-203
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• 2002

This paper is the first step fur thermo-mechanical stress analyses of part with coated layer under contact load. A lot of coated material is applied in many structures to endure severe situation, like thermal stresses, high temperature gradients, irradiation, impacts by microscopic meteorites, and so on. In this part we are going to apply the FEM to analyze space parts with a coated layer subjected to a contact load thermo-mechanically. Coating layer is very thin in comparision with the structure, therefore it should take more times and behaviors to analyze whole model. In these reason we develop the FEM method of analyzing part with coated layer under contact load using partial model. Steady state temperature distribution of the part is obtained first, and then we apply quasi-static external load on the part. To obtain the final stage of solution, we compute the total solution, and by subtracting the thermal strain from the total ones we get the mechanical strains to compute stresses of the parts. In using the FEM, one has to discretize the model into many sub-domain, finite elements. The method is consisited of two steps. First step is to analyze the whole model with rather coarse meshes. Second step we cut a small region near the loading point, and analyze with very fine meshes. This method is allowable by the Saint-Venant's principle. And then, we finally shall check the therma1 load on the stresses of the space part with coating layer with or without substrate cracks. Then, we predict the actual behaviors of the part used in space.