• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.1001-1004
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• 1987

In this study mathematical properties of variational solution and solution of the boundary integral equation of the linear elasticity problem are studied. It is first reviewed that a variational solution for the three-dimensional linear elasticity problem exists in the Sobolev space [ $H^{1}$(.OMEGA.)]$^{3}$ and, then, it is shown that a unique solution of the boundary integral equation is identical to the variational solution in [ $H^{1}$(.OMEGA.)]$^{3}$. To represent the boundary integral equation, the Green's formula in the Sobolev space is utilized on the solution domain excluding a ball, with small radius .rho., centered at the point where the point load is applied. By letting .rho. tend to zero, it is shown that, for the linear elasticity problem, boundary integral equation is valid for the variational solution. From this fact, one can obtain a numerical approximatiion of the variational solution by the boundary element method even when the classical solution does not exist.exist.

• Journal of the Korea Convergence Society
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• v.10 no.4
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• pp.139-145
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• 2019

This paper investigated the strength and stiffness of composite truss unit structures. The model used is a core-filled model combining the Kagome model and the cube truss model. The material properties used for the analysis are 304 stainless steel with elastic modulus of 193 GPa and yield stress of 215 MPa. The theoretical equation is derived from the relative elasticity relation of Gibson - Ashby ratio, the analysis was performed using Deform 3D, a commercial tool. In conclusion, the relative elasticity for this unit model correlates with 1.25 times the relative density and constant coefficient, elasticity is inversely proportional to pore size. The relative compressive strength has a correlation with relative density of 1.25 times. Proof of this is a real experiment, the derived theoretical relationship should further consider mechanical behavior such as bending and buckling. In the future, it is hoped that the research on the elasticity and the stress according to the structure of the three-dimensional space will be continued.

• Structural Engineering and Mechanics
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• v.6 no.5
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• pp.497-516
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• 1998

A relatively simple two-dimensional multilayered shell model is presented for predicting both global quantities and stress distributions across the thickness of multilayered thick shells, that is based on a third-order zig-zag approach. As for any zig-zag model, the layerwise kinematics is accounted for, with the stress continuity conditions at interfaces met a priori. Moreover, the shell model satisfies the zero transverse shear stress conditions at the upper and lower free surfaces of the shell, irrespective of the lay-up. By changing the parameters in the displacement model, some higher order shell models are obtained as particular cases. Although it potentially has a wide range of validity, application is limited to cylindrical shell panels in cylindrical bending, a lot of solutions of two-dimensional models based on rather different simplyfying assumptions and the exact three-dimensional elasticity solution being available for comparisons for this benchmark problem. The numerical investigation performed by the present shell model and by the shell models derived from it illustrates the effects of transverse shear modeling and the range of applicability of the simplyfying assumptions introduced. The implications of retaining only selected terms depending on the radius-to-thickness ratio are focused by comparing the present solutions to the exact one and to other two-dimensional solutions in literature based on rather different simplyfying assumptions.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.113-128
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• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

• Coupled systems mechanics
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• v.2 no.4
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• pp.389-410
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• 2013

Three-dimensional Lagrangian fluid finite element is applied to seismic response analysis of an oil storage tank with a floating roof. The fluid element utilized in the present analysis is formulated based on the displacement finite element method considering only volumetric elasticity and its element stiffness matrix is derived by using one-point integration method in order to avoid volumetric locking. The method usually adds a rotational penalty stiffness to satisfy the irrotational condition for fluid motion and modifies element mass matrices through the projected mass method to suppress spurious hourglass-mode appeared in compensation for one-point integration. In the fluid element utilized in the present paper, a small hourglass stiffness is employed. The fluid and structure domains for the objective oil storage tank are modeled by eight-node solid elements and four-node shell elements, respectively, and the transient response of the floating roof structure or the free surface are evaluated by implicit direct time integration method. The results of seismic response analyses are compared with those by other method and the validation of the present analysis using three-dimensional Lagrangian fluid finite elements is shown.

• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.260-267
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• 2002

For an elastically suspended rigid body with the planes of symmetry in a three dimensional space, a novel analysis fur the vibration modes is presented. From the decompositions of the stiffness and inertia matrices, the conditions for the existence of pure translation and pure couple modes are analyzed for an elastically suspended rigid body with the planes of symmetry. From this analysis, it can be showed that how the structure of stiffness and inertia must be related in order to produce the pure translation and pure couple modes when an elastically suspended rigid body has one, two, or three planes of symmetry.

• Transactions of Materials Processing
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• v.27 no.6
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• pp.363-369
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• 2018

This study measured the mechanical properties of an ash wood under various temperature and humidity conditions and a finite element model was developed to predict the behavior of the wood. A humidity-controlled chamber was developed and used for measuring the dimensional changes of woods under various humidity conditions. The thermal expansion coefficient and the elastic stiffness constants were measured by using a thermal chamber and the three-point bending test along the three principal axes of the wood. A constitutive model was proposed to describe the moisture content and temperature dependent behavior of wood. The proposed model was validated for the warping test of a wood plate. The warping of the plate was calculated using the finite element method. The calculated amount of warping was in consistence with the measurements.

• Transactions of Materials Processing
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• v.20 no.2
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• pp.132-139
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• 2011

Three dimensional simulations were performed for the deformation of a slab in a roller hearth type slab reheating furnace. The main objective of this study was to examine the deformation pattern of the slab due to the shadow effect, i.e., the temperature difference between the upper and lower slab surfaces, in particular, the variations of displacement and effective stress in the vertical direction. A commercially available FE code, ANSYS Workbench $12.1^{TM}$, was used in a fully coupled thermo-elasticity analysis. Several cases with different slab surface temperatures were selected for the simulations. For the sake of simplicity, the temperature environment inside the furnace was assumed to be homogeneous for the upper and lower faces of the slab. Two cases of with different slab width were selected as model geometry. The deformation patterns were computed and explained in terms of periodicity and symmetry. The results indicated that the shadow effect leads to a significant displacement in the vertical direction and, thereby, is one of the main reasons for the separation of the slab and its supports. These simulations also predicted that the deformation is more severe along the transverse direction than along the longitudinal direction.

• Geomechanics and Engineering
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• v.11 no.5
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• pp.671-690
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• 2016

This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.