• Structural Engineering and Mechanics
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• v.88 no.2
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• pp.189-200
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• 2023

Silicate glass is usually a brittle and plate-like material, and it is difficult to measure the elastic modulus by the traditional method. This paper develops a test method for the glass elastic modulus based on the fundamental frequency of the cantilever beam with an elastic support and a free end. The method installs the beam-type specimen on a semi-rigid support to form an elastic support-free end beam. The analytic solution of the stiffness coefficients of the elastic support is developed by the fundamental frequency of the two specimens with known elastic modulus. Then, the glass elastic modulus is measured by the fundamental frequency of the specimens. The method significantly improves the measurement accuracy and is suitable for the elastic modulus with the beam-type specimen whether the glass is homogeneous or not. Several tests on the elastic modulus measurement are conducted to demonstrate the reliability and validity of the test method.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.49-56
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• 1992

This study was carried out to investigate the mechanical behaviour of the plate on a Winkler's foundation according to the soil-structures relative stiffness and the applicability of the conventional analysis method. For the above purpose, Winkler's constant of 4, 15, 25 and 100kg/$cm^2$/cm was considered and the plate thickness of 20, 30, 50, 100 and 150cm was adopted. Results obtained from the numerical examples are summarized as follow: 1. The effects of elastic foundation is considerable for plates with small flexural rigidity. 2. As the Winkler's constant increases, the bending moment in the plate becomes localized near the loading point. 3. The stresses evaluated by the conventional method not correct even for rigid ground such as rock. 4. If the relative stiffness of the plate is very large, for example the plate thickness is larger than 100cm, the conventional analysis method can be justified for the design purposes. 5. On assumption the flexural rigidity of the plate is infinite, the interaction of soil and plate can be ignored in design consideration. The numerical examples in this paper show that when the plate thickness is more than 100cm, the effects of elastic foundation almost disappear. In practical design, soil-plate interaction should be taken into account, because the 100cm-thickness of the plate will not be practical value in usual sites.

• Structural Engineering and Mechanics
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• v.41 no.5
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• pp.617-632
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• 2012

An isogeometric approach is presented for static analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection, as for description of the geometry. The governing equation based on Kirchhoff plate theory, is discretized using the standard Galerkin method. The essential boundary conditions are enforced by the Lagrange multiplier method. Several typical examples of thin plate and thin plate on elastic foundation are solved and compared with the theoretical solutions and other numerical methods. The numerical results show the robustness and efficiency of the proposed approach.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.133-140
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• 2003

The sandwich plate has been widely used as an efficient structural member because it has high strength-to-weight and high stiffness-to-weight ratios. To properly design the aluminum extrusion plate , it is necessary to analyze structural behaviors of the extrusions, however, the aluminum extrusions have been rarely studied until now. In the optimization process through numerous iterative calculations, finite element analysis of the sandwich plate with hollow core section requires a considerable amount of computation time and cost. In this paper, the aluminum extrusion plate with truss-core is transformed into an equivalent homogeneous orthotropic plate with appropriate elastic constants. The procedure to evaluate accurate equivalent elastic constants is also established. Using these elastic constants, simple theoretical formulas of the stresses and deflection are proposed in case of the simply-supported orthotropic thick plate under uniform pressure. Through the comparison with the results by commercial FEM code(ANSYS), it is verified that the proposed simpified formula has a good efficiency and accuracy.

• Steel and Composite Structures
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• v.18 no.2
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• pp.443-465
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• 2015

In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.

• International Journal of Safety
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• v.2 no.1
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• pp.39-44
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• 2003

The present study deals with an approximate integral equation approach to finite deflection of elastic plates with arbitrary plane form. An integral formulation leads to a system of boundary integral equations involving values of deflection, slope, bending moment and transverse shear force along the edge. The basic principles of the development of boundary element technique are reviewed. A computer program for solving for stresses and deflections in a isotropic, homogeneous, linear and elastic bending plate is developed. The fundamental solution of deflection and moment is employed in this program. The deflections and moments are assumed constant within the quadrilateral element. Numerical solutions for sample problems, obtained by the direct boundary element method, are presented and results are compared with known solutions.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.29 no.1
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• pp.39-55
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• 1993

Modal Analysis is the process of characterizing the dynamic properties of an elastic structure by identifying its modes of vibration. A mode of vibration is a global property of an elastic structure. That is, a mode has a specific natural frequency and damping factor which can be identified from response data at practically any point on a structure, and it has a characteristic mode shape which identifies the mode spatially over the entire structure. Modal testing is able to be performed on structural and mechanical structure in an effort to learn more about their elastic behavior. Once the dynamic properties of a structure are known its behavior can be predicted and therefore controlled or corrected. Resonant frequencies, damping factors and mode shape data can be used directly by a mechanical designer to pin point weak spots in a structure design, or this data can also be used to confirm or synthesize equations of motion for the elastic structure. These differential equations can be used to simulate structural response to know input forces and to examine the effects of pertubations in the distributed mass, stiffness and damping properties of the structure in more detail. In this paper the measurement of transfer functions in digital form, and the application of digital parameter identification techniques to identify modal parameters from the measured transfer function data are discussed. It is first shown that the transfer matrix, which is a complete dynamic model of an elastic plate structure can be written in terms of the structural modes of vibration. This special mathematical form allows one to identify the complete dynamics of the structure from a much reduced set of test data, and is the essence of the modal approach to identifying the dynamics of a structure. Finally, the application of transfer function models and identification techniques for obtaining modal parameters from the transfer function data are discussed. Characteristics on vibration response of elastic plate structure obtained from the dynamic analysis by Finite Element Method are compared with results of modal analysis.

• Structural Engineering and Mechanics
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• v.69 no.5
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• pp.511-525
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• 2019

This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate.

• Journal of the Korean Institute of Navigation
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• v.20 no.1
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• pp.47-58
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• 1996

The use of high tensile steel plates is increasing in the fabrication of ship and offshore structures. The main portion of ship structure is usually composed of stiffened plates. In these structures, plate buckling is one of the most important design criteria and buckling load may usually be obtained as an eigenvalue solution of the governing equations for the plate. To use the high tensile steel plate effectively, its thickness may become thin so that the occurrence of buckling is inevitable and design allowing plate buckling may be necessary. When the panel elastic buckling is allowed, it is necessary to get precise understandings about the post-buckling behaviour of thin plates. It is well known that a thin flat plate undergoes secondary buckling after initial buckling took place and the deflection of the initial buckling mode was developed. From this point of view, this paper discusses the post-buckling behaviour of thin plates under thrust including the secondary buckling phenomenon. Series of elastic large deflection analyses were performed on rectangular plates with aspect ratio 3.6 using the analytical method and the FEM.

• Composites Research
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• v.17 no.2
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• pp.9-14
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• 2004

In this study, analytical investigations on the flexural behavior of FRP reinforced concrete slab were discussed. In the derivation of analytic solution, the FRP reinforced concrete slab was modeled as a structural orthotropic plate. To determine the flexural rigidities of an orthotropic plate model, the elastic equivalence method was employed. In the finite element analysis, the approximate method to determine the rigidity matrix of orthotropic plate element was also suggested using the elastic equivalence method. The results obtained by the analytical solution and the finite element analysis were compared with that of experiment.