• Computers and Concrete
• /
• 제25권6호
• /
• pp.537-549
• /
• 2020

Geometrically nonlinear axisymmetric bending analysis of shear deformable circular plates on a nonlinear three-parameter elastic foundation was made. Plates ranging from "thin" to "moderately thick" were investigated for three types of material: isotropic, transversely isotropic, and orthotropic. The differential equations were discretized by means of the finite difference method (FDM) and the differential quadrature method (DQM). The Newton-Raphson method was applied to find the solution. A parametric investigation using seven unknowns per node was presented. The novelty of the paper is that detailed numerical simulations were made to highlight the combined effects of the material properties and the boundary conditions on (i) the deflection, (ii) the stress resultants, and (iii) the external load. The formulation was verified through comparison studies. It was observed that the results are highly influenced from the boundary conditions, and from the material properties.

• Geomechanics and Engineering
• /
• 제11권2호
• /
• pp.289-307
• /
• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.

• 한국해양공학회지
• /
• 제9권2호
• /
• pp.20-29
• /
• 1995

When structures are constructed by welding, structural elements are always accompained by welding residual stress and deformation. Therefore, when the rigidity and strength of the welded structures is considered, it is very important to have sufficient information about the effect of initial deflection and welding residual stress on them. In this paper, the square plates with welding residual stress under compression are dealt with; First, heat conduction and thermal elastic-plastic problems are analyzed by finite element method using 4-node isoparametric elements for assessment on the ultimate strength of welding joint. Later, the ultimate strength of welding joint is assessed by examining the effect of changed type of loading. The specimens are 500{\times}$500mm(a/b=1) and 750{\times}$500mm(a/b=1.5) rectangular plates of whichthicknesses is 9.0mm and simply supported plates getting axiul load in each direction.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2011년도 추계학술대회 논문집
• /
• pp.136-142
• /
• 2011

The equations of motion for composite plates incorporating magneto-thermo-elastic effects have been derived via Hamilton's principle. In order to get the insight into the implications of a number of geometrical and physical features of the system, the vibrational responses of finite composite rectangular plates immersed in a transversal magnetic field are investigated by applying the extended Galerkin method. The vibration response characteristics of a composite plate are exploited in connection with the magnetic field intensity, thermal load, and electric conductivity of fibrous composite materials. Some pertinent conclusions, which highlight the various effects induced by the magneto-thermo-elastic couplings, are outlined.

• 한국공간구조학회논문집
• /
• 제1권1호
• /
• pp.95-108
• /
• 2001

A system of equations is developed for the theory of bending of thick orthotropic elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate, i.e. ${\omega}=0,\;M_x=0,\;M_{xy}=0\;({\omega}=0,\;M_x=0,\;M_{xy}=0)$ at simple supported edges. It can be obtained general solution that is added complementary solution ${\omega}^e$ and paticular solution ${\omega}^p$ by an assumption of solution function. In the next paper, this analytical results will be obtained for perforated thick plates.

• 대한조선학회지
• /
• 제16권2호
• /
• pp.1-7
• /
• 1979

The authors had done theoretical analysis of the vibration of rectangular elastic plates in contact with water. In this analysis, using the elliptic cylindrical coordinate system, they investigated the effects of mass density ratios, chord-length to thickness ratios, aspect ratios, boundary conditions and mode shapes on the added mass of plates. The results are reported in papers quoted as the reference [4] and [5] of this paper. In this report the results of experiments conducted to verify the above theoretical analysis are presented. It shows that numerical results derived from the theoretical analysis are generally in good agreement with the experimental results.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2005년도 추계학술대회논문집
• /
• pp.604-607
• /
• 2005

The free vibration of solid circular plates has been studied using the differential transformation method(DTM). The effects such as mass at edge and elastic restraints have been considered. In order to avoid the singularity problem at the solid circular center two regularity conditions were applied with respect to the number of circumferential nodal line. The non-dimensional natural frequencies of the general circular plates were obtained for various boundary conditions. The results obtained by this method were compared with previous works. DTM showed fast convergency, accuracy, efficiency and validity in solving vibration problem of general circular plates.

• Advances in nano research
• /
• 제7권5호
• /
• pp.337-349
• /
• 2019

The size-dependent vibration analysis of a cross-/angle-ply laminated composite plate when embedded on the Pasternak elastic foundation and exposed to an in-plane magnetic field are investigated by adopting an analytical eigenvalue approach. The formulation, which is based on refined-hyperbolic-shear-deformation-plate theory in conjunction with the Eringen Nonlocal Differential Model (ENDM), is tested against considering problems for which numerical/analytical solutions available in the literature. The findings of this study demonstrated the role of magnetic field, size effect, elastic foundation coefficients, geometry, moduli ratio, lay-up numbers and fiber orientations on the nonlocal frequency of cross-/angle-ply laminated composite plates.

• Advances in aircraft and spacecraft science
• /
• 제6권3호
• /
• pp.257-272
• /
• 2019

Numerical study of the flutter of a plate on a viscoelastic foundation is carried out in the paper. Critical velocity of the flutter of a plate on an elastic and viscoelastic foundation is determined. The mathematical model for the investigation of viscoelastic plates is based on the Marguerre's theory applied to the study of the problems of strength, rigidity and stability of thin-walled structures such as aircraft wings. Aerodynamic pressure is determined in accordance with the A.A. Ilyushin's piston theory. Using the Bubnov - Galerkin method, the basic resolving systems of nonlinear integro-differential equations (IDE) are obtained. At wide ranges of geometric and physical parameters of viscoelastic plates, their influence on the flutter velocity has been studied in detail.

• Structural Engineering and Mechanics
• /
• 제58권2호
• /
• pp.347-378
• /
• 2016

Within the scope of the plane-strain state, by utilizing the three-dimensional linearized theory of elastic waves in initially stressed piezoelectric and elastic materials, Lamb wave propagation and the influence of the initial stresses on this propagation in a sandwich plate with pre-stressed piezoelectric face and pre-stressed metal elastic core layers are investigated. Dispersion equations are derived for the extensional and flexural Lamb waves and, as a result of numerical solution to these equations, the corresponding dispersion curves for the first (fundamental) and second modes are constructed. Concrete numerical results are obtained for the cases where the face layers' materials are PZT-2 or PZT-6B, but the material of the middle layer is Steel (St) or Aluminum (Al). Sandwich plates PZT-2/St/PZT-2, PZT-2/Al/PZT-2, PZT-6B/St/PZT-6B and PZT-6B/Al/PZT-6B are examined and the influence of the problem parameters such as piezoelectric and dielectric constants, layer thickness ratios and third order elastic constants of the St and Al on the effects of the initial stresses on the wave propagation velocity is studied.