• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.481-488
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• 1988

In the analysis of impulsive response of plate, Lagrange's theory, Reissner's theory and Mindlin's theory are generally used. But, in applying these theories the impulsive stresses directly underneath the concentrated impact point cannot be analyzed because the solution fails to converge. In this paper, therefore, an attempt for a supported square plate is made by using three-dimensional dynamic theory of elasticity on the supposition that the uniform distributed load acts on the central part of it. In order to clarify the validity of theoretical analysis, the strain variations are measured experimentally for a square glass plate. Finally it is shown that these theoretical results are in close agreement with the experimental results.

• 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.

• Structural Engineering and Mechanics
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• v.56 no.3
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• pp.491-506
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• 2015

Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.298-309
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• 1990

In this paper, a new method is suggested to analyze impulsive stresses at loading poing of concentrated impact load under certain impact conditions determined by impact velocity, stiffness of plate and mass of impact body, etc. The impulsive stresses are analyzed by using the three dimensional dynamic theory of elasticity so as to analytically clarify the generation phenomenon of cone crack at the impact fracture of fragile materials (to be discussed if the second paper). The Lagrange's plate theory and Hertz's law of contact theory are used for the analysis of impact load, and the approximate equation of impact load is suggested to analyze the impulsive stresses at the impact point to decide the ranage of impact load factor. When impact load factors are over and under 0.263, approximate equations are suggested to be F(t)=Aexp(-Bt)sinCt and F(t)=Aexp(-bt) {1-exp(Ct)} respectively. Also, the inverse Laplace transformation is done by using the F.F.T.(fast fourier transform) algorithm. And in order to clarity the validity of stress analysis method, experiments on strain fluctuation at impact point are performed on a supported square glass plate. Finally, these analytical results are shown to be in close agreement with experimental results.

• Steel and Composite Structures
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• v.24 no.5
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• pp.603-613
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• 2017

In this research, the free vibration response of laminated composite plates is investigated using a novel and simple higher order shear deformation plate theory. The model considers a non-linear distribution of the transverse shear strains, and verifies the zero traction boundary conditions on the surfaces of the plate without introducing shear correction coefficient. The developed kinematic uses undetermined integral terms with only four unknowns. Equations of motion are obtained from the Hamilton's principle and the Navier method is used to determine the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical examples studied using the present formulation is compared with three-dimensional elasticity solutions and those calculated using the first-order and the other higher-order theories. It can be concluded that the present model is not only accurate but also efficient and simple in studying the free vibration response of laminated composite plates.

• Advances in nano research
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• v.12 no.5
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• pp.483-488
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• 2022

The present work is an attempt to study the vibration analysis of the single-walled carbon nanotubes (SWCNTs) under the effect of the surface irregularity using Donnell's model. The surface irregularity represented by the parabolic form. According to Donnell's model and three-dimensional elasticity theory, a novel governing equations and its solution are derived and matched with the case of no irregularity effects. To understand the reaction of the nanotube to the irregularity effects in terms of natural frequency, the numerical calculations are done. The results obtained could provide a better representation of the vibration behavior of an irregular single-walled carbon nanotube, where the aspect ratio (L/d) and surface irregularity all have a significant impact on the natural frequency of vibrating SWCNTs. Furthermore, the findings of surface irregularity effects on vibration SWCNT can be utilized to forecast and prevent the phenomena of resonance of single-walled carbon nanotubes.

• Structural Engineering and Mechanics
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• v.86 no.1
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• pp.69-83
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• 2023

Analytical solutions to problems are crucial because they provide high-quality comparison data for assessing the accuracy of numerical solutions. Benchmark analytical solutions for the vibrations of cracked functionally graded material (FGM) plates are not available in the literature because of the high level of complexity of such solutions. On the basis of first-order shear deformation plate theory (FSDT), this study proposes analytical series solutions for the vibrations of FGM rectangular plates with side or internal cracks parallel to an edge of the plates by using Fourier cosine series and the domain decomposition technique. The distributions of FGM properties along the thickness direction are assumed to follow a simple power law. The proposed analytical series solutions are validated by performing comprehensive convergence studies on the vibration frequencies of cracked square plates with various crack lengths and under various boundary condition combinations and by performing comparisons with published results based on various plate theories and the theory of three-dimensional elasticity. The results reveal that the proposed solutions are in excellent agreement with literature results obtained using the Ritz method on the basis of FSDT. The paper also presents tabulations of the first six nondimensional frequencies of cracked rectangular Al/Al2O3 FGM plates with various aspect ratios, thickness-to-width ratios, crack lengths, and FGM power law indices under six boundary condition combinations, the tabulated frequencies can serve as benchmark data for assessing the accuracy of numerical approaches based on FSDT.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.473-494
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• 2015

A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.12
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• pp.2241-2251
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• 1992

This work is concerned with the investigation of end effects of a cylinder on a structure where a circular plate is attached to a solid circular cylinder. Three-dimensional elasticity solutions are used in a cylinder whereas the classical thin plate theory is employed for a plate. The end effect of the cylinder on the flexibility and the structural response is demonstrated by several numerical examples.

• Structural Engineering and Mechanics
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• v.84 no.4
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• pp.437-452
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• 2022

For the first time, the higher-order shear and normal deformable plate theory (HOSNDPT) is used for the vibration and flutter analyses of the multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) plates under supersonic airflow. For modeling the supersonic airflow, the linear piston theory is adopted. In HOSNDPT, Legendre polynomials are used to approximate the components of the displacement field in the thickness direction. So, all stress and strain components are encountered. Either uniform or three kinds of non-uniform distribution of graphene platelets (GPLs) into polymer matrix are considered. The Young modulus of the FG-GPLRC plate is estimated by the modified Halpin-Tsai model, while the Poisson ratio and mass density are determined by the rule of mixtures. The Hamilton's principle is used to obtain the governing equations of motion and the associated boundary conditions of the plate. For solving the plate's equations of motion, the Galerkin approach is applied. A comparison for the natural frequencies obtained based on the present investigation and those of three-dimensional elasticity theory shows a very good agreement. The flutter boundaries for FG-GPLRC plates based on HOSNDPT are described and the effects of GPL distribution patterns, the geometrical parameters and the weight fraction of GPLs on the flutter frequencies and flutter aerodynamic pressure of the plate are studied in detail. The obtained results show that by increasing 0.5% of GPLs into polymer matrix, the flutter aerodynamic pressure increases approximately 117%, 145%, 166% and 196% for FG-O, FG-A, UD and FG-X distribution patterns, respectively.