• 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.81 no.3
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• pp.379-394
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• 2022

Shallow footings usually belonged to the category of thick plate structures. For accurate analysis of thick plates, the contribution of out-of-plane components of the stress tensor should be considered in the formulation. Most of the available shallow footing models are based on the classical plate theories, which usually neglect the effects of the out-of-plane stresses. In this study, a mixed-field plate finite element model (FEM) is developed for the analysis of shallow footings rested on soil foundations. In addition to displacement field variables, the out-of-plane components of the stress tensor are also assumed as a priori unknown variables. For modeling the interaction effect of the soil under and outside of the shallow footings, the modified Vlasov theory is used. The tensionless nature of the supporting soil foundation is taken into account by adopting an incremental, iterative procedure. The equality requirement of displacements at the interface between the shallow footing and soil is fulfilled using the penalty approach. For validation of the present mixed FEM, the obtained results are compared with the results of 3D FEM and previous results published in the literature. The comparisons show the present mixed FEM is an efficient and accurate tool for solving the problems of shallow footings rested on subsoil.

• Structural Engineering and Mechanics
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• v.65 no.6
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• pp.645-656
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• 2018

Importance of procuring adequate knowledge about the mechanical behavior of double-layered graphene sheets (DLGSs) incensed the authors to investigate wave propagation responses of mentioned element while rested on a visco-Pasternak medium under hygro-thermal loading. A nonlocal strain gradient theory (NSGT) is exploited to present a more reliable size-dependent mechanical analysis by capturing both softening and hardening effects of small scale. Furthermore, in the framework of a classical plate theory the kinematic relations are developed. Incorporating kinematic relations with the definition of Hamilton's principle, the Euler-Lagrange equations of each of the layers are derived separately. Afterwards, combining Euler-Lagrange equations with those of the NSGT the nonlocal governing equations are written in terms of displacement fields. Interaction of the each of the graphene sheets with another one is regarded by the means of vdW model. Then, a widespread analytical solution is employed to solve the derived equations and obtain wave frequency values. Subsequently, influence of each participant variable containing nonlocal parameter, length scale parameter, foundation parameters, temperature gradient and moisture concentration is studied by plotting various figures.

• Advances in nano research
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• v.14 no.5
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• pp.463-474
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• 2023

The purpose of this paper is to present the analysis of propagating and evanescent waves in functionally graded (FG) nanoplates with the consideration of nonlocal effect. The analytical integration nonlocal stress expansion Legendre polynomial method is proposed to obtain complete dispersion curves in the complex domain. Unlike the traditional Legendre polynomial method that expanded the displacement, the presented polynomial method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. In addition, the analytical expressions of numerical integrations are presented to improve the computational efficiency. The nonlocal effect, inhomogeneity of medium and their interactions on wave propagation are studied. It is found that the nonlocal effect and inhomogeneity of medium reduce the frequency bandwidth of complex evanescent Lamb waves, and make complex evanescent Lamb waves have a higher phase velocity at low attenuation. The occurrence of intersections of propagating Lamb wave in the nonlocal homogeneous plate needs to satisfy a smaller Poisson's ratio condition than that in the classical elastic theory. In addition, the inhomogeneity of medium enhances the nonlocal effect. The conclusions obtained can be applied to the design and dynamic response evaluation of composite nanostructures.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.89-100
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• 2001

The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (h$_{m}$/L) of 0.1 and 0.2 for b/L=0.2 and 0.5. All 3-D modes are included in the analyses : e.g., flexural, thickness-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o a\ulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson\`s ratio $\upsilon$ is fixed at 0.3 for numerical calculations.s.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.90-100
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• 1993

A finite element formulation of vibration control of a laminated plate with piezoelectric sensor/ actuators is presented. Classical lamination theory with the induced strain actuation and Hamilton's principle are used to formulate the equations of motion of the system. The total charge developed on the sensor layer is calculated from the direct piezoelectric equation. The equations of motion and the total charge are discretized with 4 node, 12 degrees of freedom quadrilateral plate bending elements with one electrical degree of freedom. The mass and stiffness of the piezoelectric layer are introduced by treating them as another layer in laminated plate. Piezoelectric sensor/actuators are distributed, but discrete due to the geometry of electrodes. By defining an i.d. number of electrode for each element, modelling of electrodes with variable geometry can be achieved. The static response of a piezoelectric bimorph beam to electrical loading and sensor voltage to given displacement are calculated. For a laminated plate under the negative velocity feedback control, the direct time response by the Newmark-.betha. method and damped frequencies and modal damping ratios by modal state space analysis are derived.

• Structural Engineering and Mechanics
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• v.78 no.5
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• pp.611-622
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• 2021

Composite material-due to low density-causes weight savings, which results in lower fuel consumption of transport vehicles. The aim of the research was to change the existing base-plate of the aluminum airplane container with the composite sandwich plate in order to reduce the weight of the containers of cargo aircrafts. The newly constructed sandwich plate consists of aluminum honeycomb core and composite face-sheets. The face-sheets consist of glass or carbon or hybrid fiber layers. The orientations of the fibers in the face-sheets were 0°, 90° and ±45°. Multi-objective optimization method was elaborated for the newly constructed sandwich plates. Based on the design aim, the importance of the objective functions (weight and cost of sandwich plates) was the same (50%). During the optimization nine design constraints were considered: stiffness, deflection, facing stress, core shear stress, skin stress, plate buckling, shear crimping, skin wrinkling, intracell buckling. The design variables were core thickness and number of layers of the face-sheets. During the optimization both the Weighted Normalized Method of the Excel Solver and the Genetic Algorithm Solver of Matlab software were applied. The mechanical properties of composite face-sheets were calculated by Laminator software according to the Classical Lamination Plate Theory and Tsai-Hill failure criteria. The main added-value of the study is that the multi-objective optimization method was elaborated for the newly constructed sandwich structures. It was confirmed that the optimal new composite sandwich construction-due to weight savings and lower fuel consumption of cargo aircrafts - is more advantageous than conventional all-aluminum container.

• Structural Engineering and Mechanics
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• v.49 no.5
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• pp.569-595
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• 2014

In this paper, a novel semi-energy finite strip method (FSM) is developed based on the concept of first order shear deformation theory (FSDT) in order to attempt the post-buckling solution for thin and relatively thick functionally graded (FG) plates under uniform end-shortening. In order to study the effects of through-the-thickness shear stresses on the post-buckling behavior of FG plates, two previously developed finite strip methods, i.e., semi-energy FSM based on the concept of classical laminated plate theory (CLPT) and a CLPT full-energy FSM, are also implemented. Moreover, the effects of aspect ratio on initial post-buckling stiffness of FG rectangular plates are studied. It has been shown that the variation of the ratio of initial post-buckling stiffness to pre-buckling stiffness ($S^*/S$) with respect to aspects ratios is quite independent of volume fractions of constituents in thin FG plates. It has also been seen that the universal curve representing the variation of ($S^*/S$) with aspect ratio of a FG plate demonstrate a saw shape curve. Moreover, it is revealed that for the thin FG plates in contrast to relatively thick plates, the variations of non-dimensional load versus end-shortening is independent of ceramic-metal volume fraction index. This means that the post-buckling behavior of thin FG plates and the thin pure isotropic plates is similar. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. The study of the results may have a great influence in design of FG plates encountering post-buckling behavior.

• Steel and Composite Structures
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• v.50 no.3
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• pp.299-318
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• 2024

The main objective of this paper is to compute the far-field acoustic radiation (sound radiation) of functionally graded plates (FGM) loaded by sinusoidally varying point load subjected to the arbitrary boundary condition is carried out. The governing differential equations for thin functionally graded plates (FGM) are derived using classical plate theory (CPT) and Rayleigh integral using the elemental radiator approach. Four cases, segregated on power-law index k=0,1,5,10, are studied. A novel approach is illustrated to compute sound fields of vibrating FGM plates using the physical neutral surface with an elemental radiator approach. The material properties of the FGM plate for all cases are calculated considering the power law indexes. An in-house MATLAB code is written to compute the natural frequencies, normal surface velocities, and sound radiation fields are analytically calculated using semi-analytical formulation. Ansys is used to validate the computed sound power level. The parametric effects of the power law index, modulus ratios, different constituent of FGM plates, boundary conditions, damping loss factor on the sound power level, and radiation efficiency is illustrated. This work is the benchmark approach that clearly explains how to calculate acoustic fields using a solid layered FGM model in ANSYS ACT. It shows that it is possible to asymptotically stabilize the structure by controlling the intermittent layers' stiffness. It is found that sound fields radiated by the elemental radiators approach in MATLAB, ANSYS and literatures are in good agreement. The main novelty of this research is that the FGM plate is analyzed in the low-frequency range, where the stiffness-controlled region governs the whole analysis. It is concluded that a clamped mono-ceramic FGM plate radiates a lesser sound power level and higher radiation efficiency than a mono-metallic or metal-rich FGM plate due to higher stiffness. It is found that change in damping loss factor does not affect the same constituents of FGM plates but has significant effects on the different constituents of FGM plates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2313-2318
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• 2000

The method of photoelasticity allows one to obtain principal stress differences and principal stress directions in a photoelastic model. In the classical approach, the photoelastic parameters are measured manually point by point. This is time consuming and requires skill in the identification and measurement of photoelastic data. Fringe phase shifting method has been recently developed and widely used to measure and analyze fringe data in photo-mechanics. This paper presents the test results of photoelastic fringe phase shifting method for the stress analysis of a curved beam plate. The technique used here requires four phase stepped photoelastic images obtained from a circular polariscope by rotating the analyzer at 0˚, 45˚, 90˚ and 135˚. Experimental results are compared with those of ANSYS and calculated by the simple beam theory. Good agreement among the results can be observed.