Annular Plates Research Articles

Buckling response of moderately thick fluid-infiltrated porous annular sector plates

In the present article, the buckling of a fluid-infiltrated porous plate is investigated using Mindlin plate theory and an analytical procedure. A cosine rule for the pore distribution across the plate thickness is assumed with a coefficient defining porosity level. The governing stability equations are rewritten in terms of four auxiliary functions and decoupled with the aid of some mathematical manipulations. The decoupled partial differential equations are solved analytically by assuming simply supported radial edges for the plate. The critical buckling loads are calculated by considering fluid-saturated and fluid free conditions for the interconnected network of pores for different sector angles, thickness–radius ratios, coefficients of plate porosity, aspect ratios, and boundary conditions. It is found that the pore fluid compressibility affects the buckling load significantly.

Localization in Thin Metallic Annuli due to Diametrical Extension

The art form of kirigami has recently attracted interest from engineers and scientists for generating complex three-dimensional structures from flat sheet-like materials. When thin metal sheets are used, the deformation can become plastic and localized, allowing for permanent intricate shapes to be formed. In this study, the illustrative case of an annular plate under diametral tension is considered, and it is shown that the deformed shape can be considered as a spatial mechanism of localized plastic yield lines connected to largely undeformed regions. This technique provides useful information for the design of novel permanently deployable structures.

An analytical study on the free vibration of moderately thick fluid-infiltrated porous annular sector plates

An exact analytical approach based on Mindlin plate theory is considered for free vibration analysis of fluid-saturated porous annular sector plates. The interconnected network of pores is saturated by inviscid fluid and the fluid is trapped in the network. The plate’s radial edges are considered to be simply supported and four auxiliary functions are used to evaluate the natural frequencies of porous plates under undrained condition. The mechanical properties of the material are considered to vary through the thickness by expressing shear modulus and density in terms of a simple cosine rule in case of plates with pores free of fluid. The present method is validated by comparing it with the results of other accurate solutions found in the literature. The influence of the coefficient of plate porosity, geometrical parameters as well as the effect of fluid on natural frequency response of porous annular sector plates under various boundary conditions are comprehensively investigated. It is found that the presence of fluid in the interconnected network of pores causes the fundamental natural frequency to increase. The method proposed in this paper may provide useful information for the future assessments of the dynamic response of porous structures when fluid–solid interaction effects are fully taken into account.

Free in-plane vibration analysis of elastically restrained annular panels made of functionally graded material

In this paper, free in-plane vibration of elastically restrained annular plate made of functionally gradient material (FGM) is investigated by an improved Fourier series method. The material property is assumed to be gradually changed in power law along the radial direction. The energy equation is formulated for the in-plane free vibration description of FGM annular plate, with the admissible functions constructed as the superposition of standard Fourier series and boundary smoothed polynomials to make the spatial differential continuous enough in the entire solving domain. In conjunction with the Rayleigh-Ritz procedure, system characteristic equation in matrix form is straightforwardly derived. Several numerical examples are then presented to validate the proposed model, and study the in-plane vibration characteristics of FGM annular panel with various boundary conditions. Based on the model established, the influence of important parameters, such as FGM power-law exponent and boundary restraints, on the in-plane vibration characteristics of FGM annular panel is addressed and investigated in detail. This work can shed some light for a better understanding on the in-plane dynamic characteristics of such complex structure.

An Improved Fourier–Ritz Method for Analyzing In-Plane Free Vibration of Sectorial Plates

A modified Fourier–Ritz approach is developed in this study to analyze the free in-plane vibration of orthotropic annular sector plates with general boundary conditions. In this approach, two auxiliary sine functions are added to the standard Fourier cosine series to obtain a robust function set. The introduction of a logarithmic radial variable simplifies the expressions of total energy and the Lagrangian function. The improved Fourier expansion based on the new variable eliminates all the potential discontinuities of the original displacement function and its derivatives in the entire domain and effectively improves the convergence of the results. The radial and circumferential displacements are formulated with the modified Fourier series expansion, and the arbitrary boundary conditions are simulated by the artificial boundary spring technique. The number of terms in the truncated Fourier series and the appropriate value of the boundary spring retraining stiffness are discussed. The developed Ritz procedure is used to obtain accurate solution with adequately smooth displacement field in the entire solution domain. Numerical examples involving plates with various boundary conditions demonstrate the robustness, precision, and versatility of this method. The method developed here is found to be computationally economic compared with the previous method that does not adopt the logarithmic radial variable.

Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading

In this article, an analytical solution for free vibration of moderately thick annular sectorial porous plates in the presence of in-plane loading is presented. Because of the in-plane loading, before the vibrational analysis, a buckling analysis is performed. To this end, equations of motion together with the stability equations are derived using Hamilton principle. Both the governing equations of motion and stability are highly coupled differential equations, which are difficult to solve analytically. So, they are decoupled through performing some mathematical operations. The decoupled equations are then solved analytically for annular plates with simply supported boundary conditions on the radial edges and different boundary conditions on the circumferential edges. Natural frequencies and also critical buckling load are obtained and the effects of thickness ratio, radii ratio, porosity, and boundary conditions are studied in detail. Finally, the effect of in-plane loading on the natural frequency of the plate is studied comprehensively. Numerical results show that the natural frequency decreases as the load ratio approaches one and vanishes as it reaches one.

A new modified higher-order shear deformation theory for nonlinear analysis of macro- and nano-annular sector plates using the extended Kantorovich method in conjunction with SAPM

In this research, the nonlinear local and nonlocal analysis of an annular sector plate is studied and solved based on a new modified higher-order shear deformation theory. Due to the shortcomings of HSDT in the two-dimensional nonlinear analysis, it is modified by eliminating the defects, and a comprehensive theory is presented for analyzing the mechanical behavior of an annular sector sheet in general form. The strain field is developed by considering the von Karman assumptions and also the nonlocal theory of Eringen from which the classical local analysis can be deduced conveniently by neglecting the small-scale effects. Whereas the annular sector plate is assumed, the sector, annular/circular, rectangular and solid circular plates can be simulated. Afterward, the nonlocal constitutive equations are derived and solved by using the two-dimensional SAPM (Dastjerdi et al. in Compos B Eng 98, 78–87, 2016). Moreover, a combination of the extended Kantorovich method and one-dimensional SAPM is applied. Since the presented theory is relatively new and similar studying was not available in order to compare the results, a comparison is done with the results of lower-order theories. Finally, the effect of various parameters, such as boundary conditions, different theories, nonlocal and local analyses, loading and the size of the plate, on the mechanical behavior of an annular sector plate are investigated.

Nonlinear free vibration analysis of thermally induced FG-CNTRC annular plates: Asymmetric versus axisymmetric study

Due to axisymmetric fundamental vibrational mode shape, the most studies on the large-amplitude free vibration of annular plates have been presented based on the axisymmetric formulation. However, the initial thermal loading can change the vibration behavior of annular plates. To analyze this effect, the nonlinear free vibration of carbon nanotube (CNT) reinforced composite annular plates is investigated under thermal loading based on the asymmetric formulation. The material properties of the CNT-reinforced composites are assumed to vary continuously along the thickness direction and estimated through a micromechanical model by which the temperature-dependency is taken into account. The governing equations are derived on the basis of first-order shear deformation theory, and an efficient numerical variational method is employed to solve the problem. In this regard, the quadratic form of the energy functional is directly discretized using numerical differential and integral operators, and the pseudo-arc length continuation method is then applied to find the frequency response of the structure. The numerical results of asymmetric and axisymmetric formulations are compared and it is observed that in the presence of initial thermal loading, the axisymmetric analysis leads to inaccurate results and complete asymmetric formulation should be considered.

NON-CLASSICAL PROBLEM OF BEND OF AN ORTHOTROPIC ANNULAR PLATE OF VARIABLE THICKNESS WITH AN ELASTICALLY CLAMPED SUPPORT

A model of elastically clamped support for an inner edge of an axisymmetric annular round bending plate is proposed. Values of parameters of the support as well as relationship between them is determined. With the collocation method the problem of bending of a cylindrically orthotropic annual plate of a variable thickness under a uniformly distributed load is solved taking into account the transverse shear. It is assumed that the inner edge of the plate is elastically fastened and the outer one is hingedly supported. Based on the analysis of calculated values of immeasurable quantities qualitative conclusions are drawn.

Unified approach for vibration analyses of annular sector and annular plates with general boundary conditions

This paper presents a unified approach for predicting the free and forced (steady-state and transient) vibration analyses of annular sector and annular plates with various combinations of classical and non-classical boundary supports. In spite of the types of the boundary restraints and the shapes of the plates, the admissible displacement function is described as a modified trigonometric series expansion, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. Mathematically, the unification of various boundary value problems for annular sector and annular plates is physically realized by setting a set of coupling springs to ensure appropriate continuity conditions along the radial edges of concern. Numerous examples are presented for the free vibration analyses of annular sector and annular plates with different boundary restraints. With regard to the forced vibration analysis, annular sector and annular plates with different external excitations are examined. The accuracy, convergence and numerical robustness of the current approach are extensively demonstrated and verified through numerical examples which involve plates with various shapes and boundary conditions.

Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings

In this article, stresses and free-vibration behaviors of annular circular piezoelectric nanocomposite plate reinforced by functionally graded single-walled boron nitride nanotubes (FG-SWBNNTs) embedded in an elastic foundation based on modified couple stress theory (MCST) are explored. The mechanical properties of FG-SWBNNT-reinforced nanocomposite plate are assumed to be graded in the direction of thickness and estimated through the micro-mechanical approach. The governing equations are obtained using the energy method. The natural frequencies and stresses of FG-SWBNNT-reinforced nanocomposite plate are computed using the differential quadrature method (DQM). An excellent agreement is observed between the obtained results and the results in the literature. Influences of the internal radius to the external radius, the thickness to the internal radius ratio, the material length scale parameter, the functionally graded parameter, temperature changes and elastic coefficients on the natural frequencies and stresses of the hollow circular nanocomposite plate are investigated. The results of this research show that the natural frequencies of the piezoelectric nanocomposite plate increase by increasing the material length scale parameter, the elastic foundation parameters, the ratio of the inner radius to the outer radius, the ratio of the thickness to the inner radius, and decreasing the power index and temperature change. The radial stress of the nanocomposite plate varies proportionally to its mode shape. The results can be employed to design smart structures in micro-electro-mechanical systems (MEMS).

On an extended Kantorovich method for the mechanical behavior of functionally graded solid/annular sector plates with various boundary conditions

Based on the first-order shear deformation plate theory, two approaches within the extended Kantorovich method (EKM) are presented for a bending analysis of functionally graded annular sector plates with arbitrary boundary conditions subjected to both uniform and non-uniform loadings. In the first approach, EKM is applied to the functional of the problem, while in the second one EKM is applied to the weighted integral form of the governing differential equations of the problem as presented by Kerr. In both approaches, the system of ordinary differential equations with variable coefficients in r direction and the set of ordinary differential equations with constant coefficients in $$\theta $$ direction are solved by the generalized differential quadrature method and the state space method, respectively. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with the available published works in the literature. It is observed that the first approach is applicable to all supports with an excellent accuracy while the second approach does not give acceptable results for a plate with a free edge. Furthermore, various response quantities in FG annular sector plates with different boundary conditions, material constants, and sector angles are presented which can be used as a benchmark.

An exact solution of thermal stability analysis of bimorph functionally graded annular plates

DOI: 10.7764/RDLC.16.1.66 The present study aims to provide an exact solution for thermal buckling of bimorph functionally graded circular plates under uniform thermal loading with regard to von Karman’s classic theory and non-linear assumptions in clamped-clamped, simple-simple, clamped-simple and simple-clamped support conditions. Martials properties will change in association to the middle surface of symmetric plate and according to the power law in direction of thickness. So that, the middle surface of the annular plate was pure metal and the sides of plate were pure ceramic. Using non-linear equations energy, the equilibrium was determined and the stability equations were employed by the method of equilibrium in vicinity in order to specify the critical temperature of buckling. Finally, a closed solution was obtained. We also measured the impact of varying factors like the rate of thickness to plate radius changes, volume fraction percentile changes of materials, and the ratio of the inner radius to the outer radius over the critical buckling temperature. Then, the results were compared together and with former studies. The findings indicated that for bimorph functionally graded materials, thermal moment does not occur, while buckling critical temperature in bimorph functionally graded materials of annular plates increases as the ratio of thickness to radius increases. Moreover, by increasing the ratio of inner to outer radius in clamped-clamped and clamped-simple support conditions we have an increase in thermal buckling free parameter.

3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates

• 3D thermo-elastic bending solutions are obtained for functionally graded circular and annular plates reinforced with GPLs. • Thinner GPLs are preferred to achieve better enhancement in bending stiffness hence reduced bending deflection. • The parabolic GPL distribution offers the best reinforcing effect, followed by uniform then linear distribution patterns. • For plates reinforced by uniformly distributed GPLs, the temperature field and radial stress distribution are not affected by GPL's total content. Within the framework of three-dimensional elasticity theory, this paper investigates the axisymmetric bending of novel functionally graded polymer nanocomposite circular and annular plates reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of nanocomposite circular and annular plates under a combined action of a uniformly distributed transverse load and a through-thickness steady temperature field. Three different distribution patterns of GPLs within the polymer matrix are considered. The present analytical solutions are validated through comparisons against those available in open literature for the reduced cases. A parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, plate thickness to radius ratio, and boundary conditions on the stress and deformation fields of the plate. The results show that GPL nanofillers with a low content can have a significant reinforcing effect on the bending behavior of the thermo-mechanically loaded plate.

Frequencies Values of Orthotropic Composite Circular and Annular Plates

Free vibration analysis of orthotropic composite annular plate is investigated. First-order shear deformation theory (FSDT) is used for equation of motion. Two different kernels such as Regularized Shannon delta (RSD) kernel and Lagrange delta sequence (LDS) kernel are used. The method of discrete singular convolution (DSC) is used for numerical simulation of governing equations to obtain the frequency values. It is shown that the convergence and accuracy of the DSC method is very good for vibration problem of orthotropic annular plate.

Vibration of laminated composite panels and curved plates with different types of FGM composite constituent

Abstract Free vibration analysis of truncated conical panels and annular sector plates with functionally graded materials (FGM) is carried out. Governing equations of motion are obtained based on two different shell theories such as Love's shell theory and first-order shear deformation theory (FSDT). The resulting governing differential equations have been solved using the differential quadrature (DQ) and discrete singular convolution (DSC) methods. As the FGM cases two different material properties of structures are assumed to change continuously in the thickness direction according to the volume fraction power law and the general four-parameter power law distributions in terms of the volume fractions of constituents. Accuracy, convergence and reliability of these two methods have been validated by comparing the obtained results with the existing results available in the open literature. Furthermore, the effects of the grid numbers on results for each method have been also investigated for different boundary conditions and mode numbers for conical panel vibrations. Then, using the DQ and DSC methods, the frequencies values have been calculated for different material and geometric parameters, modes and boundary cases for truncated conical panels with FGM. The effects of material power-law distribution are also discussed. The convergence, advantages and accuracy of the present two methodologies are examined in conjunctions with the vibration problem of truncated conical panels with functionally graded materials (FMG). Some results for annular sector plates and circular cylindrical panels have also been obtained via conical panel equations.

Thermo elasticity solution of functionally graded, solid, circular, and annular plates integrated with piezoelectric layers using the differential quadrature method

ABSTRACTStatic analysis of functionally graded (FG) solid circular/annular plates imbedded in piezoelectric layers under thermo-electro mechanical load is investigated using the differential quadrature method. The plate has various edge boundary conditions and its material properties are assumed to vary in an exponential law with the Poisson ratio to be constant. The method is validated by comparing numerical results with the results obtained in the literature. The effects of the gradient index, thickness to radius ratio, and edges boundary conditions on the thermoelastic behavior of FG solid circular and annular plates are investigated.

Elasticity solutions for a transversely isotropic functionally graded annular sector plate

This paper presents three-dimensional elasticity solutions for an annular sector plate made of transversely isotropic functionally graded material (FGM) subjected to concentrated forces \(\left( X,Y,0 \right) \) or couples \(\left( M_X,M_Y,M_Z\right) \) applied at one of its radial edges. The elastic coefficients can vary arbitrarily through the plate thickness. The analysis was based on the assumed forms of displacements for bending of an FGM plate (Mian and Spencer in J Mech Phys Solids 4:2283–2295, 1998), in which the four analytical functions were constructed properly. Appropriate boundary conditions and end conditions similar to those in the classic plate theory were employed to determine the unknown constants contained in the analytical functions so as to accomplish the analysis. When the material coefficients are all constant, the obtained analytical solutions can be degenerated into those for a homogeneous transversely isotropic annular sector plate, which have never been reported before. The solutions may be further reduced to those for a homogeneous isotropic annular sector plate, among which the ones for concentrated couples \(\left( M_X ,M_Y,0 \right) \) are also new to the literature.

Experimental and numerical investigation of stress in a large-scale steel tank with a floating roof

Research on steel tanks, particularly large-scale oil storage tanks, has increased significantly with the rapid development of the petrochemical industry. The focus on these thin-walled structures is related not only to the cost of the infrastructure, but also because failures due to accidents may generate huge economic costs, environmental losses, and casualties. The aim of the present study is an extensive experimental and numerical investigation of stress in a large-scale oil tank with a floating roof. Stresses in the shell and bottom of a large-scale oil storage tank are measured by a resistance strain gauge technique. Meanwhile, an improved 3-D finite element model is developed to analyze stresses in the tank. By comparing calculated results with experimental data, the validity of the developed finite element model is verified. Both experimental and numerical results suggest that the stress on the fillet joint is relatively high in the tank. The finite element model is used to study the effects of three key steel tank parameters on the stress of the fillet joint in the oil storage tank: the thickness of the annular bottom plate at the base, the radial width of the projection of the annular bottom plate outside the shell, and the radial width of the concrete ringwall. In addition, a new method related to the design of the annular bottom plate and concrete ringwall is proposed. This method will be helpful in improving the design of large-scale oil tanks and assessing their structural integrity.

Free vibration of thick laminated circular and annular plates using three-dimensional finite element analysis

This paper presents a numerical analysis of free vibration of thick laminated circular plates, having free, clamped as well as simply-supported boundary conditions at outer edges. The finite element method that works on the basis of three-dimensional theory of elasticity is employed to evaluate the first ten natural frequencies of uniform circular plate. The effect of thickness ratios, fiber orientation angle (angle-ply and cross-ply), stacking sequences (symmetric and antisymmetric), radius ratios and boundary conditions on frequency parameter are discussed in detail. The first five natural modes of flexural vibrations for different boundary conditions are presented in pictorial forms. Verification of the accuracy of these results is verified by appropriate convergence study and checked with the results available in the literature.