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A fluid-structure model based on nonlinear Mindlin-Reissner plate theory and linearized piston theory is used to study the aeroelastic flutter of panels of arbitrary planforms at supersonic...

In this paper, a new quasi-three-dimensional (3D) hyperbolic shear deformation theory for the bending and free vibration analysis of functionally graded plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, the number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only five, as against six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory.

A number of simplified design methods have been developed to predict composite slab capacities in fire. Most of these extend ambient-temperature large-deflection slab behavior to the elevated-temperature phase by reducing the strengths of fire-exposed concrete and reinforcement while neglecting the effects of thermal expansion and thermal bowing of the slab. Experiments have shown that there are significant differences between the predictions from these methods and the actual behavior and failure modes of ambient- and elevated-temperature concrete slabs in tensile membrane action. Therefore, this paper describes the development of a new analytical method that incorporates both thermal and mechanical effects into the prediction of slab behavior in fire conditions. It uses the variational Rayleigh-Ritz approach to classical large-deflection plate theory. The method is found to produce accurate predictions of deflections and membrane tractions; however, it requires further refinement for accuracy of ...

In the current study, a semianalytical closed-form solution is presented for the first time for buckling analysis of two-directional, functionally graded (FG) circular plates with variable thickness supported by both constrained edges and two-parameter elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. While variations of the elasticity modulus in the transverse direction is described by a power-law, variations of the material properties and the thickness in the radial direction are assumed to obey exponential laws. Mindlin’s shear deformation plate theory and the differential transform technique are employed to develop the governing equations. A sensitivity analysis including evaluation of effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, and material heterogeneity is performed. Results reveal that the strength degradation caused by t...

The localized effects and, particularly, the stress and deformation concentrations near edges, mortar joints, and irregular points in walls strengthened with externally bonded composite materials are studied. To quantify the structural behavior and to cope with the coupling of large-scale and localized-scale effects, a substructuring procedure that uses a specially tailored high-order finite element is developed. The specially tailored element accounts for the bidirectional behavior of the wall and for the interfacial interaction between the adhesively bonded components. The formulation uses a first-order shear deformation orthotropic plate theory for the independent modeling of the existing wall and the composite layers and a high-order theory for the modeling of the displacement fields of the adhesive layers. A static condensation-based substructuring procedure is used for the formulation of a superelement. The computational strength and the convergence characteristics of the high-order superele...

In this paper, stability analysis of thick annular sector plates under mechanical and thermal loads based on third-order shear deformation theory (TSDT) is investigated. The equilibrium and stability equations based on TSDT are obtained and solved analytically by doing some mathematical manipulation. Then, for nine possible boundary conditions, the buckling load and temperature are calculated and compared with those obtained using different plate theories. As the results show, for boundary conditions that include simply supported and clamped edges, the minimum value for buckling load and temperature is predicted by first-order shear deformation theory (FSDT) and maximum value is predicted by classical plate theory (CPT). Also, for boundary conditions containing free edges, the value obtained by TSDT is larger than that obtained using CPT and FSDT for some values of thickness/length ratio. It is worthy to mention that the results obtained from CPT for boundary conditions containing free edges in a ...

Current models to determine the local buckling stress of inelastic plates under in-plane loading are based on plastic deformation theory and semirational or empirical relationships. A successful J2 flow theory describing inelastic local buckling of initially perfect plates needs to avoid two well-known pitfalls known as the “inelastic column buckling paradox” and the “plastic buckling paradox.” While the former problem, which found its origin in 1895 in Engesser’s double modulus approach, was resolved by Shanley in the late 1940s, a convincing solution of the plastic buckling paradox has not yet been presented. This paper proposes a modification to the J2 flow theory which hinges on the determination of the shear stiffness from second-order considerations. A differential equation is derived which describes the incremental plate deformations at the inelastic local buckling load. The differential equation is studied for two cases of boundary conditions: a plate simply supported along four edges and a plate ...

In most publications on vibration of annular plates, the natural frequencies are only presented for inner radius as small as one-tenth of its outer radius, but there are hardly any results presented for cores smaller than this inner radius value. This is attributed to severe scaling problems upon using numerical techniques to obtain the fundamental frequency of plates when the inner radius becomes very small. This study aims to solve this class of plate vibration problem where the annular plates are thick and their core radii are much less than one-tenth of the outer radius. The analysis involved using the Mindlin plate theory so as to allow for the effects of transverse shear deformation and rotary inertia and the truncation of the terms in the Bessel functions defining the characteristic equations in order to overcome the scaling problem. Eventually, the fundamental frequency of a thick annular plate could be deduced as finite or zero when the inner radius approaches zero.

This study presents the thermal buckling of a radially solid sandwich circular plate made of a piezoelectric actuator and porous material. The porous material properties vary through the thickness of the plate for a specific function. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The geometrical nonlinearities are considered along with the higher-order shear deformation plate theory. The problem is simplified to an axisymmetric one, and then closed-form solutions for circular plates subjected to temperature load are obtained. The buckling temperatures that are derived for solid circular plates under uniform temperature rise through the thickness for an immovable clamped edge of the boundary conditions. The effects of the porous plate thickness, piezoelectric thickness, applied actuator voltage, and variation of porosity on the critical temperature loa...

This paper studies the dynamic geometrically nonlinear behavior of walls that are strengthened with fiber-reinforced polymer (FRP) composite materials but include preexisting debonded regions. For that purpose, two specially tailored finite elements corresponding to the perfectly bonded regions and debonded regions within the layered wall are formulated under the umbrella of a dynamic analysis. The two finite elements are based on a high-order multilayered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains. The convergence and validity of the geometrically nonlinear dynamic model are studied for the case of a locally debonded FRP-strengthened wall under in-plane shear loads applied at a constant rate. The unified model of the strengthened wall with a local delamination is then used for studying the dynamic nonlinear behavior under different levels of shear loading rate. The dynamic results and the comparison with static analyses reveal the impact ...

The paper deals with the fully coupled response characteristics of a multilayered composite plate with piezoelectric layers. The response quantities of the plate are coupled by the mechanical field and the electric field. Based on the three-dimensional linear piezoelectricity and the first-order shear deformation theory, the fundamental unknowns, such as the displacements and the electric potential, are assumed to be expandable through the plate thickness coordinate. The governing equations of motion of the plate are presented in terms of the unknown displacement and electrical potential coefficients. When the boundary conditions and electromechanical inputs are specified, the double Fourier series is used to obtain the response of the simply supported multilayered plates. Numerical results for the static and dynamic response of the laminated composite plates with different lamination schemes and having a PIC-151 piezoelectric material layer are obtained. The effects of the plate thinness ratio, plate aspect ratio, lamination scheme, fiber orientations, and piezoelectric coupling on the static and dynamic response are presented.

A robust analytical model for predicting full response and ultimate load of concrete bridge decks constructed with fiber-reinforced polymer (FRP) stay-in-place (SIP) structural forms is presented. It adopts the plate theory to establish surface deflections, while incorporating concrete nonlinearity in compression and cracking in tension, as well as the degree of bond between the FRP SIP form and the concrete. The model accounts for various boundary conditions at the edges of the deck in both directions, including both finite and infinite width in the direction of traffic, and either fixed or hinged conditions in the other direction, depending on the connection to the support girders. A punching shear failure criterion was incorporated to predict the ultimate load. The model was validated against a large experimental database, and reasonable agreement was observed. The average percent difference in ultimate loads was 5.5%. The model was then used in a parametric study to assess the FRP reinforcement ratio in terms of the FRP plate thickness, the width of the deck parallel to traffic, and the span of the deck, which is the girder spacing. It was shown that reducing the FRP reinforcement ratio from 10.7 to 2.7% results in about a 20% reduction in punching shear ultimate load. The ultimate loads obtained for decks with (width/span) aspect ratios of 2.73, 1.33, 0.87, and 0.55 were 100, 94, 83, and 73%, respectively, of the ultimate load of the real condition of infinite width. Finally, the punching shear load decreased by about 18% as the deck span-to-depth ratio increased from 10 to 16.5.

The bending response of sandwich plates with stiff laminated face sheets is studied by a six-noded triangular element having seven degrees of freedom at each node. The element formulation is based on a refined higher-order plate theory having all the features for an accurate modeling of sandwich plates with affordable unknowns. The refined plate theory is quite attractive but suffers from a problem concerned with an interelement continuity requirement when it is used in finite element analysis. The problem has been dealt satisfactorily in this new element, which is applied to the analysis of sandwich plates of different kinds.

This paper is concerned with the elastic buckling problem of circular Mindlin plates with a concentric internal ring support and elastically restrained edge. In solving this problem analytically, the circular plate is first divided into an annular segment and a core circular segment at the location of the internal ring support. Based on the Mindlin plate theory, the governing differential equations for the annular and circular segments are then solved exactly and the solutions brought together by using the interfacial conditions. New exact critical buckling loads of circular Mindlin plate with an internal ring support and elastically restrained edge are presented for the first time. The optimal radius of the internal ring support for maximum buckling load is also found. An approximate relationship between the buckling loads of such circular plates based on the classical thin plate theory and the Mindlin plate theory is also explored.

By considering the total transverse displacement of a sandwich plate as the sum of the displacement due to bending of the plate and that due to shear deformation of the core, a 72 degrees of freedom high precision high order triangular-plate element is developed for the thermal postbuckling analysis of rectangular composite sandwich plates. Due to an uneven thermal expansion coefficient in the two local material directions, the buckling mode of the plate can be changed from one mode to another as the fiber orientation or aspect ratio of the plate is varied. By examining the local minimum of total potential energy of each mode, a clear picture of buckle pattern change is presented. Numerical results show that for a sandwich plate with cross-ply laminated faces, buckle pattern change may occur when the plate has a long narrow shape. However, for sandwich plates with angle-ply laminated faces, the buckling mode is dependent on the fiber orientation and aspect ratio of the plate. The effect of temperature gradient on the postbuckling behavior of the sandwich plate is limited except for angle-ply laminated sandwich plates with fiber angle greater than 70° or less than 20°.

In this technical note, a thin circular plate resting on a two-parameter (Pasternak-type) foundation is studied under concentrated central and distributed loads. The governing equations of the plate are derived for static loading case considering the lift off (uplift) of the plate from the foundation. For the approximate solution, a Galerkin technique is adopted and the free vibration mode shapes of the completely free plate are chosen as the displacement functions. The technique yields a system of algebraic nonlinear equations, and its solution is accomplished by using an iterative method. The numerical results are obtained for evaluation of the behavior of the plate and then given comparatively in figures. Although in the case of a tensionless Winkler foundation, the lift off of the plate from the foundation takes place, when the displacement of plate is negative, while in case of the two-parameter foundation the lift off appears when the slopes of the foundation surface and that of the plate are not equal.

The paper deals with the theoretical investigation of the postbuckling of laminated composite rectangular plates subjected to uniform in-plane temperature. An analytical method based on Chebyshev polynomial is employed. The formulation is based on Reissner–Mindlin plate theory and von Karman nonlinear kinematics. The resulting nonlinear coupled differential equations are linearized using quadratic extrapolation technique. Double Chebyshev finite series is used to discretize the differential equations. An incremental iterative approach is employed for the solution. The effects of temperature dependent mechanical and thermal properties on the limiting/critical temperature and the postbuckling response are studied. The numerical results for different boundary conditions and lamination schemes are presented. Analysis results indicate that temperature dependent properties reduce the critical/limiting temperature and postbuckling strength.

A triangular element based on Reissner–Mindlin plate theory is developed and it is applied to free vibration analysis of plates in different situations. The element has three corner nodes, three mid-side nodes and an internal node at the element centroid where each node contains three usual degrees of freedom (transverse displacement and bending rotations). To make the element free from the shear locking problem, the formulation is done in an efficient manner taking transverse displacement and transverse shear rotations as the field variables. The degrees of freedom of the internal node are condensed out to improve the computational elegance. As the condensation cannot be done with a consistent mass matrix, a lumped mass matrix having no mass contribution at the internal node is used. In this context two mass lumping schemes are proposed where the effect of rotary inertia is considered in one of these schemes. All these features have made the element quite elegant, which is tested with numerical examples ...

The dynamic behavior of an orthotropic plate simply supported on a pair of parallel edges and under a system of moving loads is analyzed based on Lagrange equation and modal superposition. Thin plate theory is assumed for the plate model and no restriction is placed on the type of loading. Parameters of the plate affecting its dynamic behavior are discussed, and a new classification of the plates for computing the mode shapes and natural frequencies is proposed. The impact factors and the dynamic responses of a typical bridge deck are studied using the proposed method. Preliminary results indicate that the effect of eccentric loads on the impact factor depends on the proportion ratio between the flexural and torsional rigidities of the bridge deck, and the multilane loading case is less critical than a single-lane loading case.

Postbuckling analysis is essential to predict the capacity of composite plates carrying considerable additional load before the ultimate load is reached, and manufacturing-induced geometric imperfections often reduce the load-carrying capacity of composite structures. A higher-order finite strip method based on the higher-order shear deformation plate theory is developed for postbuckling analysis of laminated composite plates with initial geometric imperfection subjected to progressive end shortening. The arbitrary nature of initial geometric imperfection induced during manufacturing is accounted for in the analysis. Nonlinear equilibrium equations are solved by a Newton-Raphson procedure. Examples of postbuckling analyses of unsymmetric cross-ply, angle-ply, and arbitrary laminates are presented, and the accuracy and performance of the method are examined. The numerical higher-order finite strip method presented can be used as an accurate and efficient tool for postbuckling analysis of imperfect composite plates.

In this paper a solution to the bending problem of reinforced concrete slab-and-beam structures including creep and shrinkage effect is presented. The adopted model takes into account the resulting in-plane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists of isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral deflection and in-plane deformation to the plate and lateral deflection and axial deformation to the beam, are established using continuity conditions at the interface. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the plate and the beams is taken into account. The solution of the arising plate and beam problems, which are nonlinearly coupled, is achieved using the analog equation method. The adopted model, compared with those ignoring the in-plane forces and deformations, describes better the actual response of the plate-beams system and permits the evaluation of the shear forces at the interfaces, the knowledge of which is very important in the design of prefabricated ribbed plates. The resulting deflections are considerably smaller than those obtained by other models.

The influence of hygrothermal effects on the nonlinear bending of shear deformable laminated plates subjected to a uniform or sinusoidal load is investigated using a micro-to-micromechanical analytical model. The material properties of the composite are affected by the variation of temperature and mositure, and are based on a micromechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory with von Karman-type kinematic nonlinearity, and including hygrothermal effects. A perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The results presented show the effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on the nonlinear bending behavior of the plate.

This paper presents exact axisymmetric bending solutions of circular and annular plates based on the higher-order plate theory of Levinson. The solutions are displayed in terms of the corresponding Kirchhoff (or classical thin) plate solutions. These Kirchhoff-Levinson bending relationships are derived using the mathematical similarity of the governing equations of the two plate theories and the basis of load equivalence. The relationships allow one to readily deduce the more accurate Levinson plate solutions that account for the effect of transverse shear deformation, without having to solve the more complicated Levinson plate equations.

The generalized bending of a large plate with a circular elastic inclusion is discussed here. The solution for a hole or a rigid inclusion, which is the limiting case of an elastic inclusion, has been discussed frequently, but there is little work on an inclusion with arbitrary rigidity. Early investigators solved the problem of a large thin plate with a circular elastic inclusion, subjected to uniaxial bending, balanced biaxial bending, pure twisting, and transverse shear. This work was recently generalized to arbitrary bending loading, and explicit formulas were presented for dimensionless maximum circumferential bending moments in the plate and in the inclusion. This paper solves the analogous problem with Reissner's shear-deformable plate theory. Arbitrary bending loading is considered. A general solution is derived for the governing differential equations. Explicit formulas are developed for the maximum circumferential and radial moments in the plate and the inclusion. The results for four typical lo...

A Ritz-based static analysis procedure is described for fiber-reinforced plastic, skew bridge superstructure, or deck, with a parallel grid core. This is a simplified analysis method based on a transformed plate formulation and the classical Ritz method. The rib core bridge superstructure, or deck, is idealized as a homogeneous, orthotropic skew plate to which the Ritz method is applied to discretize the resultant, equivalent orthotropic skew plate. Three laminated skew plate examples are presented; the results are compared with finite-element solution to verify the validity of the simplified method. A practical demonstration of a rib core skew bridge superstructure is investigated using the simplified method. The procedure provides a useful analysis tool that can be used in the preliminary design stage without the use of finite-element analysis.

The main objective of this research was to investigate the stability analysis of the composite laminated plate-Pasternak-type (two-parameter) foundation interaction and the influence of the second parameter on the critical buckling loads. Two-parameter foundation models are more accurate than the one-parameter (Winkler) foundation model. A functional for thin laminated composite plates was obtained with the proper dynamic and geometric boundary conditions using the Gateaux differential via potential operator concept. The functional was linearized by the incremental formulation, and the necessary steps of the stability analysis for the mixed finite-element method were given. As a special case, if the second parameter was neglected, the mechanical modeling of the foundation using the Pasternak formulation converged to the Winkler formulation. A four-noded quadrilateral, isoparametric, C-sup-0 class element with 4-by-9 degrees of freedom was generated. The independent variables per node were three translations, three membrane forces, and three moments. The element was verified by the numerical studies existing in the literature. It was observed that the influence of the second parameter on the critical buckling loads was noticeable, and the results were closely related to the foundation modeling.

Analytical solutions are obtained for the interior and edge-zone equations of Mindlin-Reissner plate theory in bending of composite circular sector plates laminated of transversely isotropic layers. Circular sector laminates, under various boundary conditions, are considered. It is shown that, depending on the boundary conditions of the laminate, the boundary-layer effect on the response quantities of the laminate will be strong, weak, or nonexistent.

Postbuckling analysis is presented for a simply supported, shear deformable laminated plate subjected to a uniform lateral pressure and thermal loading, and resting on an elastic foundation. The temperature fields considered are associated with a nonuniform tentlike and parabolic distribution over the plate surface. The material properties are assumed to be independent of temperature. The lateral pressure is first converted into an initial deflection, and the initial geometric imperfection of the plate also is taken into account. The formulations are based on Reddy's higher-order shear deformation plate theory and include the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the thermal postbuckling equilibrium paths. The numerical illustrations concern the thermal postbuckling behavior of preloaded antisymmetric angle-ply laminated plates under a tentlike temperature field and symmetric cross-ply laminated plates under a parabolic tem...

This study presents exact relationships between the bending solutions of sectorial plates based on the Kirchhoff (or classical thin) plate theory and the Mindlin plate theory. While the former plate theory neglects the effect of transverse shear deformation, the latter theory allows for this effect, which becomes significant when dealing with thick plates and sandwich plates. The considered sectorial plates have simply supported radial edges, while the circular curved edge may be either simply supported, or clamped or free. The availability of such relationships allow easy conversion of the existing Kirchhoff sectorial plate solutions into the corresponding Mindlin solutions, thus bypassing the need to solve the more complicated bending equations of the Mindlin plates. The use of the relationships is illustrated using some sectorial plate examples, and sample solutions obtained were checked with previous researchers' results and those computed from the software ABAQUS.

Natural frequencies and buckling stresses of a thick isotropic plate on two-parameter elastic foundations are analyzed by taking into account the effect of shear deformation, thickness change, and rotatory inertia. Using the method of power series expansion of the displacement components, a set of fundamental dynamic equations of a two-dimensional, higher-order theory for thick rectangular plates subjected to in-plane stresses is derived through Hamilton's principle. Several sets of truncated approximate theories are used to solve the eigenvalue problems of a simply supported thick elastic plate. To assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress are examined in detail. The distribution of modal transverse stresses are obtained by integrating the three-dimensional equations of motion in the thickness direction. The present approximate theories can accurately predict the natural frequencies and buckling stresses of thick plates on elastic foundations as compared with Mindlin plate theory and classical plate theory.

The nonlinear response of laminated fiber reinforced plastic (FRP) plates modeled with finite elements and excited by stochastic loading is studied. FRPs are being used widely for structural applications in recent years due to their outstanding mechanical properties. Most FRP materials have strong anisotropic properties and exhibit significant nonlinearity in the shear stress-strain law. A high-order shear theory is used to account for the variation of strains through the thickness, since Kirchhoff and Mindlin plate theories are usually inadequate for modeling laminated FRP plates of reasonable thickness. Nonlinear random vibration analysis is performed using the method of equivalent linearization to account for material nonlinearity. A formulation for deterministic dynamic analysis is also developed and performed to verify the accuracy of the approximate nonlinear random vibration method. The random vibration analysis is found to be sufficiently accurate and is considerably more cost-effective than the u...

A large deflection analysis is presented for a rectangular Reissner-Mindlin plate with free edges exposed to a stationary temperature field, subjected to a transverse partially distributed load, and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on the Reissner-Mindlin plate theory, considering the first-order shear deformation effect and including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of moderately thick plates with free edges subjected to combined loading and resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. In this study, the influence is affected by the foundation stiffness, transverse shear deformation, loaded area, plate aspect ratio, and initial thermal bending stress. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.

The problem of finding the buckling load of unilaterally constrained infinite plates is considered. The plates are modeled along the lines of classical plate theory employing Kirchhoff-Love hypotheses. The condition of contact at buckling, which renders the problem to be of the nonlinear eigenvalue type, is resolved by modeling the plate as having two distinct regions, a contacted and an uncontacted region. This results in a problem of the linear eigenvalue type. Simply supported and clamped-free boundary conditions on the unloaded edges are considered. An exact solution for the case of a simply supported plate resting on a rigid foundation is derived. Plates made up of isotropic as well as different orthotropic materials are examined. Due to the constraint on the deformation being one-sided, an increase in the buckling load of approximately 30% over the unconstrained situation is obtained. This study clearly shows that the neglect of unilateral constraints in a plate buckling problem can lead to inaccurate results, which in turn will lead to poor estimates, for example, in assessing the residual compressive stiffness of delaminated plates.

In this paper, the axisymmetric bending analysis of moderately thick circular plates based on the Reissner-Mindlin plate theory is conducted numerically by using the differential quadrature (DQ) method. The governing equations and boundary conditions of the problem are transformed by the DQ procedures into a set of linear algebraic equations, from which the solutions of the problem are determined. Several example plate problems are presented in detail to reveal the convergence characteristics, accuracy, and versatility of the DQ method for the bending analysis of Reissner-Mindlin plates subject to various boundary conditions and loading conditions. The results from the numerical simulations are compared with the exact solutions to validate the accuracy of the DQ method. A comparison between the DQ results and the finite element solutions for the example plate problems is also made.

This paper presents relationships between the buckling loads determined using classical Kirchhoff plate theory and shear deformable plate theories. The latter theories considered are the first-order shear deformation plate theory of Reissner-Mindlin and the third-order plate theory of Reddy. The relationships are exact for isotropic, simply supported polygonal plates under an isotropic inplane load and resting on a Pasternak foundation. Using the relationships, buckling solutions of the Reissner-Mindlin and Reddy plate theories can be readily obtained from known buckling solutions of the Kirchhoff plate theory without the Pasternak foundation.

A stochastic model for the accumulation of fatigue damage in composite laminates subjected to fatigue loading is proposed. Damage accumulation is treated as an evolutionary stochastic process characterized by changes in the components of laminate compliance with the number of load cycles. Compliance changes are modeled as an embedded discrete time, finite state, nonstationary Markov process. Distributions for these changes are used in conjunction with laminated plate theory to derive distributions for the individual ply strains within a laminate. The ply-strain distributions are used to obtain a probabilistic description of the response of the laminate, as well as for input into an appropriate failure criterion to determine the evolutionary probability of failure of a laminate. The applicability of the model is illustrated through a numerical example.

This paper investigates the effect of foundation rigidity on impedance functions for a circular foundation on a viscoelastic soil medium. In addition to vertical and rocking impedances, the paper also investigates the influence on coupling impedance for horizontal and rocking motions of foundation and horizontal impedance. To generate impedance functions for flexible foundation, a substructure technique is used. For the substructure of the flexible foundation, classical plate theory with neglecting inertial force is employed to obtain the deformation of the foundation due to the interaction stress. For the substructure of the soil medium, the technique, which can deal with wave equations in cylindrical coordinates with arbitrarily prescribed boundary conditions, is employed to obtain the displacement field in the soil medium due to the interaction stresses. Then, with the help of the variational principle, the displacement continuity condition of both substructures is imposed to generate the impedances fo...

Based on generalized laminate plate theory (GLPT), the formulation of a one-dimensional laminated beam finite element with layerwise constant shear (BLCS) is presented. BLCS formulation is equivalent to a first-order shear deformation beam theory (Timoshenko beam theory) on each layer, and a cross section of the beam therefore does not necessarily remain plane through the laminate, but only through each layer. Plane stress is assumed through both the thickness and width of the beam in the constitutive equation for a lamina. Details are presented for transforming the layerwise constant shear stresses obtained from constitutive relations into parabolic shear stress distributions. The layerwise representation of in-plane displacement through the thickness results in the formulation of a relatively simple beam element. Numerical analyses are presented for a three-node BLCS element integrated with two Gauss points. The accuracy of the element is evaluated by comparing the predictions to elasticity and experimental results.

The behavior of one‐ply and two‐ply unidirectional cord‐rubber composite plates in pure bending is presented. The model developed takes in account the extension‐twisting coupling of the cord, as well as the exact location of the cord within the composite plate, and the bending stiffness of an individual cord. The Kirchhoff plate assumptions are used as the kinematic relationships for the composite plate. The cord mechanics are based on the work of Costello. The current results are compared to the classical lamination theory results using the material constants of Gough and Tangorra, as well as the constants of Akasaka and Hirano, to show the limits of usefulness for classical lamination theory for this class of composites. The results of the one‐ply composite plate investigations vary significantly from the results of classical lamination theory, especially for cases with large mismatch between the cord and matrix modulus of elasticity.

This note deals with the buckling mode change of antisymmetric angle‐ply laminates on the basis of YNS plate theory. The cusps phenomenon due to the change of buckling mode is presented in the relations of critical buckling loads versus some parameters, such as lamination angle, moduli ratio, aspect ratio, length‐to‐thickness ratio, and boundary condition. An analytical approach is applicable in conjunction with the concept of state‐space to investigate the Levy‐type solution of the title problem. The rank of final matrix, which is used to determine the critical buckling load, has been reduced to half of the relative one given in previous publications due to shifting the location of boundary conditions. Because the rank of matrix is smaller, the computing time is shorter and the calculation is of higher precision.

This study considers thick skew plates under isotropic in-plane pressure based on the Mindlin plate theory. In this study buckling factors for skew Mindlin plates with simply supported and clamped edges have been obtained using the Rayleigh-Ritz method. Although only two boundary conditions are considered due to length limitation, the Ritz functions proposed can readily satisfy any combination of boundary conditions. The method can be used to analyze any general plate shape as well. The study shows that the effect of shear deformation on buckling capacity is more significant for skew plates with relatively large values of thickness-to-width ratios and skew angles.

A hitherto unavailable analytical or strong (differential) form of solution to the boundary‐value problem of a shear‐flexible (moderately thick) rigidly clamped isotropic homogeneous rectangular plate, subjected to transverse loading, is presented. A novel generalized Navier solution technique is developed to solve the three highly coupled second‐order partial differential equations (with constant coefficients) resulting from the application of the first‐order shear deformation theory (FSDT), based on Mindlin hypothesis, in conjunction with the Dirichlet boundary conditions. The assumed solution functions are in the form of double Fourier series, which satisfy the rigidly clamped boundary conditions a priori in a manner similar to Navier's method. Numerical results presented include convergence characteristics of transverse displacement (deflection) and bending moment, and variation of these quantities with respect to aspect ratios. Comparison with the available classical plate theory (CPT) and FSDT‐based...

This paper presents a spline finite element for bending analysis of thin‐plate structures. A new set of B‐spline shape functions is developed for the interpolation of displacements. The element has nine nodes, in the shape of an arbitrary quadrilateral with biquadratic Lagrangian shape functions for geometric interpolation. The classical Kirchhoffs plate theory is used, and the element is formulated through standard displacement approach. Although in recent years, the use of Reissner‐Mindlin plate theory is more popular among researchers, it is believed that for thin‐plate problems, elements based on Kirchhoff's plate theory is more efficient and reliable. The comparison of numerical results of present element with some highly successful Mindlin‐plate elements have favored the argument. The accuracy and validity of the element have also been investigated through the analysis of a representative set of test problems. It is shown that the use of B‐spline shape functions in general two‐dimensional finite ele...

In this paper, a new approach to the development of the transition plate-bending elements with variable midside nodes is presented. These elements will facilitate abrupt changes in mesh refinement between domains consisting of quadrilateral elements. For compatible mesh gradation, special shape functions with slope discontinuity at midside nodes are used. The transition elements are formulated based on the Mindlin-Reissner plate theory to take shear deformation into account. To evaluate the proper element stiffness pertinent to shear, the substitute shear strain polynomials in Cartesian coordinates are constructed. A modified Gaussian integration is adopted to eliminate the slope discontinuity problem in the element domain. Some numerical examples are presented that illustrate the validity and effectiveness of these transition elements for the efficient analysis of plate-bending problems.

This study presents a relationship between the buckling loads of sectorial plates based on the Kirchhoff (or classical thin) plate theory and the Mindlin plate theory. Whereas the former plate theory neglects the effect of transverse shear deformation, the latter plate theory allows for it. This effect becomes significant when dealing with moderately thick plates and sandwich plates. The relationship allows easy and accurate deduction of the buckling loads of the Mindlin plates from their corresponding Kirchhoff solutions.

This note shows that the strain energy of a plate suffers a finite jump when the boundary contour of the plate is subject to a change, however small, from a smooth curve to a piecewise linear curve, if either the displacement or the slope, both of which are prescribed, is homogeneous at every point along the plate boundary. The proof is based on an observation that the plate strain energy depends linearly on Poisson’s ratio when the lateral load, the boundary displacement and slope are specified. It also makes use of a previous result that the Gaussian curvature term in plate strain energy is a discontinuous functional of the boundary contour, and extends the theorem to that of the plate strain energy itself. This note suggests that this singular behavior may result from a discontinuous dependency of the solution to plate equation on small changes of the domain of existence.

This study presents a derivation of an exact relationship between the deflection values of a simply supported Mindlin plate and the corresponding simply supported Kirchhoff plate. The relationship is valid for any polygonal plate shape and transverse loading condition. Based on this relationship, the deflection due to the shear deformation effect in plates can be easily calculated from Kirchhoff plate solutions without the necessity of a more complicated shear-deformable-plate analysis. This exact relationship ought to be useful as a basis for the development of practically meaningful results for plates with other boundary and loading conditions, and may serve to check numerical values computed from thick-plate analysis software.

A refined theory for the bending of plates with moderately large deflections is proposed. The presented theory is an extension of the technical theory of plates for small strains. The plate theory presented by Voyiadjis and Baluch incorporates rotatory inertia. The proposed equations governing the bending of plates take into account all transverse effects including the transverse normal strain. The transverse normal strain is introduced through a transverse displacement function w, whose distribution through the thickness of the plate is explicitly obtained on physical grounds as a function of z. Using the proposed nonlinear refined theory, the problem of straight‐crested waves in an infinite plate is solved. The results obtained using the proposed theory are compared to those of Lamb's exact solution and Mindlin's theory. The presented nonlinear theory of plates is also compared to a number of technical plate theories in cylindrical bending.