Showing papers on "Plate theory published in 1979"

Finite element analysis of stress intensity factors for plane extension and plate bending problems

Abstract: This paper deals with the finite element calculation of the stress intensity faactors for plane extension and plate bending problems. On the basis of the plate theory including the effect of transverse shear deformation, the influences of plate thickness, crack length and plate width on the stress intensity faotors are investigated. The numeriacal analyses are carried out using the superposition method of analytical and finite element solutions. It is found that the present stress intensity factors calculated for cracked plates under plane extension as well as bending compare favorably with the analytical ones.

Shear Correction Factors for Laminated Plates

Abstract: S HEAR deformations are considered in laminated plate theory in terms of correction factors ktj (or k-j) and modified shear stiffnesses K^ — k^A^ = k-jA^; (ij = 4,5), where AJJ (or A-J) are obtained from assumed "constant strain (or stress)" fields.1 This work reports the correction factors, obtained by matching cutoff frequencies for propagation of thickness shear waves (ratio of wavelength X to plate thickness H approaching infinity) predicted by plate and elasticity theories. Contents For an exact elasticity solution, the stiffness matrix relating tractions to displacements on the surfaces of each layer is expressed as a function of shear moduli and frequency.2 Cutoff frequencies co/2 for the first two modes dominated by strains yxz and yyz, respectively, are calculated such that determinant of the global stiffness matrix goes to zero. k'n are then evaluated as Kn/A'u, where

Nonlinear Stress-Strain Response of Laminated Composites

Abstract: This paper presents a simplified method of predicting the nonlinear stress-strain curves upt to the tensile and compressive failures for an unidi rectionally orthotropic lamina, symmetric biaxial and triaxial laminates. The analytical procedure is based on the classical Laminated Plate Theory (L.P.T.). With applying L.P.T. to the small sress or strain increments of the stress-strain curve, nonlinear stress-strain curve is continuously predicted for various laminates. Comparisons are made between analytical predic tions and experimental results. As the results, the nonlinear stress-strain curves for various cases could be estimated and the results have consider ably good agreement with experimental ones.

The Interaction between a Uniformly Loaded Circular Plate and an Isotropic Elastic Halfspace: A Variational Approach

Abstract: The axially symmetric flexural interaction of a uniformly loaded circular plate resting in smooth contact with an isotropic elastic halfspace is examined by using an energy method. In this development the deflected shape of the plate is represented in the form of a power series expansion which satisfies the kinematic constraints of the plate deformation. The flexural behavior of the plate is described by the classical Poisson-Kirchhoff thin plate theory. Using the energy formulation, analytical solutions are obtained for the maximum deflection, the relative deflection, and the maximum flexural moment in the circular plate. The results derived from the energy method are compared with equivalent results derived from numerical techniques. The solution based on the energy method yields accurate results for a wide range of relative rigidities of practical interest.

Thermal residual stresses in filament-wound carbon-fiber-reinforced composites

Abstract: Explicit algebraic expressions are first proposed to predict easily and precisely the thermal-expansion coefficients of unidirectional reinforced plastics. They are given as functions of the thermal and elastic properties of the constituent materials and of the fiber-volume fraction. They are derived by considering circular anisotropic fibers arranged in a hexagonal array in a matrix. Then, analytical expressions are derived for the thermal-expansion coefficients and curing stresses in filament-wound laminated composites under the assumption of elastic behavior and within the framework of laminated plate theory. Experiments on carbon-fiber/epoxy composite cylinders reinforced by helical and circumferential windings show good agreement with the calculated values. The residual stresses induced by curing are found not to be negligible compared with the low tensile strength transverse to the fibers. Such algebraic expressions for thermal coefficients, together with those for elastic moduli and failure criteri...

The Problem of an Inclined Crack in an Orthotropic Strip

Abstract: The elastostatic problem for an infinite orthotropic strip containing crack was considered. It was assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack was located along an axis of orthotropy, hence, at an arbitrary angle with respect to the sides of the strip. The general problem was formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes 1 and 2 stress intensity factors were calculated for the strip having an internal or an edge crack with various lengths and angular orientations.

The derivation of dual extremum and complementary stationary principles in geometrical non-linear shell theory

Abstract: In non-linear elasticity dual extremum principles can be formulated for some class of elastic deformations, for which uniqueness of the solution is assured. These results are used in the present paper to derive extremal variational principles for geometrical non-linear shells with moderate rotations. Furthermore two complementary variational principles are considered, which are stationary principles without any extremum property. The proposed theorems are valid also for the special cases of linear plates and shells, for the non-linear von Karman plate theory and for non-linear Donnell-Marguerre type shells.

Large deflection static and dynamic analysis of isotropic and orthotropic annular plates

Abstract: In the present paper, Chebyshev series are employed to obtain the non-linear static and dynamic response of isotropic and orthotropic annular plates. The non-linear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the Chebyshev series in the space domain and the Houbolt numerical integration scheme in the time domain. Two different sets of boundary conditions of the annulus are investigated and detailed numerical results have been obtained for different cases of orthotropy and geometry.

Application of a simplified method of calculating longitudinal moments to the Ontario highway bridge design code

Abstract: A manual method for calculating the design live load longitudinal moments in superstructures of most right bridges is presented. The bridge types that can be analysed by this method are: slab bridges, beam and slab bridges incorporating both steel and concrete beams, bridges incorporating wooden beams, and slabs on hollow trapezoidal or other such torsionally stiff beams.The proposed method was developed by orthotropic plate theory, and was checked by the grillage analogy method. The basis of the method and details of development methodology are presented. The effect of the various parameters on the transverse distribution of longitudinal moments is discussed.The method is useful not only for the ease with which design longitudinal moments can be obtained, but also because it enables the designer to investigate the effects of making changes in the design on distribution characteristics.To demonstrate the simplicity of the solution a worked example is included.

Experimental determination of the nonlinear shear behavior of fiber-reinforced laminae under impact loading

Abstract: A procedure is developed for the experimental determination of the nonlinear shear behavior of fiber-reinforced composites by testing angle-ply laminates. It is shown that, for the E glass/epoxy used in this work, the popular ±45 deg specimens fail prematurely due to transverse stresses, thus limiting the range for which the shear stress-strain curve can be obtained. By selecting an appropriate fiber orientation, ±41 deg in the present work, premature failure can be prevented and the nonlinear shear response can be obtained almost to shear failure. The experimental program involved four groups of tensile specimens (±30 deg, ±35 deg ±41 deg and ±45 deg) tested under impact conditions using a drop weight testing machine. Analysis was performed using classical plate theory and an incremental loading procedure. Some problems involved in conducting dynamic tests are discussed and a solution is presented.

Vibrations of Annular Plates of Variable Thickness

Abstract: An exact solution for the circular frequencies of a polar orthotropic annular plate of uniform and parabolic thickness under the action of in-plane forces is presented. The annular plate is reinforced with simply supported edge beams at both the inner and outer boundaries. The edge beams are subjected to uniform, radial compressive loadings. Frequency parameters are determined for both axisymmetric and higher modes and are found to be functions of the in-plane loads, plate dimensions and rigidities, edge beam stiffness and moment of inertia parameters, and the profile of the plate. The use of edge beams in this investigation provides a practical method of simulating various types of edge conditions for the polar orthotropic annular plate — including the limiting cases of the simply supported and clamped edge.

Moving load on initially stressed thick plates attached together by a flexible core

Abstract: Vibrations of an infinitely long, prestressed double strip-plate system are studied analytically. The plates are attached together by a flexible core and one of the plates is subjected to a line load which moves with a constant speed along the plate. The constant, uniform prestresses are parallel to and perpendicular to the infinite edges of the plates. The solution is presented within the framework of a plate theory which includes the effects of shear deformation and rotary inertia. Critical characteristic parameters of the system are defined. An example is provided where the bending moments of the plates are calculated. From the results of theoretical analysis, it becomes evident that the prestresses in the system have considerable effect upon the dynamic behaviour of the system.

Impact Induced Stress Waves in an Anisotropic Plate

Abstract: Stress wave propagation in an anisotropic plate due to impact forces has been examined. The plate is modeled as a number of identical anisotropic layers. Mindlin's approximate theory of plates is applied to each layer to obtain a set of difference-differential equations of motion with use of the interlaminar stresses and displacements as explicit variables. Dispersion relationships for harmonic waves are found when traction-free boundary conditions are applied to both surfaces of the plate and appropriate correction factors are found. The difference-differential equations are reduced to difference equations via integral transforms. With given impact boundary conditions, these equations are solved for an arbitrary number of layers in the plate and the transient propagation of stress waves is calculated by means of a Fast Fourier Transform algorithm.

On the Stiffening Effect of Hat-Shaped Stiffeners on a Plate

Abstract: The object of this research is to clarify the stiffening effect of relatively large-sized hat-shaped stiffeners on a plate which are often utilized in FRP ship constructions. In the previous reports, both the bending and buckling deformation of a fundamental single stiffener model was described and it was shown that the lower width of a hat-shaped stiffener is the most important parameter in view of the stiffening effect on a plate. It was also shown that a simple model considering the rotational spring constant of a stiffener web gives a good explanation of the local buckling mode as well as the bending deformation of a fundamental symmetric structural model.One of the main structural characteristics of a hat-shaped stiffener is that the effect of its torsional rigidity cannot be neglected since it is attached to a plate along two separated lines and makes a closed section. In this report, an analytical model considering two joint lines of stiffener webs to a plate is proposed to modelize the stiffening effect of the torsional rigidity of a hat-shaped stiffener on the bending deformation of a plate.In the first part of this report, the bending deformation of a unidirectionally stiffened plate is analyzed by means of Ritz method on a simply supported orthotropic plate with a single or double hat-shaped stiffeners under uniform lateral load and compared with detailed finite strip analyses. It is shown that the stiffening effect depends greatly on the position on a plate where a stiffener is attached and that the effective torsional rigidity is reduced by the cross-sectional deformation of a stiffener.In the second part of this report, the bending deformation of a stiffened plate with multiple hat-shaped stiffeners is analyzed and compared with an equivalent orthotropic plate model using an effective torsional stiffness. It is made clear that the deformation behavior cannot be well explained by the conventional equivalent rigidity method on a stiffened plate with multiple hat-shaped stiffeners.

Acoustical behavior of thick, composite, fluid-loaded plates, calculated using Timoshenko-Mindlin plate theory

Abstract: : The reflected and radiated acoustic fields of a thick, composite plate of infinite extent, consisting of a substrate layer bonded at an interface to a coating layer, which has fluid on one side and which is unconstrained on the other side, are calculated theoretically. The reflected and radiated acoustic fields are related by means of a structural response function that completely characterizes the elastic behavior of the composite plate and of the fluid. The composite-plate acoustical problem is analyzed by extending the Timoshenko-Mindlin theory of thick homogeneous plates. The Timoshenko-Mindlin thick-plate equations are used to describe the flexural waves generated in each of the two layers of the composite plate, owing either to a plane acoustic wave in the fluid impinging on the plate or to a point-force excitation of the plate. Two ideal types of bonding between the coating and the substrate are considered: the 'welded' bond, for which contiguous plate elements on either side of the interface move in complete unison, and the 'perfectly slipping' bond, for which such plate elements move in unison normal to the interface but independently parallel to the interface. The analytic form of the structural response function of a composite plate shows that in general a thick bilaminar composite plate of the type considered cannot be modeled by a simple homogeneous thick plate with artificial or 'average' material constants. The analysis also shows that the bond between the substrate and the coating significantly affects the acoustic reflection and radiation characteristics of the composite plate. (Author)

Frequency analysis of thick orthotropic plates on elastic foundation using a high precision triangular plate bending element

Abstract: A high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees-of-freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.

Assemblage Method for Folded-Plate Analysis

Abstract: A method is proposed for the elastic analysis of isotropic or orthotropic folded plate structures. In this method, harmonic functions that satisfy the boundary condition in the longitudinal direction are used in conjunction with exponential functions for the transverse direction. Stiffness matrices for both bending and in-plane actions have been developed for a plate with an orthotropic elastic property, and by dividing the folded plate structure into a number of plate elements bounded geometrically by lines of fold. Any combination of loadings may be considered. After obtaining the joint displacements, the stresses and displacements at any point of the structure are readily calculated. A special digital computer program is developed for the analysis.

Vibration of a plate having a circular inside edge and a cornered outside edge consisting of arcs

Abstract: This paper is concerned with a transverse vibration problem of a thin plate having a circular inside edge and a cornered outside edge consisting of some arcs. The classical plate theory is applied and the eigenvalue problem of the plate is solved by the use of the exact solution of the equation of motion which satisfies the inner boundary conditions. The boundary conditions at the outer edge are satisfied by means of the Fourier expansion method. Numerical calculations are carried out for a plate having a clamped circular inside edge and a free outer one consisting of three arcs. Experimental results are also given as an additional check of this analysis.