Showing papers on "Bending of plates published in 1993"
TL;DR: In this article, a finite element formulation for vibration control of a laminated plate with piezoelectric sensors/actuators is presented, and the static responses of a bimorph beam are calculated.
Abstract: A finite element formulation for vibration control of a laminated plate with piezoelectric sensors/actuators is presented. Classical laminate theory with the induced strain actuation and Hamilton's principle are used to formulate the equations of motion. 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 four-node, 12-degreeof-freedom quadrilateral plate bending elements with one electrical degree of freedom. The piezoelectric sensor is distributed, but is also integrated since the output voltage is dependent on the integrated strain rates over the sensor area. Also, the piezoelectric actuator induces the control moments at the ends of the actuator. Therefore, the number, size, and locations of the sensors/actuators are very important in the control system design. By selective assembling of the element matrices for each electrode, responses with various sensor/actuator geometries can be investigated. The static responses of a piezoelectric bimorph beam are calculated. For a laminated plate under the negative velocity feedback control, the direct time responses are calculated by the Newmark-/? method, and the damped frequencies and modal damping ratios are derived by modal state space analysis.
464 citations
TL;DR: In this article, the results obtained from this theory are compared with those obtained from a full-fledged three-dimensional elasticity analysis and various equivalent single-layer theories that are available, such as the classical laminated plate theory (CLPT), the first-order shear deformation laminated plates theory (FSDPT), and the third-order Shear Deformation Plate theory (THSDPT).
Abstract: Reddy's layerwise theory is used. The results obtained from this theory are compared with those obtained from a full-fledged three-dimensional elasticity analysis and various equivalent single-layer theories that are available. These include the classical laminated plate theory (CLPT), the first-order shear deformation laminated plate theory (FSDPT), and the third-order shear deformation plate theory (THSDPT). The elasticity equations are solved by utilizing the state space variables and the transfer matrix
230 citations
TL;DR: In this article, the authors investigated the post-buckling behavior of steel plate shear walls under monotonic loads and cyclic loads and found that the postbuckling strength of a steel plate can be several times the theoretical buckling strength.
Abstract: In current design practice the capacity of a steel‐plate shear wall is limited to the elastic buckling strength of its plate panels. This practice results not only in a conservative design, but also in an undesirable one where the columns yield and may buckle before the plate reaches a fraction of its capacity. Plate buckling is not synonymous with failure and if the plate is adequately supported along its boundaries, as in the case of the shear wall, the postbuckling strength can be several times the theoretical buckling strength. Furthermore, due to the unavoidable out‐of‐plane imperfections, no change in the plate behavior will be observed at the theoretically calculated buckling load. Although the post‐buckling behavior of plates under monotonic loads has been under investigation for more than half a century, this behavior under cyclic loading has not been investigated until recently. One test was conducted at the University of Alberta and 10 tests were conducted at the University of Maine. In this pa...
188 citations
TL;DR: In this article, a new four-node, 12-d.o.f. quadrilateral plate bending element called DKMQ was presented for the analysis of thin and thick plates.
Abstract: This is the second part of a two-part paper on plate bending elements with shear effects included.
This paper presents a new four-node, 12-d.o.f. quadrilateral plate bending element valid for the analysis of thick to thin plates. The element called DKMQ, has a proper rank (contains no spurious zero-energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates by the element. An extended DKT element for thick-plate bending analysis is evaluated in Part I.19
149 citations
TL;DR: In this paper, a simple plate bending triangle with good performance in both thin and thick situations was developed, and its performance was better than that of other nine DOF elements and its computer implementation simpler.
Abstract: The formulation and shape functions given in Part I are extended to develop a simple plate bending triangle with good performance in both thin and thick situations. Indeed, its performance is better than that of other nine DOF elements and its computer implementation simpler. When used with selective reduced integration, the element produces identical results as that of Xu.1,2 To save space, details given in Part I are not repeated and some results are also presented in the figures of Part I.
136 citations
TL;DR: In this article, the von Karman type non-linear plate model was used to deal with the large amplitude vibrations of imperfect antisymmetric angle-ply and symmetric cross-ply laminated plates.
92 citations
TL;DR: In this paper, a general quadrilateral multilayered anisotropic plate element is formulated on the basis of a refined third-order shear deformation plate theory, which makes use of a displacement field that fulfils a priori the geometric and stress continuity conditions at the interfaces between the layers.
90 citations
TL;DR: In this paper, a general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented, which is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of a deflection gradient along the sides using a finite volume-like approach.
Abstract: A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.
88 citations
TL;DR: In this article, both the Trefftz direct and indirect approximations of the Kirchhoff plate bending problem were studied, in which non-singular, complete complete trefftz functions were used as the weighting and/or trial functions.
Abstract: Kirchhoff plate bending problems were studied by both the Trefftz direct and indirect approximations in which non-singular, complete Trefftz functions are used as the weighting and/or trial functions. The Trefftz direct method involved only the quantities of engineering interest. Numerical results are given to show the efficiency and the excellent accuracy of the present method.
74 citations
TL;DR: In this paper, the elastic constants of an orthotropic material were determined by studying the free vibrations of a rectangular plate in completely free boundary conditions, based on series expansions of the deformed plate shape and requiring the boundary conditions to be satisfied.
63 citations
TL;DR: In this paper, a complete set of equations for describing the mechanical and electrical behavior of a piezoelectric medium is given, and the electromechanical equations describing the dynamical behavior of discrete PZTs and their mounting plate are derived.
Abstract: The complete set of equations for describing the mechanical and electrical behavior of a piezoelectric medium is given. From these equations, the electromechanical equations describing the dynamical behavior of discrete PZTs and their mounting plate are derived. The electromechanical equations are used to explain active damping with the PZTs as actuators and an accelerometer as the sensor. The active damping model is applied to a more realistic case. The transverse displacement and the plate vibration damping are calculated using the electromechanical equations and compared with the experimental results. A comparison of the open loop transverse displacement of the plate as a function of the applied PZT voltage with the corresponding experimental case shows good agreement. The damping of the plate vibration is found to be approximately 20 dB for both the calculation and the corresponding experiment when the plate is driven at the lowest modal plate frequency. A sensor equation describing the output of a PZT used as a sensor is derived with the PZT terminated with an arbitrary impedance. Using the sensor equation, a concise and unified approach is developed for constructing both active and passive damping methods. Two limiting active damping cases (the terminal impedance zero or infinity) and one passive damping case are considered using the sensor equation. A useful design guide for the corresponding active and passive damping methods is determined.
TL;DR: For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy as mentioned in this paper.
Abstract: For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy It is shown that the strain energy release rate for the Reissner's plate approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small By using this result, the limiting expression of the stress intensity factor can be explicitly obtained For general problems, the modified crack closure method is shown to be an efficient tool for evaluating the strain energy release rates from which the stress intensity factor can be calculated Both the classical plate element and the Mindlin plate element are investigated, and the applicability of the classical plate element is evaluated Because the stress-free conditions along the crack face lead to inter-penetration of the plate, a line contact model is assumed to investigate the closure effect using Reissner plate theory Closure at the compressive side is shown to reduce crack opening displacement and consequently the stress intensity factors When closure is considered, the strain energy rate based on the Reissner plate theory converges to the classical plate solution This is similar to the nonclosure case
TL;DR: In this paper, the mean square estimates on transverse displacement and normal stress/strain by the equivalent linearization technique were obtained for the singlemode prototype model of Galerkin representation.
Abstract: At elevated temperatures the dynamics of vibrating plate (or shell) must include the three thermal effects: (i) the global expansion by uniform plate temperature, (ii) the local expansion by temperature variation over the plate, and (iii) the thermal moment induced by temperature gradient across the plate thickness. For the single-mode prototype model of Galerkin representation, (i) and (ii) give rise to the combined stiffness that is responsible for thermal buckling, whereas (iii) contributes to the combined forcing of acoustic and thermal excitations. For the high-temperature sonic fatigue test facility at the Wright Lab, the present study is devoted to the mean square estimates on transverse displacement and normal stress/strain by the equivalent linearization technique.
TL;DR: In this paper, the authors present a theory for laminated plates in which each lamina exhibits monoclinic symmetry about its own midplane, and the elastic constants used in the plate analysis are obtained in closed form from the through-the-thickness analysis, along with approximate, closed-form three dimensional distributions of displacement, strain, and stress.
Abstract: This method is a technique by which the geometrically nonlinear, three dimensional analysis of plate deformation can be split into a linear, one dimensional, through-the-thickness analysis and a nonlinear, two dimensional, plate analysis. The elastic constants used in the plate analysis are obtained in closed form from the through-the-thickness analysis, along with approximate, closed-form three dimensional distributions of displacement, strain, and stress. The development of such a theory is presented herein for laminated plates in which each lamina exhibits monoclinic symmetry about its own midplane
TL;DR: In this article, the analytical solution of thermally induced cylindrical bending of layered elastic plates is obtained for a sinusoidal temperature distribution along the span and constant and linear variations across the thickness of the plate.
TL;DR: In this article, the general theory of isoparametric spline finite strip for analysis of plane structures is outlined, and the method, when applied to most problems, yields a relatively narrow band matrix and requires little computational effort.
TL;DR: In this article, a finite strip method is described for the analysis of the geometrically non-linear elastic response of composite laminated, orthotropic prismatic plate structures subjected to progressive uniform end shortening.
TL;DR: In this paper, a finite element analysis of the large deflection behavior of stiffened plates using the isoparametric quadratic stiffened plate bending element is presented, based on Mindlin's hypothesis.
TL;DR: In this article, the free vibration and static stability of a rectangular plate with localized zones of damage is studied using a finite element analysis, and the influence of parameters such as size of damage, extent of damage and position of damage on vibration and instability behavior are discussed.
TL;DR: In this paper, a procedure to analyze a stiffened plate system consisting of a plate supported by a network of steel girders is presented, which is commonly used for highway bridge decks and building-floor systems.
TL;DR: In this article, a plate partial differential equation is reduced to an ordinary differential equation and the resulting plate characteristic functions are very good approximations to the normal modes of the plate.
Abstract: Natural frequency coefficients of rectangular plates and the corresponding plate characteristic functions are obtained by reduction of plate partial differential equation to an ordinary differential equation and solving it exactly. The reduction is carried out by assuming a deflection shape in one direction consistent with the boundary conditions and applying Galerkin’s averaging technique to eliminate the variable. The reduction method, commonly known as Kantorovich method, is applied sequentially on either directions of the plate and iterated until convergence is achieved for the natural frequency coefficients. The resulting plate characteristic functions are very good approximations to the normal modes of the plate. The results are tabulated for plates with combination of clamped, simply-supported, and free edge conditions.
TL;DR: Sandman et al. as discussed by the authors analytically studied active control of sound radiation from a simply supported rectangular fluid-loaded plate, where the plate is assumed to be excited by a point force at subsonic frequencies.
Abstract: Active control of sound radiation from a simply supported rectangular fluid‐loaded plate is analytically studied. The plate is assumed to be excited by a point force at subsonic frequencies. The solution to the plate motion is based on the admissible functions for an in vacuo homogeneous plate, which is also the basis for Fourier decomposition of the fluid loading [B. E. Sandman, J. Acoust. Soc. Am. 61, 1502–1510 (1977)]. Feed‐forward control is carried out by using point forces applied to the plate. The amplitudes of the control forces are determined by the optimal solution of a quadratic cost function that integrates the far‐field radiated acoustic pressure over a hemisphere in the radiation half‐space. The results show that for subsonic disturbances, a high global reduction in radiated pressure is possible. For on‐resonant excitations, a reasonable sound reduction can be achieved with up to two properly located active control forces, and for off‐resonant excitations, up to four control forces may be ne...
TL;DR: In this paper, several different ways of defining the boundary element system of equations are proposed, and compared among them, emphasizing some interesting behaviours that can be considered to improved numerical solutions.
Abstract: This paper is related to the applications of BEM to practical plate bending problems in engineering. Some aspects of the boundary formulations are shown, describing particular characteristics that can be considered to improved numerical solutions. Several different ways of defining the boundary element system of equations are proposed. Comparisons among them are also shown emphasizing some interesting behaviours.
TL;DR: In this article, the authors studied the contact problem of an isotropic square plate indented by a rigid spherical indentor and found that the contact area was either a circle or a hypotrocoid of four lobes featuring a shorter length of contact along the through-the-corner directions of the plate.
TL;DR: In this paper, a quadrilateral hybrid stress element with two translational and one rotational degrees of freedom at each corner is presented, where the rotational degree of freedom provides factual torsional stiffness.
Abstract: A quadrilateral plane element for analysis of spatial structures is often formulated by combining a plane stress (membrane) element with two translational inplane degrees of freedom at each corner to a plate bending element with two rotational degrees of freedom and one translational (normal to the plane of element) at each corner. An additional rotational degree of freedom normal to the plane of the element and a fictitious torsional spring are added at each corner. This brings the total corner nodal degrees of freedom to three rotations and three translations and makes the element usable for general spatial structures. A quadrilateral hybrid stress element with two translational and one rotational degrees of freedom at each corner is presented in this paper. When used as the membrane constituent of a shell element, the rotational degree of freedom provides factual torsional stiffness. The element matrices are derived by minimization of a functional consisting of displacement and stress fields. Allman's ...
TL;DR: In this article, a three dimensional analytical model to compute the deflection, stresses, and eigen values in the rotor blades is proposed using bending triangular plate finite element, both membrane and bending stiffness are considered in deriving the element stiffness matrix.
TL;DR: In this paper, a survey on theoretical solutions to elastoplastic treatments in failure mechanics, in which the plastic zones are simulated as slip bands, is presented, and experimental studies are discussed on plastic-strain localization in thin layers near cracks.
Abstract: A survey is presented on theoretical solutions to elastoplastic treatments in failure mechanics, in which the plastic zones are simulated as slip bands. Some experimental studies are discussed on plastic-strain localization in thin layers near cracks. Two-dimensional treatments of plastic band growth in bodies with cracks are considered for the conditions of planar stress, planar strain, and longitudinal shear, together with the corresponding axisymmetric and three-dimensional treatments. A note is also made of papers in which the plasticity band model is used for the bending of plates and shells containing cracks.
TL;DR: In this paper, the analysis of vertical oscillations of a flexible circular plate on the surface of an elastic half-space and an elastic layered system by the ring method is presented.
TL;DR: A modern theory of thin elastic plates with transverse shear deformation where the disturbance is represented by a train of harmonic waves and it is shown that uniqueness for exterior problems is guaranteed for a range of flexural waves.
Abstract: In this paper, the authors present a modern theory of thin elastic plates with transverse shear deformation where the disturbance is represented by a train of harmonic waves. Dirichlet- and Neumann-type problems are formulated together with appropriate radiation conditions (in the case of the exterior domain). The paper shows that uniqueness for exterior problems is guaranteed for a range of flexural waves. In the interior problems, the presence of eigenfrequencies means that there is no general uniqueness result. The paper also indicates how corresponding results can be proved for micropolar plates.
TL;DR: In this article, a substructure method is presented for analysis of the free vibration of a rectangular plate with mixed edge boundary conditions, which involves the partitioning of the entire plate domain into appropriate elements to approximate the deflection function of each element by a set of admissible orthogonal polynomials.