Showing papers on "Plate theory published in 1981"
612 citations
01 Jan 1981
TL;DR: In this article, the authors developed composite relations for the variation of the heat transfer coefficient along the plate surfaces, and the mathematical development and verification of such composite relations as well as the formulation and solution of the optimizing equations for the various boundary conditions of interest constitute the core of the presentation.
Abstract: While component dissipation patterns and system operating modes vary widely, many electronic packaging configurations can be modeled by symmetrically or asymmetrically isothermal or isoflux plates. The idealized configurations are amenable to analytic optimization based on maximizing total heat transfer per unit volume or unit primary area. To achieve this anlaytic optimization, however, it is necessary to develop composite relations for the variation of the heat transfer coefficient along the plate surfaces. The mathematical development and verification of such composite relations as well as the formulation and solution of the optimizing equations for the various boundary conditions of interest constitute the core of this presentation.
481 citations
TL;DR: In this article, the problem of maximizing the integral stiffness of solid elastic plates described by thin plate theory is considered and an efficient and quite general numerical algorithm by means of which a number of stationary solutions for rectangular and axisymmetric annular plates with various boundary conditions are obtained.
389 citations
TL;DR: In this paper, the plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered and the problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form.
Abstract: The plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. The transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. The plate theory not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results.
216 citations
TL;DR: In this article, the eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2 ϵ, are shown to converge (in a specific sense) to the 2-dimensional biharmonic operator of plate theory, as ϵ approaches zero.
92 citations
TL;DR: In this article, a series-type method was applied to the free vibration of an orthotropic rectangular plate with mixed boundary conditions, where one, two or three parts are constrained along the boundary of the square plate, and the effects of varying constraint and orthotropic parameters on the natural frequencies and mode shapes were studied.
58 citations
01 Nov 1981
TL;DR: In this paper, an improved transverse shear deformation theory for laminated anisotropic plates under bending is presented, which eliminates the need for an arbitrarily chosen shear correction factor.
Abstract: An improved transverse shear deformation theory for laminated anisotropic plates under bending is presented. The theory eliminates the need for an arbitrarily chosen shear correction factor. For a general laminate with coupled bending and stretching, the constitutive equations connecting resultants with average displacements and rotations are derived. Simplified forms of these relations are also obtained for the special case of a symmetric laminate with uncoupled bending. The governing equation for this special case is obtained as a sixth-order equation for the normal displacement requiring prescription of the three physically natural bounday conditions along each edge. For the limiting case of isotropy, the present theory reduces to an improved version of Mindlin's theory. Numerical results are obtained from the present theory for an example of a laminated plate under cylindrical bending. Comparison with results from exact three-dimensional analysis shows that the present theory is more accurate than other theories of equivalent order.
57 citations
TL;DR: In this article, a description of a versatile method of analysis of sound waves generated at a junction of plates as a result of a wave incident on any one of the plates is given.
56 citations
TL;DR: In this paper, the authors proposed a new plate model, where a uniform plate is equipped with an infinite number of infinitely thin integral stiffeners, and numerical and analytical investigations of a new formulation of the minimum compliance design problem for thin, solid, elastic plates are carried out.
46 citations
TL;DR: In this paper, a plane wave is incident onto a finite plate set in a rigid baffle, and the scattered field is examined in the limit when fluid-plate coupling effects are large.
Abstract: A plane wave is incident onto a finite plate set in a rigid baffle, and the scattered field is examined in the limit when fluid-plate coupling effects are large. An asymptotic solution is obtained, matching an outer region with inner regions at either edge of the plate. Waves are found to be present on the flexible surface, and resonance is shown to occur for particular values of the plate half-length, a. Away from a resonance, the leading term in the expansion of the outer potential is the solution of the boundary value problem in the absence of the plate. As a resonance is approached, however, eigensolutions, with singularities at the plate edges, also become present at this order.
TL;DR: In this paper, a finite-element analysis of the large deflection bending of annular plates with variable thickness is presented, where the more general Reissner plate equations as well as von Karman plate equations are used in the formulation.
TL;DR: A survey of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plate subject to such constraints as fundamental frequency maximization, can be found in this paper.
Abstract: A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.
TL;DR: In this paper, the proper ratio of beamwidth-to-beam-depth is used to determine whether the bent structural element can be considered as a beam and, if not, what is the correction factor that should be used with the simple beam formula.
Abstract: Formulas associated with simple beam or plate theories are used extensively in structural design, to determine You's modulus, and to determine fracture strength of brittle nonmetallic materials. The question may arise as to whether the proper ratio of beam-width-to-beam-depth is such that the bent structural element can be considered as a beam and, if not, what is the correction factor that should be used with the simple beam formula. These questions are answered for a range of structural metallic and brittle nonmetallic materials.
01 Jan 1981
TL;DR: In the usual applications of elastic plate theory to mascon loading problems, a number of assumptions have been made whose consequences on the final results have not been fully in- vestigated.
Abstract: In the usual applications of elastic plate theory to mascon loading problems, a number of assumptions have been made whose consequences on the final results have not been fully in- vestigated. We examine some of these assumptions here. Two modifications of the elastic thin plate theory have been made to account for the depth dependence of the rheology and for any lateral variation in the flexural ridigity of the lithosphere. Viscoelastic and elastic-viscoelastic layers over an inviscid media have also been considered. These modifications can significantly perturb the surface stress distribution from that predicted by the thin plate theory. The use of the latter for estimating the thickness of the lithosphere, by relating predictions of the stress field to surface evidence of stress, can lead to significant underestimation of the real thickness of the outer stress-bearing layer of the moon.
01 Jan 1981
TL;DR: In this article, a finite element method has been utilized to conduct the stress analysis of the laminate with a loaded fastener hole, where the hole is assumed to be filled with a rigid core, simulating a bolt, and displacement boundary conditions are applied at the semicircular contact surface.
Abstract: Composite laminates with a through-the-thickness fastener hole, free or loaded, have been treated for stress and strength analysis under uniaxial tensile loading conditions. This investigation has been carried out within the framework of laminated plate theory. A finite element method has been utilized to conduct the stress analysis of the laminate with a loaded fastener hole. For this case the hole is assumed to be filled with a rigid core, simulating a bolt, and displacement boundary conditions are applied at the semicircular contact surface. The strength analysis is based on the tensor polynomial failure criterion applied to each ply. The results for a free hole boundary condition are obtained by using closed form solutions. An approximation procedure is suggested to calculate stress levels for multidirectional laminates using the stress fields in individual ply laminate systems. This procedure works for both the loading conditions. The strength predictions for the loaded hole case are close to the experimental results.
TL;DR: The efficiency of a transient dynamic plate bending solution procedure based on the use of Mindlin plate elements with a central difference time stepping scheme is improved by suitably modifying the rotatory inertia terms in the diagonalized mass matrix.
Abstract: The efficiency of a transient dynamic plate bending solution procedure based on the use of Mindlin plate elements with a central difference time stepping scheme is improved by suitably modifying the rotatory inertia terms in the diagonalized mass matrix.
01 Jun 1981
TL;DR: In this article, a half-scale model of a 50 ft by 30 ft four-beam bridge was constructed to study the feasibility of post-tensioning existing single span steel beam concrete deck bridges.
Abstract: Following a literature review and field inspection, a half-scale model of a 50 ft by 30 ft four-beam bridge was constructed to study the feasibility of strengthening existing single span steel beam concrete deck bridges. The model was instrumented with electrical resistance strain gages and deflection dial gages. During four constructional stages the model was loaded and its performance recorded. Two types of static loading were utilized for testing: 5-kip and 10-kip weights, as individual concentrated loads placed at points on the center line or quarter-point line, and an eccentric three axle truck load simulated by means of hydraulic jacks. During the composite stages, post-tensioning was applied in various sequences either to the exterior beams only or to all of the beams. In addition to testing of the model bridge, both half-scale and full-scale post-tensioning brackets were tested to failure. Brackets were designed for placement above as well as below the bottom flanges on beams. Strain gage data were collected through a data acquisition system, punched on paper tape and then organized and corrected by means of FORTRAN computer programs. Some conclusions are as follows: (1) Post-tensioning can be used to provide strengthening for composite bridges. (2) Post-tensioning need not be applied symmetrically to the beams. (3) A post-tensioning strengthening design requires check of flexural stresses at five different locations within a span: the two post-tensioning bracket locations, the two cover plate cutoff points, and the midspan section. (4) When post-tensioning only exterior beams, 2/3 of the force (for a four-beam bridge) affects the exterior beams. Therefore, more force must be applied to compensate for post-tensioning distributed to the remainder of the bridge. (5) Post-tensioning did not significantly affect the overall load distribution characteristics of the bridge. (6) Orthotropic plate theory may be used to predict approximate distribution of post-tensioning axial forces and moments. Further conclusions relate to cracking, effect of low curbs, diaphragms, and brackets.
TL;DR: In this article, the elementary theory of the bending of thin plates which forms the basis of the analysis in Ref. is restricted to the maximum plate deflection being less than about the plate thickness.
TL;DR: In this article, the authors model the laminated composite as a multilayered plate each layer being made of a different material and develop a laminate plate theory by application of the minimum complementary energy theorem in variational calculus such that the qualitative threedimensional character of the crack edge stresses is retained while approximations are made in a quantitative sense on the stress intensity factor.
TL;DR: In this article, the distribution of the stresses in a cylindrically orthotropic plate with a circular hole was studied for the case when the plate was subjected to uniform uniaxial traction.
Abstract: The equations governing the distribution of the stresses in a cylindrically orthotropic plate with a circular hole are solved for the case when the plate is subjected to uniform uniaxial traction. Closed-form solutions are given for the circumferential stresses along the edge of the hole.
TL;DR: In this paper, the necessary and sufficient optimality conditions are derived for a mean compliance design when the potential energy is to be maximized with an upper bound imposed on the total structure cost.
Abstract: Large deflections plate theory with shear effects taken into account is first discussed. Next the necessary and sufficient optimality conditions are derived for a mean compliance design when the potential energy is to be maximized with an upper bound imposed on the total structure cost. The strain energy is assumed to depend on a set of design parameters o representing dimension and configuration variables of cross sectional members. Particular forms of the optimality conditions are discussed for some cases. A specific example of optimal design of a sandwich beam undergoing large deflections is presented in detail.
TL;DR: In this article, the authors derived the input admittance of a plate using the Mindlin's plate equation taking into account rotatory inertia and finite shear stiffness, and compared the calculated results with measurements, and found that the real part of the admittance is similar to the well-known result from Kirchhoff's plate theory; only at higher frequencies does one find differences depending on the size of the exciting area.
TL;DR: In this paper, the elastic instability of a uniformly compressed, thin, circular annular plate with axisymmetric initial deflection was studied. But the authors focused on the axismmetric deformation of the plate.
Abstract: This paper presents a theoretical study of the elastic instability of a uniformly compressed, thin, circular annular plate with axisymmetric initial deflection. The dynamic version of the nonlinear Marguerre plate theory is used, and the linear free vibration problems around the axisymmetric finite deformation of the plate are solved by a finite difference method. By examining the frequency spectrum with various asymmetric modes, the critical compressive load under which the axisymmetric additional deformation of the plate becomes unstable due to the bifurcation buckling is determined, which is found to depend severely on the magnitude of the axisymmetric initial deflection.
01 Jan 1981
TL;DR: In this article, the authors apply the asymptotic expansion method to the nonlinear, three-dimensional, equations for the equilibrium of elastic plates under suitable loads and appropriate boundary conditions.
Abstract: The asymptotic expansion method, with the thickness as the parameter, is applied to the nonlinear, three-dimensional, equations for the equilibrium of elastic plates under suitable loads and appropriate boundary conditions. It is shown that the leading term of the expansion is a solution of a system of equations equivalent to a well-known two-dimensional nonlinear plate model, namely the von Karman equations. The existence of solutions of the two-dimensional problem is established in all cases (by contrast with the three-dimensional model, where no satisfactory existence theory is as yet available). It is also shown that the displacement and the stress corresponding to the leading term of the expansion have the specific form generally assumed a priori in the usual derivations of two-dimensional plate models. In particular, the displacement field is of Kirchhoff-Love type. This approach clarifies in particular the nature of the admissible three-dimensional boundary conditions for a given two-dimensional plate model. A discussion is also given regarding the class of admissible three-dimensional models.
01 Jan 1981
TL;DR: In this paper, an economical elastic-plastic laminated finite element is formulated by combining the theory of plasticity for homogeneous materials with the classical laminated plate theory, and the outcome is a plate element, rectangular by choice, capable of representing the flexural behaviour of the laminated system.
Abstract: The need for elastic-plastic flexural analysis of ductile composites continues to grow with the development of new laminated systems and applications which, in turn, often require more demanding performance specifications. To address this need, an economical elastic-plastic laminated finite element is formulated by combining the theory of plasticity for homogeneous materials with the classical laminated plate theory. The outcome is a plate element, rectangular by choice, capable of representing the flexural behaviour of the laminated system.
Patent•
28 May 1981TL;DR: An element for bending or hardening a movable plate in a plastic state is described in this paper, where the surface has a plurality of bending profiles taken in a plane at right angles to the direction of movement of the plate.
Abstract: An element for bending or hardening a movable plate in a plastic state. The element has a surface adapted to contact the plate where the surface has a plurality of bending profiles taken in a plane at right angles to the direction of movement of the plate. Means are provided to rotate the element in the plane in order to vary the radius of curvature of the surface contacting the plate.