Showing papers on "Plate theory published in 1983"
TL;DR: In this article, the upper and lower bounds of elastic stiffness and compliance constants of woven fabric composites are derived, based upon a mosaic-like model as well as the assumptions of constant stress and constant strain.
Abstract: The upper and lower bounds of elastic stiffness and compliance constants of woven fabric composites are derived, based upon a mosaic-like model as well as the assumptions of constant stress and constant strain. An approximate analysis taking into account fiber undulation and continuity also is conducted. Fiber undulation leads to a slight softening of the in-plane stiffness and does not affect the stretching/bending coupling constants. A transverse shear deformation is adopted and modified to examine the one-dimensional bending response of fabric composites. The results of a two-dimensional finite element analysis are in good agreement with the predictions of the in-plane, coupling, and bending constants based upon the fiber undulation, mosaic, and transverse shear deformation theory, respectively. The effect of fiber undulation shape on the in-plane compliance also is investigated.
327 citations
TL;DR: In this article, a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense) was used to calculate frequencies, static response and dynamic response under applied loads.
Abstract: Forced motions of laminated composite plates are investigated using a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense). The present results when specialized for isotropic plates are found to be in good agreement with those available in the literature. Numerical results of the nonlinear analysis of composite plates are presented showing the effects of plate thickness, lamination scheme, boundary conditions, and loading on the deflections and stresses. The new results for composite plates should serve as bench marks for future investigations. mation are assumed to remain straight and normal to the midsurface after deformation (i.e., transverse shear strains are zero), has been used to calculate frequencies, static response, and dynamic response under applied loads. Recent studies in the analysis of plates have shown that the effect of the transverse shear strains on the static and dynamic response of plates is significant. For example, the natural frequencies of vibration predicted by the classical plate theory are 25% higher, for plate side-to-thickness ratio of 10, than those predicted by a shear deformation theory (SDT). In transient analysis of plates the classical plate theory predicts unrealistically large phase velocities in the plate for shorter wavelengths. The Timoshenko beam theory,3 which includes transverse shear and rotary inertia effects, has been extended to isotropic plates by Reissner 4'5 and Mindlin,6 and to laminated anisotropic plates by Yang et al.7 A generalization of the von Karman nonlinear plate theory for isotropic plates to include the effects of transverse shear and rotary inertia in the theory of orthotropic plates is due to Medwadawski,8 and that for anisotropic plates is due to Ebcioglu.9 With the increased application of advanced fiber composite material to jet engine fan or compressor blades, and in high performance aircraft, studies involving transient response of plates made of such materials are needed to assess the capability of these materials to withstand the forces of impact due to foreign objects (e.g., the ingestion of stones, nuts and bolts, hailstones, or birds in jet engines). Previous in- vestigations into the linear transient analysis of composite plates include Moon's10'11 investigation of the response of infinite laminated plates subjected to transverse impact loads at the center of the plate; Chow's12 study of laminated plates (with transverse shear and rotary inertia) using the Laplace transform technique; the Wang et al. 13 investigation, by the method of characteristi cs, of unsymmetrical orthotropic laminated plates; and Sun and Whitney's14'15 study of plates under cylindrical bending. More recently, the present author16'17 investigated the linear transient response of layered anisotropic composite rectangular plates and presented extensive numerical results for center deflection and stresses.
166 citations
TL;DR: In this paper, an improved displacement methodology based on Mindlin theory is developed and applied to a four-node, twelve degrees-of-freedom quadrilateral element, with special attention directed toward enhancement of the transverse shear energy representation.
152 citations
TL;DR: In this article, a 54 degree-of-freedom, high-order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems.
Abstract: A 54 degree-of-freedom, high-order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems. The finite element formulation is based on Kirchhoffs theory of thin plates. The quasisteady aerodynamic theory is used. Numerical solution procedures are presented. The limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped, respectively. The effects of in-plane compressive force, mass ratio, and in-plane edge stress free condition are considered. Stress distributions for the limit cycle oscillation of a two-dimensional panel are plotted. For the case of panels under static pressure differential, the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels, respectively. The effect of biaxial in-plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region, dynamically stable buckled region, and the limit cycle oscillation region are found. Alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement.
81 citations
TL;DR: In this article, the von Karman equations for orthotropic plates were used to determine the parameters required to establish postbuckling behavior, and it was found that only two new parameters are needed beyond those required for buckling.
Abstract: The nonlinear large deflection equations of von Karman are written for 'specially' orthotropic plates. The equations are then manipulated to determine the parameters required to establish postbuckling behavior. It is found that only two new parameters are needed beyond those required for buckling. By assuming trigonometric functions in one direction, the plate equations are converted into ordinary nonlinear differential equations which are solved numerically using a two point boundary problem solver that makes use of Newton's method. The postbuckling behavior is obtained for simply supported and clamped, long, rectangular, orthotropic plates covering the complete range of dimensions and material properties.
80 citations
TL;DR: A method for the numerical analysis of rectangular plates based on Mindlin's theory is presented in this paper, where any two opposite edges are assumed to be simply supported in the present analysis.
Abstract: A method for the numerical analysis of rectangular plates based on Mindlin's theory is presented. Any two opposite edges are assumed to be simply supported in the present analysis. A variety of boundary conditions including the mixed and the nonhomogeneous types can be specified along either of the remaining two opposite edges. Numerical results are presented for four examples. The present results clearly show the discrepancies in the results of the usual thin plate theory. Some of the problems associated with the use of the thin plate theory based on Kirchhoff's assumptions are clarified. Finally it is shown that the present segmentation method which is based on the numerical integration of the governing equation system is efficient, economical, reliable, and very accurate in such applications.
58 citations
TL;DR: In this article, a theoretical study of elastic buckling modes of I-section beams under various loading conditions is presented, based on energy considerations and the energy equations governing instability are derived using plate theory to allow for distortion of the cross-section.
Abstract: A theoretical study of the elastic buckling modes of I-section beams under various loading conditions is presented. The analysis is based on energy considerations and the energy equations governing instability are derived using plate theory to allow for distortion of the cross-section. The resulting analysis is able to predict lateral, local and distortional buckling modes. The results are compared with classical lateral buckling solutions based on beam theory.
49 citations
TL;DR: In this article, an optimal selective integration rule was found for the 4-node quadrilateral plate bending element, which requires 2 × 2 Gaussian integration for bending energy and 1 × 2 and 2 × 1 rules for the shear energy terms from (θ x - w,x) and (�y - w-y), respectively.
Abstract: A clearer understanding of the problems associated with reduced integration and optimum integration schemes for the development of Mindlin plate elements is presented. It is shown that an optimal selective integration rule can be found for the 4-node quadrilateral plate bending element which requires 2 × 2 Gaussian integration for bending energy and 1 × 2 and 2 × 1 rules for the shear energy terms from (θ x - w,x) and (θy - w,y), respectively. This will give an element of correct rank, without any zero energy mechanisms and without shear locking in the thin plate limit, and better performance in moderately thick situations than the currently available 4-node quadrilaterals using one-point shear integration or modified one-point shear integration due to Hughes et al. The effects of arbitrary orientation of the grid and the non-rectangular form of element are discussed.
48 citations
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TL;DR: In this article, the authors derived analytical expressions for the displacements and stresses due to loading of a floating, uniform, elastic plate of arbitrary thickness by a plane or axisymmetric harmonic load.
Abstract: Analytical expressions are derived for the displacements and stresses due to loading of a floating, uniform, elastic plate of arbitrary thickness by a plane or axisymmetric harmonic load. The solution is exact except for assumptions of small strains and linear boundary conditions, and gravitation within the plate is neglected. For typical earth parameters its predictions are comparable to those of the usual thin plate theory frequently assumed in studies of lithospheric flexure, gravity and regional isostasy. Even for a very thick lithosphere, which may exist in some regions of Mars, the thin plate theory is a better approximation to the thick plate solution than the elastic half-space limit, except for short-wavelength loads.
47 citations
TL;DR: In this article, an elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source and the scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions.
38 citations
28 Nov 1983-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, the authors considered the nonlinear and linear thermomechanical theories of deformable shell-like bodies in which account is taken of electromagnetic effects, and the development is made by a direct approach with use of the two dimensional theory of directed media called Cosserat surfaces.
Abstract: This paper is concerned with the nonlinear and linear thermomechanical theories of deformable shell-like bodies in which account is taken of electromagnetic effects. The development is made by a direct approach with use of the two-dimensional theory of directed media called Cosserat surfaces . The first part of the paper deals with the formulation of appropriate nonlinear equations governing the motion of shell-like bodies in the presence of electromagnetic and thermal effects, as well as a general discussion of appropriate constitutive equations and symmetry restrictions. In the second part of the paper, attention is confined to special or more restrictive nonlinear and linear theories of shells including, for example, the nonlinear membrane theory, a restricted nonlinear bending theory (corresponding to the classical Kirchhoff-Love theory of shells) and a plate theory, all in the presence of electromagnetic effects. Finally, in the third part of the paper, attention is confined to specific topics, e.g. piezoelectricity in elastic plates and electromagnetic effects in a non-conducting plate, and a demonstration of the relevance and the applicability of the present direct formulation of a theory of electromagnetism for shell-like bodies.
01 Jan 1983
TL;DR: In this article, the problem of minimizing the static compliance of a solid elastic plate, for given total plate volume, is considered, and the existence of solutions in the case of a design space consisting of thickness functions for an isotropic, homogeneous plate is identified as being caused by the nonclosedness of the corresponding set of responses (deflections).
Abstract: The problem of minimizing the static compliance of a solid elastic plate, for given total plate volume, is considered. Nonexistence of solutions in the case of a design space consisting of thickness functions for an isotropic, homogeneous plate is identified as being caused by the nonclosedness of the corresponding set of responses (deflections). It is shown that existence can be obtained if a bound on the gradient of the thickness function is imposed. It is also shown that this restriction of the design space ensures the existence of solutions to a broad class of plate optimization problems, static as well as dynamic.
TL;DR: In this article, the transverse displacement of a statically loaded, rectangular plate with arbitrary boundary conditions specified on the remaining edges is generalized to the case when transverse shear deformation is taken into account.
TL;DR: In this paper, a constrained theory of shells in the presence of small strain accompanied by moderate rotation is presented, which accounts for the effect of transverse normal strain and includes, of course, the special case (corresponding to the Kirchhoff-love theory of the shells) in which the effect is absent, and a complete theory is formulated with the use of linear constitutive equations.
Abstract: This paper is concerned with a constrained theory of shells in the presence of small strain accompanied by moderate rotation. The constrained theory accounts for the effect of transverse normal strain and includes, of course, the special case (corresponding to the Kirchhoff-Love theory of shells) in which the effect of transverse normal strain is absent. After precise estimates for (local) moderate rotation and relative displacement gradients in terms of infinitesimal strain have been effected, a complete theory is formulated with the use of linear constitutive equations. The nature of the complete theory is further examined when initially the shell-like body is a plate; and it is shown that our kinematical formulae (strain-displacement relations), as well as the relevant differential equations of the theory in the absence of the effect of transverse normal strain, systematically reduce to those used in the von Karman plate equations. Also, in the light of the present results, an assessment of kinematical aspects of previously developed theories of shells undergoing small strain and moderate rotation is indicated.
TL;DR: In this article, the authors derive a 7th order system of one-dimensional equations for finite deformations of prismatical beams including the effect of warping stiffness, which is based on the classical derivation of finite-deflection plate theory.
Abstract: We derive a seventh order system of one-dimensional equations for finite deformations of prismatical beams including the effect of warping stiffness. The analysis is patterned after the classical derivation of finite-deflection plate theory, supplemented by an explicit consideration of transverse shear deformation. A problem of axially uniform stretching and twisting is considered as an illustration.
TL;DR: In this article, the Fourier coefficients in the expansions representing the transverse deflection and rotations of normals to the plate midsurface are analyzed for both Mindlin's plate theory and a new plate theory, which allows for warping of transverse sections of the plate.
TL;DR: In this article, a finite strip formulation which allows to treat bridges, axisymmetric shells or plate structures of constant transverse cross-section in an easily and unified manner is presented.
TL;DR: In this paper, the combined effects of the aerodynamic and structural types of damping on the flutter boundaries for simply supported panels in high supersonic Mach number flows are investigated.
Abstract: The idea of a unified panel flutter theory, investigated previously by the author, is amplified to make the inclusion of damping effects possible. The paper attempts to study the combined effects of the aerodynamic and structural types of damping on the flutter boundaries for simply supported panels in high supersonic Mach number flows. Classical plate theory and two-dimensional first-order aerodynamics are used. A closed-form rather than modal approach is used in the solution of the partial differential equation in the analysis to avoid convergence problems. The standing and traveling wave theories of panel flutter are compared. The dual nature of damping (stabilizing and destabilizing) is exposed. While the trends are similar to those already established for isotropic panels, the variables compared are generically defined to account for both the isotropic as well as the orthotropic properties of the panels.
TL;DR: In this paper, an approximate solution for the motion of an infinite elastic plate, excited by a vertical force and by a moment in the vertical plane (with the axis of the moment parallel to the plate), was derived from a three-dimensional approach.
TL;DR: In this paper, generalized ray theory for a thick plate driven by a step function point force is compared with experimental waveforms obtained on a glass plate using an improved piezoelectric displacement sensing transducer.
Abstract: Waveforms calculated by generalized ray theory for a thick plate driven by a step‐function point force are compared with experimental waveforms obtained on a glass plate using an improved piezoelectric displacement‐sensing transducer.
TL;DR: In this article, the axially symmetric problem of a finite circular plate loaded at its center by a smooth, rigid punch is solved by superposing an infinite layer elasticity solution with a pure bending plate theory solution.
TL;DR: A theory unifying the flutter analyses of orthotropic and isotropic panels having very low aspect ratios and exposed to an inviscid potential flow on the upper surfaces is developed in this article.
Abstract: A theory unifying the flutter analyses of orthotropic and isotropic panels having very low aspect ratios and exposed to an inviscid potential flow on the upper surfaces is developed. The analysis considers an infinitely long panel of finite width, simply supported on the side edges, and resting on a spring foundation. Three-dimensional linearized aerodynamic and classical plate theories are used. Traveling wave modes are utilized as solutions to the panel's aeroelastic equation of motion. The resulting aerodynamic integral is evaluated approximately using both numerical and analytical methods. The structural and aerodynamic generic variables, which are instrumental in establishing this unified theory, are derived using affine transformations. Subsonic as well as supersonic flutter and divergence boundaries are determined. The effects of air to panel mass ratios and midplane forces are examined. Viscous structural damping is found to be destabilizing. There is a general agreement between the results of this analysis and those obtained for isotropic panels by previous investigators.
TL;DR: In this article, the free transverse vibrations of an isotropic nonhomogeneous infinite plate of variable thickness have been studied on the basis of classical plate theory, and the governing differential equation of motion has been solved by Frobenius method by expressing the transverse displacement as an infinite series.
Abstract: The free transverse vibrations of an isotropic nonhomogeneous infinite plate of variable thickness have been studied on the basis of classical plate theory. The governing differential equation of motion has been solved by Frobenius method by expressing the transverse displacement as an infinite series. The frequencies corresponding to the first two modes of vibration are computed for different values of thickness variation constant, nonhomogeneity parameter, and different combinations of boundary conditions.
01 Jul 1983
TL;DR: In this article, two approaches to determine the dynamic response of beams and plates to loads which are extreme within a certain class of admissible loads are suggested. And the optimality of design is then determined by standard numerical techniques.
Abstract: Studies are conducted to determine the dynamic response of beams and plates to loads which are extreme within a certain class of admissible loads. Two approaches to this problem are suggested. In approach one, Pontryagin's maximality principle is regarded as an additional constraint. The optimality of design is then determined by standard numerical techniques. The "adjoint variable approach' to sensitivity of structural design is applied for a given inhomogeneous term. The inhomogeneous term is an extremal element of admissible load vectors, which constitute a closed subspace of a Sobolev space. Again, the maximality principle is invoked. While only beam and plate theory problems are used as examples, generalizations are easy to perceive.
01 Jan 1983
TL;DR: In this paper, the authors used the statically measured contact law of contact between the steel ball and the graphite/epoxy laminate to compute the dynamic contact force and found that use of this contact law in conjunction with the finite element modeling of the laminate yields excellent agreement with the experimental results.
Abstract: Harmonic wave and wave front propagations in a graphite/epoxy laminate are investigated using a plate theory that includes transverse shear deformation. Transient waves produced by impact of a steel ball are studied experimentally and by using finite elements. The statically measured law of contact between the steel ball and the laminate is used in the finite element program to compute the dynamic contact force. It is found that use of this contact law in conjunction with the finite element modeling of the laminate yields excellent agreement with the experimental results.
TL;DR: In this article, the Lighthill theory has been extended to describe the sound generated by turbulence near an elastic wall, and the case of a thin elastic slab with identical fluid in contact with both faces is investigated in detail by solving the elastic equations in the slab together with the acoustic boundary-layer equations in fluid, with all stresses and displacements continuous across the fluid-elastic interface.
TL;DR: In this article, a wheel disc with a flat web was considered and the eigenfrequencies and mode shapes of the wheel were calculated with the assumption that a fixed point on the rim is connected elastically to the rail.
TL;DR: In this paper, the radiation efficiency of an edge-clamped circular plate, which is vibrating flexurally in one of its natural modes and is mounted in an infinite baffle, is theoretically determined from the total power radiated to the far field.
01 Jan 1983
TL;DR: In this article, the buckling of moderately thick, rectangular CFRP plates is described, with their loaded edges being clamped and with simple supports provided just inboard of the unloaded edges.
Abstract: An investigation of the buckling of moderately thick, rectangular CFRP plates is described. The plates are subjected to uniform uniaxial compression, with their loaded edges being clamped and with simple supports provided just inboard of the unloaded edges. The investigation comprises both experimental and theoretical work. Details of the test procedure are given first and these relate to the buckling of four laminated plates, two of the cross-ply and two of the angle-ply type. Brief description is then given of a finite strip method of calculating the buckling loads which is based on the use of Mindlin plate theory and hence takes account of transverse shear effects. Finally, the measured and calculated buckling loads are recorded and compared.