Showing papers on "Bending of plates published in 1985"
Book•
01 Jun 1985
TL;DR: In this paper, the authors present a review of elementary mechanics of materials and their application in the field of energy engineering, including failure and failure criteria, stress, principal stresses, and strain energy.
Abstract: 1. Orientation, Review of Elementary Mechanics of Materials. 2. Stress, Principal Stresses, Strain Energy. 3. Failure and Failure Criteria. 4. Applications of Energy Methods. 5. Beams on an Elastic Foundation. 6. Curved Beams. 7. Elements of Theory of Elasticity. 8. Pressurized Cylinders and Spinning Disks. 9. Torsion. 10. Unsymmetric Bending and Shear Center. 11. Plasticity in Structural Members. Collapse Analysis. 12. Plate Bending. 13. Shells of Revolution with Axisymmetric Loads. 14. Buckling and Instability. References. Index.
1,200 citations
TL;DR: In this article, a 4-node plate bending element for linear elastic analysis is presented, as a special case, from a general nonlinear continuum mechanics based four-node shell element formulation.
Abstract: This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.
1,000 citations
TL;DR: In this article, a higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia.
629 citations
TL;DR: In this paper, a higher-order deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads, and applications of the element to bending, vibration and stability of laminated plates are discussed.
Abstract: A higher-order deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.
364 citations
TL;DR: In this article, two simple and improved models were developed to calculate impact force and duration during low velocity impact of circular composite plates, including the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations.
Abstract: Two simple and improved models--energy-balance and spring-mass--were developed to calculate impact force and duration during low velocity impact of circular composite plates. Both models include the contact deformation of the plate and the impactor as well as bending, transverse shear, and membrane deformations of the plate. The plate was transversely isotropic graphite/epoxy composite laminate and the impactor was a steel sphere. Calculated impact forces from the two analyses agreed with each other. The analyses were verified by comparing the results with reported test data.
300 citations
TL;DR: A multilayered anisotropic flat plate element which includes the effects of the transverse shear deformation is developed by making use of the displacement formulation as mentioned in this paper, which is a rectangle with 32 degrees of freedom.
135 citations
TL;DR: In this paper, the influence of the initial deflection on the performance of the plate, especially on the ultimate strength has been clarified, and two methods, a deflection method for thin plates and a curvature method for thick plates, have been formulated and they have been shown to predict the final strength of plates with very good accuracy.
127 citations
01 Jan 1985
106 citations
TL;DR: In this paper, the authors derived finite element stiffness matrices using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element.
68 citations
TL;DR: In this paper, the stiffness matrix for the DKT plate-bending element is formulated explicitly in a global co-ordinate system, which avoids transformations of stiffness, and elasticity properties for anisotropic materials, from local to global coordinates.
Abstract: The stiffness matrix for the DKT plate-bending element is formulated explicitly in a global co-ordinate system. This approach avoids transformations of stiffness, and elasticity properties for anisotropic materials, from local to global co-ordinates, which were required in previous formulations. A FORTRAN listing of the algorithm is appended for potential users.
64 citations
TL;DR: In this paper, a beam characteristic orthogonal polynomials in Rayleigh-Ritz formulation was constructed as the simplest polynomial that satisfies all the boundary conditions of the corresponding beam problems accompanying the plate problem.
Abstract: Bending deflection of plates under static loading has been determined using beam characteristic orthogonal polynomials in Rayleigh‐Ritz formulation. The first member of the orthogonal polynomial set was constructed as the simplest polynomial that satisfies all the boundary conditions of the corresponding beam problems accompanying the plate problem. The rest of the set was generated using the Gram Schmidt orthogonalization process. Results are obtained for plates with all edges clamped and those with three edges clamped and one edge free. Two types of loadings, uniform and hydrostatic, are considered. The results are found to agree closely with those obtained by previous methods. Since the Gram Schmidt orthogonalization process can include a weight function also, even plates with nonuniform properties can be studied using this method.
TL;DR: In this paper, an integral equation formulation for finite deflection analysis of thin elastic plates is presented, based on general nonlinear differential equations which are equivalent to the von Karman equations and by virtue of generalized Green identities.
TL;DR: In this article, a nine-node isoparametric quadrilateral element is developed to model laminated plates under initial deformation and initial stress according to the Mindlin plate theory and von Karman large deflection assumptions.
TL;DR: In this article, the temperature distribution during flame bending of a plate is studied using a distributed heat source moving along the plate surface at a constant speed, where the numerical solution of the partial differential equation describing the heat conduction in the plate is solved using the finite-element program ADINAT in the transient analysis mode.
Abstract: The flame bending of metal hull plates involves a complex thermoplastic process. In order to investigate the thermoplastic behaviour it is first necessary to determine the time-varying temperature field in the plate. In this paper the temperature distribution during flame bending of a plate is studied using a distributed heat source moving along the plate surface at a constant speed. The temperature distribution is determined by the numerical solution of the partial differential equation describing the heat conduction in the plate as the distributed heat source passes. The equation is solved using the finite-element program ADINAT in the transient analysis mode. A number of results are presented to illustrate the transient behaviour of the temperature near the plate edge as well as the quasi-steady-state temperature distribution. The results are shown to be in qualitative agreement with published experimental data. Additional studies are presented to clarify the influence on the temperature distribution from different material parameters, torch parameters and plate thickness.
TL;DR: In this article, the steady state response to a sinusoidally varying force is determined for a viscoelastically point-supported square or rectangular plate, where the transverse deflection of the plate is written in a series of the product of the deflection functions of beams parallel to the edges, and the response equation is derived by the generalized Galerkin method.
TL;DR: In this article, the authors investigated the harmonic flexural vibration of a rectangular plate with an arbitrarily located rectilinear crack and derived the square root singularities of the bending moment at the crack's tips.
TL;DR: In this paper, an evaluation of skew sensitivity of thirty three plate bending elements covering nineteen finite element systems was performed and the results showed that many elements are very sensitive to the skew angle.
TL;DR: In this article, a finite element technique is described which produces a sequence of improved solutions for static analysis of plate bending problems, which is applied to both bending and stretching problems for which solutions were available from the literature.
Abstract: A finite element technique is described which produces a sequence of improved solutions for static analysis of plate bending problems. Adaptive mesh refinement is used to improve an initially uniform mesh which was generated from boundary geometry only. Emphasis is placed upon producing high-quality results using only a single refinement. The method is applied to both bending and stretching problems for which solutions were available from the literature.
TL;DR: In this paper, the authors used large deflection theory to determine when wrinkling occurs in a simply supported circular elastic plate loaded at the center by a spherical punch, and calculated that elastic wrinkling occurred in thin plates (a/h > 80) when ( a 2 / Rh > 8) where a is the plate radius and R is the punch radius.
TL;DR: In this article, the elastic reciprocal theorem is used to generate necessary conditions which the prescribed data at the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for the case of axisymmetric stretching and torsion of a circular plate when stress or mixed conditions are prescribed at the plate edge.
Abstract: The stretching of flat plates is investigated by methods first introduced by the authors in the context of plate bending. The elastic reciprocal theorem is used to generate necessary conditions which the prescribed data at the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for the case of axisymmetric stretching (and torsion) of a circular plate when stress or mixed conditions are prescribed at the plate edge. The conditions which any interior solution must satisfy at the plate edge are then deduced. As an example we obtain the complete interior solution (correct to within exponentially small error) for the problem of a simply supported thick circular plate under a concentrated load. It is shown conclusively that applications of Saint-Venant's principle lead to wrong corrections to the Kirchhoff thin plate theory.
TL;DR: In this article, a new three-noded triangular element for plate bending is described, which is based on an earlier stress-smoothed triangular element due to Razzaque, but extra internal bubble functions are included to make it more flexible.
Abstract: A new three-noded triangular element for plate bending is described. The element is based on an earlier stress-smoothed triangular element due to Razzaque,1 but extra internal ‘bubble’ functions are included to make it more flexible. The accuracy of the new element is compared with that of a number of other high-performance triangular elements. It is concluded that the present element and that due to Hansen, Bergan and Syvertsen2 are the two most accurate triangular thin plate elements currently available. The extra lines of FORTRAN required to convert Razzaque's shape function subroutine to that for the new element are given, thus making the new element easy to implement in any general-purpose finite element program.
TL;DR: In this article, the von Karman-type non-linear bending of an unsymmetrically laminated angle-ply rectangular plate under lateral load has been analyzed for various high-modulus materials, aspect ratios, geometries of lamination and boundary conditions.
Abstract: This paper is analytically concerned with non-linear bending of an unsymmetrically laminated angle-ply rectangular plate under lateral load The plate edges are subjected to the varying rotational constraints A series solution satisfying the von Karman-type non-linear equations and the required boundary conditions of the plate is presented In the formulation the edge moments are replaced by an equivalent lateral pressure near the plate edges Governing equations are reduced to a set of algebraic equations Numerical results for maximum deflection, bending moment and inplane force of unsymmetric angle-ply plates are graphically presented for various high-modulus materials, aspect ratios, geometries of lamination and boundary conditions Present results are also compared with available data
TL;DR: In this paper, a plate bending element, labeled DKL (for Discrete Kirchoff element with Loof nodes), with the same nodal configuration as a triangular Semiloff plate element, but not formulated through the isoparametric concept is presented.
TL;DR: In this article, a quasi-conforming element (QCE) technique is introduced for calculating penalty finite element problems, which uses multiple sets of functions to approximate strains and is independent of the integration order.
TL;DR: In this paper, the equations governing the bending of plates, taking into account the influence of transverse normal strain, are recast into a form involving the average transverse displacement function, w. The resulting sixth order bending system of equations is solved for the Levy-type plates, with a variety of boundary conditions considered in the direction orthogonal to the simply supported direction.
Abstract: The equations governing the bending of plates, taking into account the influence of transverse normal strain, are recast into a form involving the average transverse displacement function, w. The resulting sixth order bending system of equations is solved for the Levy-type plates, with a variety of boundary conditions considered in the direction orthogonal to the simply supported direction. Results are tabulated for the displacement, w, together with the plate moments M\dx and M\dy. Comparisons are made to corresponding quantities as obtained from the classical plate theory and the shear deformation theory where available.
TL;DR: In this paper, a two-dimensional slow viscous flow in a region bounded by a plane wall and an inclined semi-infinite flat plate at a distance is investigated on the basis of Stokes' approximation.
Abstract: Two-dimensional slow viscous flow in a region bounded by a plane wall and an inclined semi-infinite flat plate at a distance is investigated on the basis of Stokes' approximation. The motion is caused by the translation of the plane wall parallel to itself. A formal expression for the flow is obtained by solving a pair of simultaneous Wiener-Hopf equations. Streamlines and stress distributions on the plate are determined by evaluating the formal expression. The case in which the flow is caused by a pressure difference between up- and down-stream infinity with the plane wall at rest is also considered. When the plate is not perpendicular to the plane, it is found that separation occurs at the leading edge of the plate for both cases and that for the flow due to pressure difference a viscous eddy of which size diminishes as the inclination angle approaches 90° appears adjacent to the broader side of the plate.
TL;DR: In this article, the performance, convergence and accuracy of four different displacement crack-tip elements used in modelling a cracked plate subjected to out-of-plane bending was evaluated and a methodology was developed for calculating the singular field from the computed results and optimizing the mesh used in the numerical solution.
Abstract: The objective of this work is to assess the performance, convergence and accuracy of four different displacement crack-tip elements used in modelling a cracked plate subjected to out-of-plane bending. A methodology is developed for calculating the singular field from the computed results and optimizing the mesh used in the numerical solution. It was found that using the quarter-node triangular elements surrounded by quadrilateral transition elements yields very accurate estimates of the singular fields of displacements and stresses as well as the stress-intensity factor for various materials and thicknesses of plates. It was also found that when the transition elements are incorporated, the optimum length of the singular element ranges from 0.5 to 1 per cent of half of the crack length.
Patent•
14 Feb 1985
TL;DR: An apparatus for bending a plate utilizing a bending punch and a die into which the bending punch penetrates to a greater or lesser extent depending on the bending angle α is described in this article.
Abstract: An apparatus for bending a plate utilizing a bending punch and a die into which the bending punch penetrates to a greater or lesser extent depending on the bending angle α. The magnitude and variation of the bending force required during deformation of the plate unit are determined and utilized to determine the depth h of punch penetration.
TL;DR: In this article, the authors systematically classify Volterra's "distorsioni", demonstrating their significance for plane-elasticity and plate-bending problems, and discussing the related displacement fields.