Showing papers on "Bending of plates published in 1986"
TL;DR: In this article, an assumption based on the theory of composite beams is presented for the analysis of cross-ply composite laminated plates, under the assumption the in-plane displacements between layers are continuous and the transverse shear stresses between layers is also continuous.
175 citations
TL;DR: This paper presents a new hybrid element approach based on displacement fields which fulfil a priori the non-homogeneous Lagrange equation (Trefftz method) and applies it to plate bending, showing the excellent accuracy and efficiency of the new elements.
Abstract: This paper presents a new hybrid element approach and applies it to plate bending. In contrast to more conventional models, the formulation is based on displacement fields which fulfil a priori the non-homogeneous Lagrange equation (Trefftz method). The interelement continuity is enforced by using a stationary principle together with an independent interelement displacement. The final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs. The formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve-sided elements to be generated. Where relevant, known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain, for example, particular singular corner elements, elements presenting circular holes, etc. Thus a high degree of accuracy may be achieved without a troublesome mesh refinement. Another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements (triangles, quadrilaterals, etc.), presenting an increasing degree of accuracy. The paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements. The conclusions present some ideas concerning the adaptive version of the new elements, extension to nonlinear problems and some other developments.
152 citations
TL;DR: In this article, the direct boundary element method based on the Rayleigh-Green identity is employed for the static analysis of Kirchhoff plates, and the focus is on the implementation of the method for linear elements and a Hermitian interpolation for the deflection w.
Abstract: The direct boundary element method based on the Rayleigh-Green identity is employed for the static analysis of Kirchhoff plates. The starting point is a slightly modified version of Stern's equations. The focus is on the implementation of the method for linear elements and a Hermitian interpolation for the deflection w. The concept of element matrices is developed and the Cauchy principal values of the singular integrals are given in detail. The treatment of domain integrals, the handling of internal supports, the properties of the solution and the effect of singularities are discused. Numerical examples illustrate the various techniques. In the appendix the influence functions for the second and third derivatives of the deflection w are given.
113 citations
TL;DR: In this article, the residual surface stresses generated in ceramic materials by diamond grinding were studied, characterized both by X-ray measurements of stress magnitudes and by line forces obtained from the bending of plates that were machined on one side.
Abstract: Residual surface stresses generated in ceramic materials by diamond grinding were studied. The stresses are characterized both by X-ray measurements of stress magnitudes and by line forces (product of stress and layer thickness) obtained from the bending of plates that were machined on one side. The line forces tend to increase with the hardness of the material but are insensitive to the rate of material removal during grinding (over a limited range of variation). Residual stress measurements are compared with measurements of strengths of the ground surfaces.
110 citations
TL;DR: In this paper, a variational model for a laminated plate consisting of an arbitrary number of fiber-reinforced composite material layers has been developed, using the variational principles.
Abstract: Governing equations of motion for a laminated plate consisting of an arbitrary number of fiber-reinforced composite material layers have been developed, using the variational principles. Each layer was considered to be of an orthotropic material with its directional elastic properties depending on the fiber orientation. The extension, bending, inplane shear, and transverse shear deformations in each separate layer were considered. The analytical results were verified with the literature-reported data. A study of the optimum fiber orientations in a criss-cross laminated plate has shown that different fiber orientations lead to the maximum frequency and the maximum damping. For a cross-ply laminated plate, the maximum flexural frequency ratio has been obtained for large aspect ratio plates and with large values of elastic modular ratio E11/E22. The maximum loss factor for a cross-ply plate was obtained with square plate and with small values of E11/E22. 15 references.
96 citations
TL;DR: In this paper, an approximate analysis for buckling of a rectangular specially-orthotropic plate with a central circular hole is applied to symmetrically-laminated angle-ply plates.
Abstract: An approximate analysis for buckling of a rectangular specially-orthotropic plate with a central circular hole is applied to symmetrically-laminated angle-ply plates Results obtained from finite element analyses and experiments indicate that the approximate analysis predicts accurately the buckling loads of (+/-theta sub m)s plates with integer values of m not below 6 and with hole diameters up to 50 percent of the plate width Moreover, the results indicate that the approximate analysis can be used to predict the buckling trends of plates with hole diameters up to 70 percent of the plate width Results of a parametric study indicate the influence of hole size, plate aspect ratio, loading conditions, boundary conditions, and orthotropy on the buckling load Results are also presented that indicate the relationship of the bending stiffness and the prebuckling load distribution to the buckling load of a plate with a hole
83 citations
TL;DR: In this article, the authors studied the behavior of base plates under the action of axial loads and moments by eccentric loading on the column and found that at the lowest eccentricity, failure was caused by cracking of the concrete, while at other eccentricities the primary mode of failure was by yielding of the base plate.
Abstract: Experiments are conducted to study the behavior of base plates under the action of axial loads and moments by eccentric loading on the column. The parameters in the study are the thickness of the base plate and the eccentricity of the load. At the lowest eccentricity, failure was by cracking of the concrete, while at other eccentricities the primary mode of failure was by the yielding of the base plate. Comparisons of the test results with the predictions from the Working Stress Method gave a range of 1.09–1.89 for the factor of safety with a mean value of 1.35 for specimens that failed by yielding of the base plate. The strain distributions in the base plate were obtained at various stages of loading. They indicate the existence of a critical section of maximum strain, a section of zero strain and strain reversal. The eccentricity of the load seems to have a greater influence on the strains than the thickness of the base plate. The test results show that flexible base plates when loaded at high eccentric...
81 citations
TL;DR: In this paper, an exact solution is presented for the problem of an infinite cantilever anisotropic plate with only a single plane of elastic symmetry parallel to the xy-plane and with elastic coefficients changing through the thickness.
73 citations
TL;DR: In this article, a simple and accurate method to determine stress intensity factors in cracked plates subjected to bending loads is proposed, based on Reissner's transverse shear theory.
66 citations
TL;DR: In this article, the authors considered the elastic buckling of rectangular, symmetrically-laminated composite plates and the vibration in the presence of applied in-plane stress of such laminates.
57 citations
TL;DR: In this article, the authors considered the flexural vibration of symmetrically laminated rectangular plates, based upon the adoption of a shear-deformation plate theory, which is an extension of Mindlin's theory for isotropic plates and includes the effects of both transverse shear deformation and rotary inertia.
TL;DR: In this paper, the higher order shear deformation plate bending theory was used as a basis for the development of two new finite elements, which allowed a parabolic distribution of transverse shear strains through the plate thickness.
Abstract: The higher order shear deformation plate-bending theory introduced by Reddy and others is used as a basis for the development of two new finite elements. This higher order theory allows a parabolic distribution of transverse shear strains through the plate thickness. Solutions obtained using the new elements are compared with exact closed-form solutions based on three-dimensional, first and higher order shear deformation plate bending theories.
TL;DR: In this paper, the large deflection problem of a thin elastic simply supported beam is analyzed for a symmetrical three-point bending and the derived nonlinear differential equation governing beam deflections is solved by applying the numerical method (R-K-G method) and the analytical method based on Legendre-Jacobi form's elliptic integrals of the first and second kinds.
Abstract: The large deflection problem of a thin elastic simply supported beam is analysed for a symmetrical three-point bending .The derived nonlinear differential equation governing beam deflections is solved by applying the numerical method (R-K-G method) and the analytical method based on Legendre-Jacobi form's elliptic integrals of the first and the second kinds. Moreover, a reduction technique is proposed to estimate representative flexural quantities such as a maximum deflection, an end slope, and a maximum bending stress in large deflection states from the conventional linear bending theory in place of the exact large deflection theory. An experiment is also performed to confirm the applicability of the proposed large deflection theory. The experimental results agree well with those obtained from the exact large deflection theory.
01 Jan 1986
TL;DR: In this paper, the effect of transverse shear deformation on bending of elastic symmetric laminated composite plates undergoing large deformation (in the Von Karman sense) is considered, where the non-linear terms of the lateral displacement are considered as an additional set of lateral loads acting on the plate.
Abstract: The effect of transverse shear deformation on bending of elastic symmetric laminated composite plates undergoing large deformation (in the Von Karman sense) is considered in the present paper. The non-linear terms of the lateral displacement are considered as an additional set of lateral loads acting on the plate. The solution of a Von Karman type plate is therefore reduced to that of an equivalent plate with small displacements. This method offers an alternative technique for obtaining non-linear solutions to plate problems. The solutions of a number of example problems indicate that the non-linear shear deformation theory results, as expected, in higher values of the lateral displacement than the non-linear solutions from the classical plate theory. The difference in the values of the maximum displacement from both solutions, however, remains essentially constant beyond a certain value of the load. It is also noted that the linear and non-linear solutions deviate at a low value of w/h (w = maximum later...
TL;DR: In this article, a simple and efficient triangular finite element is introduced for plate bending application, which is a three-node triangular one with three basic degrees of freedom per node and two internal rotation degrees offreedom, using selective reduced integration.
Abstract: A simple and efficient triangular finite element is introduced for plate bending application. The element is a three-node triangular one with three basic degrees of freedom per node and two internal rotation degrees of freedom, using selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is not only competitively accurate, but also useful as a thick/thin triangular plate bending element. It is also pointed out that this element using selective reduced integration is in fact a mixed element.
TL;DR: In this paper, the analysis of elasto-plastic plate bending using a boundary integral equation formulation is described, where the integral equations are solved using standard boundary element techniques and the plasticity, as well as the external lateral load, appears in a domain integral.
TL;DR: In this article, the transverse normal strain effect in addition to transverse shear and normal stress effects are considered for bending of plates on elastic foundations, and the solution of the governing equations using the Navier and Levy type semi-inverse methods is demonstrated.
Abstract: The refined theory for moderately thick plates presented in references is used for the bending of plates on elastic foundations. This theory incorporates the transverse normal strain effect in addition to the transverse shear and normal stress effects. Investigation of various types of fixity of edges involving three boundary conditions is presented. The solution of the governing equations using the Navier and Levy type semi-inverse methods is demonstrated. Results are tabulated for the deflection at the center of a uniformly loaded, simply-supported rectangular plate. Applications of the theory also include an infinite plate with a line load of intensity P. Comparisons are made with the classical plate theory and the corresponding Reissner plate theory. The results show the increasing influence of the transverse normal strain on the plate behavior as the parameters characterizing the influence of the plate thickness, h/a, and the modulus k are increased.
TL;DR: In this article, the status of three-node, triangular, thin plate bending elements is summarized, from which the Hansen-Bergan (HBS) and composite triangle (CT) elements emerge as the most competitive, but still exhibit some difficulties in efficient formulation.
TL;DR: In this article, the authors present a pilot study for a larger project with the basic aim of providing engineers with an unambiguous method for obtaining stress resultants in Mindlin plate analysis.
Abstract: Finite elements based on Mindlin plate theory are used to study the distribution of shear forces and twisting moments on the boundaries of plates with various support conditons and thickness‐to‐span ratios. Differences between results obtained using Mindlin and Kirchhoff plate theories are highlighted. Potential difficulties in the interpretation of results obtained from finite element analysis are discussed and appropriate shear force sampling procedures are reviewed. The present work is a pilot study for a larger project with the basic aim of providing engineers with an unambiguous method for obtaining stress resultants in Mindlin plate analysis. Some examples are presented which illustrate the excellent results which may be obtained with judicious mesh division even in regions with steep gradients of the stress resultants near plate corners. These examples also demonstrate some of the difficulties facing engineers who have to try to interpret finite element results for plates.
TL;DR: In this paper, the authors proposed a way of reducing the domain load integrals present in plate bending formulations into boundary integrals, which can be used to deal with plates on Winkler-type elastic foundations.
TL;DR: In this article, the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis, and a family of this kind of elements is presented.
Abstract: After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.
TL;DR: In this paper, a computer oriented "exact" method of solution is presented for the bending problem of orthotropic rectangular plates, where two opposite edges are clamped or simply supported, or one edge clamped and the other simply supported.
Abstract: A computer oriented "exact" method of solution is presented for the bending problem of orthotropic rectangular plates. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could be subjected to any combination of patch, uniform, line, and concentrated loads. The plate is divided into strips whose number depends on the types and number of loads. The solution for the deflection of each plate strip is expressed as a Levy type single Fourier series, and the loads are expressed as a corresponding series. The advantage of the analytical strip method is that it overcomes the limitations of the previous "exact" methods (Navier's and Levy's), it is easy to program on a computer, and it provides an alternative to numerical, semi-numerical, and other approximate methods. Results are presented for isotropic and orthotropic plates with different loading and boundary conditions.
TL;DR: In this article, a cylindrical storage tank foundation system resting in frictionless contact on an isotropic halfspace is examined by using an energy formulation, and the effects of interaction between various components of the tank-(plate) foundation-halfspace system are investigated in detail.
Abstract: The interaction problem associated with a cylindrical storage tank-(plate) foundation system resting in frictionless contact on an isotropic halfspace is examined by using an energy formulation. The thin-plate and the thin-shell theories are considered in describing the flexural behavior of the foundation and the tank wall, respectively. The tank is assumed to be rigidly connected to the foundation. A power series in terms of the radial coordinate is used to represent the deflected shape of the plate. A variational technique is utilized to obtain the deflections and flexural moments at any point on the plate. The effects of interaction between various components of the tank-(plate) foundation-halfspace system are investigated in detail. A parametric nondimensional study shows that factors such as the relative stiffness and location of the tank wall may result in a more economical design of the (plate) foundation.
TL;DR: In this paper, the appropriate method often used for calculating the bending vibration of a single rectangular plate is extended to calculate the bending vibrations of a global system of combinations of rectangular plates with elastically supported and damped non-coupled edges.
Patent•
31 Jan 1986
TL;DR: In this paper, a simple mechanism was proposed to bend a plate stock to a prescribed angle by turning and separating a pressure supporting roll as well as descending the pressure roll with press die by placing the plate to be worked on a pair of horizontal approaching pressure supporting rolls.
Abstract: PURPOSE: To easily perform the bending of a plate stock to the prescribed angle with a simple mechanism by turning and separating a pressure supporting roll as well as descending the pressure roll with press die by placing the plate to be worked on a pair of horizontal approaching pressure supporting rolls. CONSTITUTION: The plate 1 to be worked is placed on a pair of horizontally approaching pressure supporting rolls 3 of the above of a base stand 12. The plate stock 1 is subjected to a bending to the prescribed angle reasonably by separating it with a motor 10 by giving the turn to the pressure supporting roll 3 with a motor 9 as well as by bending the plate stock 1 at the bend point 21 by descending with a motor 7 the pressure roll 2 on which the pressure die 4 supported by a frame 6 is arranged. It is possible to work in a box type material by performing the pressure bending of the different prescribed position of the plate stock 1 by turning the roll 2 for pressure by forming the die 4 for pressure in a polygonal shape and a circular pipe working is possible as well by performing a pressure turning with the roll 2 for pressure only by removing the die 4 for pressure. Consequently various plate stock bendings are performed with simple mechanism. COPYRIGHT: (C)1987,JPO&Japio
TL;DR: In this article, the natural frequencies of skew, curved and tapered plates have been determined using the isoparametric quadratic plate bending element and two approaches have been adopted for the solution of skew plates.
TL;DR: In this article, a family of special purpose hybrid stress plate bending elements is derived for use at certain types of reentrant corners where classical plate theory predicts singular moments and shear forces.
Abstract: The elastic analysis of floor slabs using the finite element method encounters special difficulties at certain types of reentrant corners where classical plate theory predicts singular moments and shear forces. Examples are the corners of floor openings and the corner points of rectangular columns or shear cores. The nature of the stress singularities at these corners is discussed, and a family of special purpose hybrid stress plate bending elements is derived for use at these locations. These elements, which may be rectangular or L‐shaped, contain the appropriate singular moments as part of their assumed moment fields. The elements are tested on three example problems and the results are compared with those obtained using regular hybrid stress elements. Improved convergence and a better representation of the moment field are obtained with these special purpose elements. It is concluded that the more rapid convergence and additional accuracy justify the increase in computational effort.
TL;DR: In this article, the authors proposed the initial value method for the analysis of isotropic plates, which consists of solving the governing differential equation of plates by an integration technique, carried in one direction, and the derivatives in the other direction represented by finite-difference operators on the deflections.