Showing papers on "Bending of plates published in 1989"
TL;DR: In this article, the authors present a procedure to establish Reissner-Mindlin plate bending elements based on the idea to combine known resuits on the approximation of Stokes problems with known results on approximation of elliptic problems.
Abstract: DCpartement de Mathtmatiyue, L'nit,ersitt 1aral Quthec, Canado SUMMARY We present in this paper a procedure to establish Reissner-Mindlin plate bending elements The procedure is based on the idea to combine known resuits on the approximation of Stokes problems with known results on the approximation of elliptic problems The proposed elements satisfy the mathematical conditions of stability and convergence, and some of them promise to provide efficient elements for practical solutions
250 citations
TL;DR: In this article, a new three node, nine d.o.f. triangular plate bending element called DST (Discrete Shear Triangle) was proposed for the analysis of thin and thick plates.
Abstract: This paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.
194 citations
TL;DR: A plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions ofthe generalized plate theory and the 3D-elasticity theory as discussed by the authors.
Abstract: .( SUMMARY A plate bending element based on the generalized laminate plate theory (GLPT) developed by the senior author is described and its accuracy is investigated by comparison with the exact solutions ofthe generalized plate theory and the 3D-elasticity theory. The element accounts for transverse shear deformation and layer wise description of the inplane displacements of the laminate. The element has improved description of the inplane as well as the transverse deformation response. A method for the computation of interlaminar (transverse) stresses is also presented. 1. BACKGROUND Laminated composite plates are often modelled using the classical laminate plate theory (CLPT) or the first-order shear deformation plate theory (FSDT). In both cases the laminate is treated as a single-layer plate with equivalent stiffnesses, and the displacements are assumed to vary through the thickness according to a single expression (see Reddy 1 ), not allowing for possible discontinuities in strains at an interface of dissimilar material layers. Recently, Reddy2 presented a general laminate plate theory that allows layer-wise representation of inplane displacements, and an improved response of inplane and transverse shear deformations is predicted. Similar but different theories have appeared in the literature. 3-6 In the generalized laminate plate theory (0LPT) the equations of three-dimensional elasticity are reduced to differential equations in terms of unknown functions in two dimensions by assuming layer-wise approximation of the displacements through the thickness. Consequently, the strains are different in different layers. Exact analytical solutions of the theory were developed by the authors 7 ,8 to evaluate the accuracy ofthe theory compared to the 3D-elasticity theory. The results indicated that the generalized laminate plate theory allows accurate determination ofinterlaminar stresses. The present study deals with the finite-element formulation of the theory and its application to laminated composite plates. In the interest of brevity only the main equations of the theory are reviewed and the major steps of the formulation are presented. The accuracy of the numerical
185 citations
TL;DR: Two plate bending elements that have been proposed and mathematically analyzed previously by Bathe, Brezzi and Fortin are presented: the MITC7 (a triangular) element and theMITC9 (a quadrilateral) element.
113 citations
TL;DR: In this paper, the Zienkiewicz-Zhu error estimator is used in combination with an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieved.
Abstract: The Zienkiewicz–Zhu error estimator is shown to be effective in problems of plate flexure. When used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieved.
111 citations
Book•
01 Jan 1989
105 citations
103 citations
TL;DR: In this paper, the orthogonality of principal modes and the state variables technique are used to investigate the dynamic response of symmetric cross-ply laminated composite plates by solving the equation of a higher-order shear deformation plate theory.
78 citations
TL;DR: In this article, a spin-up maneuver for a simply-supported rectangular plate is examined, and the vibration modes of such a plate are used to show that the present theory captures the phenomenon of dynamic stiffening.
Abstract: Equations of motion are formulated for a thin elastic plate that is executing small motions relative to a reference frame undergoing large rigid body motions (three-dimensional rotation and translation) in a Newtonian reference frame. As an illustrative example, a spin-up maneuver for a simply-supported rectangular plate is examined, and the vibration modes of such a plate are used to show that the present theory captures the phenomenon of dynamic stiffening
64 citations
TL;DR: In this paper, the problem of finding the response of a thick infinite plate to the application of body forces is considered, and transform techniques are employed to reduce the problem to that of an initial boundary value problem for a one-dimensional hyperbolic system.
54 citations
TL;DR: In this article, the effect of shear deformation on the bending moment and shear force distributions of a plate on a Winkler foundation is investigated. But the main difference between Mindlin's plate theory and classical thin plate theory is that the plates are simply supported on two opposite edges and the other two edges may be arbitrarily restrained.
TL;DR: In this paper, the impact of a ballistic pendulum on an anisotropic plate is modeled as a Dirac pulse in space and time, and a method for determining material parameters, and the mean contact time, from the interferograms is hence developed.
Abstract: Propagating bending waves are studied in plates made of aluminum and wood. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as the light source, is used to record the out of plane motion of the waves. Elliptic-like fringes visualize differences in wave speed for different directions in the anisotropic plate and circular ones are obtained for the isotropic plate. The experimental data for the isotropic plate compare favorably with analytical results derived from the Kirchhoff-plate equation with a point impact of finite duration. A similarity variable is found when starting conditions are modeled as a Dirac pulse in space and time, that brings new understanding to the importance of specific parameters for wave propagation in plates. A formal solution is obtained for a point force with an arbitrary time dependence. For times much larger than the contact time, the plate deflection is shown to be identical to that from a Dirac pulse applied at the mean contact time. A method for determining material parameters, and the mean contact time, from the interferograms is hence developed.
TL;DR: In this article, the boundary layer near the rigidly clamped edge of a thin three-dimensional plate subjected to bending loads is investigated, and it is shown that taking account of the next term in the deflection asymptotic form results in the appearance of inhomogeneities in the boundary conditions on the plate edge.
TL;DR: In this article, the authors present a technique for dealing with the integrations required in the direct boundary element method (DBEM), which is to carry out the integration analytically and code the results directly.
Abstract: The alternative to quadrature, as a procedure for dealing with the integrations required in the direct boundary element method (DBEM), is to carry out the integration analytically and code the results directly. The potential benefits are efficient computer programs; the avoidance of numerical instability; and generally, better accuracy. The technique is developed in this paper.
Serious problems arise when Gauss quadrature is employed for the integration of functions which contain, or are close to singularities. A numerical integration approach may fail at the first stage of the analysis, that is, during the assembly of the discrete equations; or it may fail at the subsequent stage of computing domain points near the boundary. The severity of the problem is dependent both on the strength of the singularity, and on geometry. These points are illustrated with examples.
TL;DR: In this paper, the thermal buckling behavior of laminated plates subjected to a nonuniform temperature field is investigated by the finite-element method, and the stiffness matrix, geometry matrix, and load vector are derived based on the principle of minimum potential energy.
Abstract: The thermal buckling behavior of laminated plates subjected to a nonuniform temperature field is investigated by the finite-element method. Being nonuniformly distributed over the plate, the thermal stresses should be determined before solving the buckling problem. The stiffness matrix, geometry matrix, and load vector are derived based on the principle of minimum potential energy. The assumed displacement state over the middle surface of the plate element is expressed as the products of one-dimensional, first-order Hermite polynomials. Numerical results show that the thermal buckling strength of a clamped plate is higher than that of a simply supported plate, and the influence of lamination angle, plate aspect ratio, and modulus ratio on thermal buckling are found to be significant for laminated plates.
TL;DR: In this article, an a posteriori error estimator is presented which allows a good pointwise evaluation of the error in predicted stresses and can easily be implemented in existing FE codes.
Abstract: An a posteriori error estimator is presented which allows a good pointwise evaluation of the error in predicted stresses and can easily be implemented in existing FE codes. Although this estimator has especially been developed for and tested on p-version Hybrid-Trefftz (HT) elements, it is anticipated that it can also be applied to conventional conforming p-version elements. The practical efficiency of the estimator is illustrated through the solution of various plate bending problems by using the HT p-version Kirchhoff plate elements.2
Patent•
26 Jan 1989
TL;DR: In this paper, a plate bending machine with a manipulator capable of handling a plate which is subjected to a bending process in a bending machine is described, and a plate position detecting device capable of detecting a position of the plate being handled by the manipulator and being subjected to the bending process.
Abstract: The present invention relates to a plate bending machine, and, in particular, to a plate bending machine such as a press break provided with a manipulator capable of handling a plate which is subjected to a bending process in a bending machine, and to a plate bending machine provided with a plate position detecting device capable of detecting a position of the plate which is being handled by the manipulator and being subjected to the bending process.
Book•
01 May 1989
TL;DR: In this article, the authors present a set of specifications for the use of three-dimensional theory in the analysis of shell elements, including the following: 1.1. Thin Plate Theory (Kirchhoff hypothesis).2.2.3 Plate Theory and Degenerated Shell Elements.3.4.
Abstract: 1 Introduction.- 1.1 Changing Trends in Shell Analysis.- 1.2 Reliability of Finite Element Analysis.- 1.3 Shell Element Formulations.- 1.4 Objective and Layout.- 2 Degenerations of Three-Dimensional Theory.- 2.1 Introduction.- 2.2 Three-Dimensional Theory.- 2.3 Plate Theory.- 2.3.1 Thin Plate Theory (Kirchhoff hypothesis).- 2.3.2 Thick Plate Theory (Mindlin-Reissner Hypothesis).- 2.4 Three-Dimensional Degenerated Curved Shell.- 2.4.1 Definition of Strains.- 2.4.2 Definition of Stresses.- 2.4.3 The Total Potential Energy.- 3 Defects of Mindlin Plate and Degenerated Shell Elements.- 3.1 Introduction.- 3.2 Formulation of Mindlin Plate Bending Elements.- 3.2.1 Formulation of Mindlin Isoparametric Bending Elements.- 3.2.2 Finite Element Representations of Boundary Conditions.- 3.3 Formulation of Degenerated Shell Elements.- 3.3.1 Coordinate Systems.- 3.3.2 Element Geometry.- 3.3.3 Displacement Field.- 3.4 Defects of Mindlin Plate and Degenerated Shell Elements.- 3.4.1 Locking Phenomena.- 3.4.2 Reduced and Selective Integration.- 3.4.3 Alternative Methods Avoiding the Locking Problems.- 4 Assumed Strain Finite Element Plate Formulations.- 4.1 Introduction.- 4.2 Essence of Shear Locking.- 4.3 Reinterpretation of Selectively Integrated Elements.- 4.4 Elimination of Shear Locking.- 4.4.1 Assumed Transverse Shear Strain Fields.- 4.4.2 Location of the Sampling Points for the Shear Strains.- 4.4.3 The Evaluation of the Stiffness Matrix.- 5 Linear Benchmark Tests for Plate Elements.- 5.1 Introduction.- 5.2 Eigen-Analyses of the Stiffness Matrices.- 5.3 Patch Tests.- 5.3.1 Patch Tests for Bending.- 5.3.2 Patch Tests for Twisting.- 5.3.3 Patch Tests for Shear.- 5.4 Locking Tests.- 5.5 Long Cantilever.- 5.6 Convergence Tests.- 5.6.1 Simply Supported Square Plates under Uniform Load.- 5.6.2 Clamped Square Plate under Uniform Load.- 5.6.3 Clamped Circular Plates.- 5.7 Skew Plates.- 5.7.1 Razzaque's 60 Skew Plate.- 5.7.2 Morley's 30 Skew Plate.- 5.8 Stress Resultant Study.- 6 Assumed Strain Finite Element Shell Formulations.- 6.1 Introduction.- 6.2 Shear Locking, Membrane Locking and Selective Integration.- 6.2.1 Shear Locking in Shells.- 6.2.2 Essence of Membrane Locking.- 6.3 Elimination of Shear Locking.- 6.4 Elimination of Membrane Locking.- 6.4.1 Orthogonal Curvilinear Coordinate System (r, s, t or ri).- 6.4.2 Assumed Membrane Strains.- 6.5 Assumed Strain Degenerated Shell Elements.- 6.5.1 Location of Sampling Points for the Membrane Strains.- 6.5.2 The Evaluation of the Stiffness Matrix.- 6.6 Discussion.- 7 Linear Benchmark Tests for Shell Elements.- 7.1 Introduction.- 7.2 Eigen-Analysis of the Stiffness Matrices.- 7.3 Patch Tests.- 7.3.1 Bending, Twisting and Shear Patch Tests.- 7.3.2 Plane Stress Patch Tests.- 7.4 Locking Tests.- 7.4.1 Shear Locking Tests.- 7.4.2 Membrane Locking Tests.- 7.5 Conclusions.- 8 Formulations and Applications for Elasto-Plastic Shell Analyses.- 8.1 Introduction.- 8.2 Laminated Plate and Shell Model.- 8.3 Shear Correction Factors.- 8.4 The Anisotropic Yield Criterion.- 8.4.1 Generalised Huber-Mises Yield Criterion.- 8.4.2 Determination of Anisotropic Parameters.- 8.4.3 Relation between Elasto-Plastic Stresses and Strains.- 8.4.4 Tangent Stiffness Matrix.- 8.5 Numerical Examples.- 8.5.1 Clamped Square Plate.- 8.5.2 Clamped Quadratic Shell.- 9 Formulations and Applications for Elasto-Plastic Dynamic Shell Analyses.- 9.1 Introduction.- 9.2 Dynamic Equilibrium Equations.- 9.3 Modelling of Mass Matrix.- 9.3.1 Consistent Mass Matrix.- 9.3.2 Lumped Mass Matrix.- 9.4 Newmark's Time Stepping Scheme.- 9.5 Numerical Examples.- 9.5.1 Rectangular Plate.- 9.5.2 Simply Supported Square Plate.- 9.5.3 Clamped Circular Plate.- 9.5.4 Spherical Shell Caps.- Appendix 1 Software Description for Elasto-Plastic Static Analysis.- A1.1 Introduction.- A1.2 Glossary of Variable Names.- A1.2.1 Main Arrays.- A1.2.2 Main Variables.- A1.3 Program Overview.- A1.4 File Handling.- A1.4.1 Subroutine INPUT.- A1.4.2 User Instructions.- A1.4.3 Files.- A1.5 Documented Example - Clamped Quadratic Shell.- A1.5.1 Input Data File.- A1.5.2 Output Data File.- A1.6 Stiffness Evaluation Module.- A1.6.1 Subroutine for Evaluation of Stiffness Matrix.- A1.6.2 Evaluation of Strain-Displacement Matrix.- A1.6.3 Subroutine BSAMP.- A1.6.4 Subroutine FUNC.- A1.6.5 Subroutine FRAME.- A1.6.6 Subroutine SFR1.- A1.6.7 Subroutine SFR3.- A1.6.8 Subroutine TBMAT.- A1.6.9 Subroutine XDIC.- Appendix 2 Software Descriptions for Elasto-Plastic Transient Analysis.- A2.1 Introduction.- A2.2 Glossary of Variable Names.- A2.2.1 Main Arrays.- A2.2.2 Main Variables.- A2.3 Program Overview.- A2.4 File Handling.- A2.4.1 Subroutine INPUTD.- A2.4.2 Subroutine INTIME.- A2.4.3 User Instructions.- A2.4.4 Files.- A2.5 Documented Example - Thin Spherical Cap.- A2.5.1 Input Data File.- A2.5.2 Output Data File.- Author Index.
TL;DR: In this paper, the improved 5-and 6-node transition plate bending elements are presented, which can be used in modelling the transition area between the portion of structure where a more refined mesh is needed in order to cope with the steep displacement or stress gradient and the rest of the structure.
TL;DR: In this article, the authors deal with the stochastic finite element analysis of nonlinear structural dynamic problems, consisting of a linearly elastic square plate lying on a nonlinear foundation and loaded with a deterministic uniform transverse dynamic load.
TL;DR: In this paper, the impact of a ballistic pendulum on a plate made of glass-fiber reinforced polyester is used to propagate bending waves, and the wave pattern for a symmetric angle-ply reinforced plate has a symmetry about the axes of reinforcements.
Abstract: Propagating bending waves are studied in plates made of glass-fiber reinforced polyester. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as light source, is used to record the out of plane motion of the waves. The interferograms have an elliptic-like symmetry for an orthotropic plate, while the wave pattern for a symmetric angle-ply reinforced plate has a symmetry about the axes of reinforcements. Experimental data are compared on one hand to analytical results obtained by assuming that the orthotropic plate can be described as if isotropic along the main axes, and on the other hand to numerical results from calculations using the finite-element method. The effective Young's modulus raised to power 1/4 is shown to be an important parameter for the description of the dispersive wave pattern. A defect in the plate alters the wave pattern in the interferograms significantly. This may have technical use.
TL;DR: In this article, the nonlinear stiffness equations that predict local and post-local buckling of plates and plate assemblies are given, validated by accurate predictions of independent test resu...
Abstract: The nonlinear stiffness equations that predict local and post-local buckling of plates and plate assemblies are given. These equations are validated by accurate predictions of independent test resu...
TL;DR: In this article, the authors extend the plane stress theory of Michell (1900, Proc. R. Math. Soc.A324, 565-594) for a laminated plate, to include stretching and bending solutions for an inhomogeneous thermoelastic plate.
TL;DR: In this paper, the authors considered the time-harmonic vertical vibratios of an elastic annular plate resting in smooth contact with a homogeneous isotropic viscoelastic half space.
Abstract: The time‐harmonic vertical vibratios of an elastic annular plate resting in smooth contact with a homogeneous isotropic viscoelastic half space is considered. The plate is subjected to a vertical distributed loading, or it may be excited by specified displacements or stress resultants applied along the plate edges. The response of the plate is goverried by classical thin‐plate theory and its vertical displacement is represented by an admissible function containing a set of generalized coordinates. A representation for contact stresses is obtained through the solution of a flexibility equation based on an exact displacement Green's function of the half space. The equation of motion of the plate in terms of generalized coordinates are established through the application of Lagrange's equation of motion. The plate edge boundary conditions are incorporated into the plate Lagrangian function as constraint terms through a set of Lagrange multipliers. Selected numerical results for displacement and contact stres...
TL;DR: In this paper, a modified version of the ACM thin plate bending element is presented for the analysis of thick plates, where shape functions used are homogeneous solutions of Mindlin's equations plus a particular solution associated with the applied load on the element.
TL;DR: In this article, the flexural vibrations of triangular composite plates are investigated for the effects of fiber orientation, plate aspect ratio and boundary conditions using a computationally efficient and accurate numerical method.
TL;DR: In this paper, the effect of crack closure in plate bending was studied using the finite element method, and the authors compared the line or surface closure model for different plate thicknesses and boundary conditions, respectively.
TL;DR: In this article, the effects of plate slenderness and stiffener depth on the full-range response of mild steel plates subjected to uniform pressure were investigated and it was shown that the stiffener acts as a "stress raiser" which lowers the first yield pressure and promotes the formation of a collapse mechanism.
TL;DR: In this article, a cylindrical inclusion of radius "a" which is embedded in a plate of arbitrary thickness 2h was solved analytically for the Navier's equations for the case of a cylinrical inclusion. And the analysis showed all stresses including the octahedral shear stress to be sensitive to the radius to half thickness ratio (a/h) as well as the material properties.
Abstract: The three-dimensional Navier’s equations are solved analytically for the case of a cylindrical inclusion of radius “a” which is embedded in a plate of arbitrary thickness 2h. Both the plate and the inclusion are assumed to be of homogeneous and isotropic materials with different material properties. Perfect bonding is assumed to prevail at the interface. As to loading, a uniform tension is appliped in the plane of the plate at points remote from the inclusion. The analysis shows all stresses including the octahedral shear stress to be sensitive to the radius to half thickness ratio (a/h) as well as the material properties. In the limit, as (μ 2/μ 1) → 0 and as (μ 2/μ 1) → 1 (where μ 2 and μ 1, are, respectively, the shear moduli of the inclusion and of the plate) the results for a cylindrical hole and a continuous plate are recovered. Similarly as (a/h)→ ∞ (very thin plate) the plane stress solution is recovered. Moreover, for (μ 2/β 1) > 1.0 the presence of a stress singularity near the point of intersection of the inclusion and the free surface of the plate is confirmed by the numerical results.