Showing papers on "Plate theory published in 1990"
TL;DR: A review of all third-order, two-dimensional technical theories of plates is presented and their equivalence is established in this paper, where a consistent-strain, thirdorder, displacement field is proposed and associated, variationally consistent, theory is developed.
Abstract: A review of all third-order, two-dimensional technical theories of plates is presented and their equivalence is established. All third-order theories published during the last two decades are shown to be based on the same displacement field, contrary to the claims by many authors. Consequently, all variationally derived plate theories are a special case of the third-order plate theory published by the author in 1984. A consistent-strain, third-order, displacement field is proposed herein and associated, variationally consistent, theory is developed.
275 citations
Book•
26 Nov 1990
TL;DR: In this paper, it was shown that the displacements and stresses corresponding to the leading term of the expansion of the 3-dimensional solution do indeed solve the classical equations of 2-dimensional nonlinear plate theories such as the von Karman equations.
Abstract: The first objective of this monograph is to show that the method of asymptotic expansions, with the thickness as the parameter, provides a very effective tool for justifying two-dimensional plate theories, in both the nonlinear and the linear case. Without resorting to any a priori assumption of a geometrical or mechanical nature, it is shown that, the displacements and stresses corresponding to the leading term of the expansion of the 3-dimensional solution do indeed solve the classical equations of 2-dimensional nonlinear plate theories such as the von Karman equations. The second objective is to extend this analysis to the mathematical modelling of junctions in elastic multi-structures, e.g. typically a structure comprising a "3-dimensional" part, and a "2-dimensional" part. These can be folded plates, H-shaped beams, plates with stiffeners, plates held by rods as in a solar panel, etc. A similar asymptotic analysis provides a systematic way of finding the models for such multi-structures, as the "thin" part approach.
207 citations
155 citations
TL;DR: In this paper, the state equation for the jth plies of a laminated thick orthotropic plate is established in the local coordinate system according to the knowledge which has been introduced in the paper by Sundara Raja Iyengar and Pandya (1983, Fiber Sci. Technol.
141 citations
TL;DR: In this article, the generalized shear deformation plate theory was applied to composite laminates to find a desired degree of approximation of the displacements through the laminate thickness allowing for piecewise approximation of inplane deformation through individual laminae.
Abstract: Analytical solutions for displacements and stresses in composite laminates are developed using the laminate plate theory of Reddy. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the inplane deformation through individual laminae. The solutions are compared with the 3-D elasticity solutions for the simply supported case and excellent agreement is found. Analytical solutions are also presented for other boundary conditions. The results indicate that the generalized shear deformation plate theory predicts accurate stress distributions in thick composite laminates.
117 citations
TL;DR: In this article, the instability of composite laminated plates under uniaxial, harmonically-varying, in-plane loads is investigated, both symmetric cross-ply and antisymmetric angle-ply laminates are analyzed.
114 citations
TL;DR: In this article, the structure of the Reissner-Mindlin plate equations is investigated, emphasizing its dependence on the plate thickness. And the error bounds for the errors in the expansions in Sobolev norms are given.
Abstract: The structure of the solution of the Reissner–Mindlin plate equations is investigated, emphasizing its dependence on the plate thickness. For the transverse displacement, rotation, and shear stress, asymptotic expansions in powers of the plate thickness are developed. These expansions are uniform up to the boundary for the transverse displacement, but for the other variables there is a boundary layer. Rigorous error bounds are given for the errors in the expansions in Sobolev norms. As applications, new regularity results for the solutions and new estimates for the difference between the Reissner–Mindlin solution and the solution to the biharmonic equation are derived. Boundary conditions for a clamped edge are considered for most of the paper, and the very similar case of a hard simply-supported plate is discussed briefly at the end. Other boundary conditions will be treated in a forthcoming paper.
103 citations
TL;DR: In this paper, a theoretical analysis of the dynamic response of shear deformable symmetrically laminated rectangular composite flat panels exposed to sonic boom and explosive blast loadings is presented.
Abstract: This paper deals with a theoretical analysis of the dynamic response of shear deformable symmetrically laminated rectangular composite flat panels exposed to sonic boom and explosive blast loadings. The pertinent governing equations incorporating transverse shear deformation, transverse normal stress, as well as the higher-order effects are solved by using the integral-transform technique. The obtained results are compared with their counterparts obtained within the framework of the first-order transverse shear deformation and the classical plate theories and some conclusions concerning their range of applicability are outlined. The paper also contains a detailed analysis of the influence played by the various parameters characterizing the considered pressure pulses as well as the material and geometry of the plate.
95 citations
TL;DR: A review of the developments in displacement-based theories of plates is presented in this paper, where a strain-consistent third-order theory is presented, which contains most existing thirdorder plate theories as special cases.
Abstract: A review of the developments in the displacement-based theories of plates is presented. It is shown that many of the third-order theories reported in the literature are based on the same or equivalent displacement field, and are thus lead to the same results. A strain-consistent third-order theory is presented, which contains most existing third-order plate theories as special cases. The layer-wise laminate plate theory proposed by the author is also reviewed. The accuracy of the theories is evaluated by comparing the numerical solutions with those of the three-dimensional elasticity theory.
86 citations
TL;DR: In this article, the authors identify the part of the Reissner/Mindlin solution that controls the boundary layer and examine the behaviour near smooth edges and corners, and demonstrate the theoretical results by some numerical studies on simple plate structures which are discretized by an accurate, higher order plate element.
Abstract: SUMMARY Plate bending finite elements based on the Reissner/Mindlin theory offer improved possibilities to pursue reliable finite element analyses. The physical behaviour near the boundary can be modelled in a realistic manner and inherent limitations in the Kirchhoff plate bending elements when modelling curved boundaries can easily be avoided. However, the boundary conditions used are crucial for the quality of the solution. We identify the part of the Reissner/Mindlin solution that controls the boundary layer and examine the behaviour near smooth edges and corners. The presence of boundary layers of different strengths for different sets of boundary conditions is noted. For a corner with soft simply supported edges the boundary layer removes the singular behaviour of Kirchhoff type from the stress resultants. We demonstrate the theoretical results by some numerical studies on simple plate structures which are discretized by an accurate, higher-order plate element. The results provide guidance in choosing efficient meshes and appropriate boundary conditions in finite element analyses.
68 citations
TL;DR: In this paper, a new triangular plate blending element based on the Reissner-Mindlin theory is developed through a mixed formulation emanating from the Hu-Washizu variational principle.
Abstract: A new triangular plate blending element based on the Reissner-Mindlin theory is developed through a mixed formulation emanating from the Hu-Washizu variational principle. A main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges
TL;DR: In this paper, a plate-bending finite element based on the theory of Reddy is developed, and stress relaxation is shown to be an important factor in the design of composite plates.
Abstract: A plate-bending finite element based on the theory of Reddy is developed. Stress relaxation is shown to be an important factor in the design of composite plates.
TL;DR: In this article, an algorithm based on a finite element approach has been developed to study the transient response of plates with arbitrary boundary conditions and subjected to moving loads, where thin plate theory is assumed for the plate model and no restriction is placed on the loading conditions.
TL;DR: In this article, it was shown that the solution of a three-dimensional linear elasticity problem in a thin folded plate converges strongly inH1 to a solution of two-dimensional model as the thickness goes to 0.
Abstract: It is shown that the solution of a three-dimensional linear elasticity problem in a thin folded plate converges strongly inH1 to a solution of a two-dimensional model as the thickness goes to 0. This model consists of two plate equations coupled through their common edge.
TL;DR: In this paper, a number of finite strip formulations for determining the buckling stresses and natural frequencies of vibration of composite prismatic plate structures of finite length and with diaphragm ends are given.
TL;DR: In this article, the authors present the theoretical formulations of the MITC plate bending elements and then present numerical convergence results for the four, nine and 16-node quadrilateral elements and their 7 and 12-node triangular elements.
Abstract: We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner‐Mindlin plate theory and a mixed‐interpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16‐node quadrilateral elements and our 7 and 12‐node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements.
TL;DR: The boundary element method is used in the geometrically nonlinear analysis of laterally loaded isotropic plates taking into account the effects of transverse shear deformation as discussed by the authors.
TL;DR: In this paper, the exact form of the shear constraints which are imposed on an element when its side-to-thickness ratio is large is derived, and the constraints are expressed in terms of the nodal degrees of freedom, and interpreted as being either the proper Kirchhoff constraints or spurious locking constraints.
Abstract: A study of the behaviour of shear deformable plate finite elements is carried out to determine why and under what conditions these elements lock, or become overly stiff. A new analytical technique is developed to derive the exact form of the shear constraints which are imposed on an element when its side‐to‐thickness ratio is large. The constraints are expressed in terms of the nodal degrees of freedom, and are interpreted as being either the proper Kirchhoff constraints or spurious locking constraints. To gain a better understanding of locking phenomena, the constraints which arise under full and reduced integration are derived for various plate elements. These include bilinear, biquadratic, eight‐node serendipity and heterosis elements. These analytical findings are compared with numerical results of isotropic and laminated composite plates, verifying the role that shear constraints play in determining the behaviour of thin shear deformable elements. The results of the present study lead to definitive conclusions regarding the origin of locking phenomena and the effect of reduced integration.
TL;DR: In this paper, a new method for calculating the intrinsic stress that develops in a film as it is deposited onto a substrate is presented, which makes no assumptions regarding the thickness of the film or the uniformity of film stress and also accounts for nonlinear geometric effects which may become significant whenever the measured deflections reach an order of magnitude equal to or greater than that of the substrate thickness.
TL;DR: In this paper, a simple shear-flexible four-noded quadrilateral laminated composite plate/shell finite-element is presented, which is based on a generalized mixed variational principle with independently assumed displacement and laminate internal strain fields.
TL;DR: In this paper, a numerical solution technique by the boundary element method is developed for the flexural vibration and buckling analysis of elastic orthotropic plates according to Kirchhoff's theory.
TL;DR: In this article, a simple C0 isoparametric finite element formulation based on a set of higher-order displacement models for the analysis of symmetric and asymmetric multilayered composite and sandwich beams subjected to sinusoidal loading is presented.
TL;DR: In this paper, a balanced adaptive mesh-refinement and increase of the polynomial degree in an hp-version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.
Abstract: Reissner-Mindlin plate theory is still a topic of research in finite element analysis. One reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well-known shear locking effect. In this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations. A balanced adaptive mesh-refinement and increase of the polynomial degree in an hp-version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.
TL;DR: In this paper, the static deflections and natural frequencies of isotropic, orthotropic/laminated composite plates using a Levy-type solution were analyzed using the Mindlin plate theory in conjunction with the state-space concept.
TL;DR: In this paper, the Hellinger-Reissner variational principle is used to formulate plate bending elements based upon Reissner-Mindlin plate theory and an explicit coupling between interpolations of the shear and moment stress resultant fields is introduced.
Abstract: In this work the Hellinger-Reissner variational principle is used to formulate plate bending elements based upon Reissner-Mindlin plate theory. The formulation introduces an explicit coupling between interpolations of the shear and moment stress resultant fields. Because of the coupling, shear locking is avoided at the element level rather than at the global level. The coupling term is obtained by constraining the shear and moment resultant fields, that are initially assumed independent, to perform no work when subjected to a set of incompatible displacement modes. The resultant fields are formulated as a complete polynomial expansion in the element's natural coordinates and then transformed to the physical domain. Thus, frame invariant elements are always obtained. The resulting elements are shown to perform well on a set of standard problems for thin and thick plates.
TL;DR: In this article, a non-linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented, where the rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference.
Abstract: In this paper, a method for the non-linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co-ordinate system using the assumptions of the classical theories of plates. Non-linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time-invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two-parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non-linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non-linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected structural elements.
TL;DR: In this article, the Von Karman strain and the effects of rotatory inertia were modeled in a finite element model and the mode shapes as functions of angular velocity, pitch angle, and sweep angle were presented.
Abstract: The theory accounts for geometric nonlinearity in the form of the Von Karman strains and the effects of rotatory inertia. The plate is permitted to have an arbitrary orientation offset from the axis of rotation. A finite element model is developed. The mode shapes as functions of angular velocity, pitch angle, and sweep angle are presented.
TL;DR: In this article, a technique for predicting the distribution of the energy release rate along a curved or straight mode I planar crack in the plane of a plate (such as a delamination crack) was proposed.
TL;DR: In this paper, the buckling analysis of prismatic plate structures made of composite laminated material is considered, and a very general description of laminate material properties, the presence of applied shear stress, the accommodation of eccentric connections between plate flats and the use of multi-level substructuring techniques, including the so-called superstrip concept are discussed.