Showing papers on "Plate theory published in 1987"
TL;DR: In this article, a new laminated plate theory was developed for arbitrary laminate configuration based upon Reissner's (1984) new mixed variational principle, where piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed.
Abstract: : In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configuration based upon Reissner's (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric and arbitrary laminates indicates that the present theory acurately estimates in-plane responses, even for small span-to-thickness ratios. (Author)
221 citations
202 citations
TL;DR: In this article, a new high-order laminated composite plate theory was developed based upon Reissner's new mixed variational principle, and a zig-zag shaped C0 function and Legendre polynomials were introduced into the approximate in-plane displacement distributions across the plate thickness.
155 citations
TL;DR: In this article, the force balance method and the principle of minimum complementary energy were used to solve the problem of interlaminar stresses at a straight free edge in a composite laminate.
Abstract: The solution to the problem of interlaminar stresses at a straight free edge in a com posite laminate is obtained in closed form for two special and important cases: angle-ply and cross-ply laminates. These solutions are derived using the Force Balance Method and the principle of minimum complementary energy. The results are favorably compared to the predictions of other analyses found in the literature. The solution procedure is found to be simpler and more efficient than other analytical methods. In addition, for some special cases of cross-ply laminates, the solution is shown to be identical to the predictions of a modified plate theory that includes through-the-thickness stretching.
99 citations
TL;DR: In this article, the eigenvalue and lateral deflection of both the surface and middle plane of the plate, as well as the bending strains, are obtained in the form of series expansions in even powers of plate thickness.
98 citations
TL;DR: In this paper, a general triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates, where the element formulation assumes transverse inextensibility and layerwise constant shear-angle.
Abstract: The development of a general triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates. The element formulation assumes transverse inextensibility and layerwise constant shear-angle. Convergence of transverse displacement, moments and stresses, the effects of two different Gauss quadrature schemes and comparison of the present solutions with the available analytical/finite-element results also form a part of the investigation. Furthermore, numerical results indicate close agreement between the LCST (layerwise constant shear-angle theory) and the three-dimensional elasticity theory with the length (or width) to thickness ratio as low as 4. Detailed comparison of the LCST-based finite-element solutions with those based on the CST (constant shear-angle theory) and the CLT (classical lamination theory) clearly demonstrates the superiority of the former over the latter two, especially in the prediction of the distribution of the in-plane displacements and stresses through the laminate thickness. This paper also introduces a new non-dimensionalized parameter, Δθ*, which is shown to be a very useful measure for classification of the laminated plates and the suitability of different plate theories over various ranges of length-to-thickness ratio.
91 citations
TL;DR: In this article, a finite element method was used to analyze the dynamic responses of a flat plate subjected to various moving loads, including eccentricity, acceleration and initial velocity of the moving load, and the effect of span length.
Abstract: SUMMARY The object of this paper is to analyse by the finite element method the dynamic responses of a flat plate subjected to various moving loads. First of all the actual continuous flat plate was replaced by a discrete system composed of isoparametric rectangular plate elements. And then the elementary and overall stiffness and mass matrices were determined and the natural frequencies and mode shapes of the flat plate were solved. Next, the Newmark direct integration method was used to find the dynamic responses of the flat plate. The effects of eccentricity, acceleration and initial velocity of the moving load, and the effect of span length were the key points of study. The dynamic behaviour of a multi-span flat plate supported by the beam members of rigid plane frames and subjected to the action of a series of moving loads (in identical or opposite directions) were also investigated.
86 citations
TL;DR: In this article, a simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields.
Abstract: A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the follwoing considerations: (1) suppression of all kinematic deformation modes, (2) the element has a favorable value for the constraint index in the thin plate limit, and (3) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.
83 citations
TL;DR: In this article, a refined transverse vibration and buckling analysis based on the same local model is presented, and numerical examples are compared with analytical solutions and classical plate theory and it is demonstrated that the present model predicts a realistic laminate global response.
71 citations
01 Jan 1987
TL;DR: In this paper, the convergence behavior of two mixed-interpolated plate bending elements, the MITC4 and MITC9, has been studied and a simplified analysis is given that renders valuable insight into the predictive capabilities of these elements.
Abstract: We consider the convergence behavior of two mixed- interpolated plate bending elements — the MITC4 element which has already found wide use and a new element, the MITC9 element. A simplified analysis is given that renders valuable insight into the predictive capabilities of these elements.
58 citations
TL;DR: In this paper, the average stress method is used to derive the governing equation for a thick rectangular plate according to a high-order deformation theory, and the applied load is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate.
TL;DR: In this article, a theory for the thermo-elastic-plastic plate bending is developed, using a boundary element method as a solution technique, and the difference between the mechanics of beam bending versus plate bending are shown.
Abstract: The flame bending process can be most useful in the present effort to automate the plate bending process in shipyards. To achieve this goal, the complicated thermo-elastic-plastic behavior of the plate during the process must be understood. A review of past analytical research efforts reveals that these attempts have been restricted to beam bending. Here a theory for the thermo-elastic-plastic plate bending is developed. Furthermore, using a boundary element method as a solution technique, the difference between the mechanics of beam bending versus plate bending is shown. Recommendations for future work are given.
01 Jan 1987
TL;DR: In this paper, an overview of the literature on buckling of composite laminates is presented, including a comprehensive study of the world's literature on this subject, encompassing approximately 300 references.
Abstract: An overview is presented of considerations involved and some of the more interesting results found in the buckling of laminated composite plates. In the case of plates which are symmetrically laminated, classical orthotropic or anisotropic plate theory applies, and numerous theoretical results are available. For unsymmetrical laminates coupling exists between bending of the plate and stretching of its midplane, and a considerably more complicated theory must be used. Additional complicating factors are considered, including: interior holes, shear deformation, sandwich construction involving other materials, local effects, nonlinear stress-strain relationships, and hygrothermal effects. Postbuckling behavior and the effects of initial geometric imperfections are also discussed. The results summarized are taken from a recent comprehensive study of the world’s literature on this subject, encompassing approximately 300 references.
TL;DR: In this article, the effects of transverse shear deformation, normal stress, normal strain and nonlinear in-plane normal strain distribution through the plate thickness are considered and a two-dimensional plate theory based on the Kirchhoff hypothesis is proposed.
TL;DR: In this paper, it was shown that it would be safer to add 15% of the web area to the flange area when finding the lateral-torsional critical buckling stress for a beam with one flange rigidly restrained along its entire length.
TL;DR: In this paper, the displacements for cylindrical bending and stretching of laminated and thick plates are expressed through-the-thickness by a few algebraic terms and a complete set of trigonometric terms.
Abstract: The displacements for cylindrical bending and stretching of laminated and thick plates are expressed through-the-thickness by a few algebraic terms and a complete set of trigonometric terms. Only a few terms of this series are needed to get sufficiently accurate results for laminated and thick plates. Equations of equilibrium based on a sufficient number of terms of this series for displacements are determined using variational theorems from three-dimensional elasticity. Several examples are worked out. The displacements and stresses are obtained for simply supported isotropic and layered beams with a rectangular cross section and a sinusoidal lateral load distribution. These results are compared to an exact elasticity solution. Results for several approximations are obtained for a simply supported and a clamped beam with a rectangular cross section loaded at the center and results are compared to experimental results. Results are also obtained for isotropic and layered beams with a rectangular cross section for several approximations for the lowest natural frequency and buckling load.
TL;DR: In this paper, a static and transient analysis of composite plates is presented using a recently proposed shear deformation theory, and the dynamic response is obtained by employing the numerical time integration scheme due to Newmark.
Abstract: Static and transient analysis of composite plates is presented using a recently proposed shear deformation theory. The dynamic response is obtained by employing the numerical time integration scheme due to Newmark. The results obtained by using the classical plate theory (CPT) and the Mindlintype shear deformation theory (SDT) are compared with those obtained by using the proposed theory. The comparison studies reveal that the linear stress distribution, as assumed in CPT and SDT, differs considerably from the predicted nonlinear distribution of the proposed theory.
TL;DR: In this paper, the dynamic structural contact problems of a rigid, smooth cylindrical striker impacting an elastically supported transversely isotropic beam and plate are solved as a superposition of a static layer solution derived through the use of integral transforms with an elementary beam or plate theory solution.
TL;DR: In this article, the natural frequencies and buckling loads of cross-ply laminated plates subjected to non-uniform initial stress were investigated, and the results obtained from the present higher-order theory were compared with first-order theories and other higher order theory results.
TL;DR: In this article, the von Karman plate theory is applied to the problem of large deflections of thin flat plates using a novel integral equation approach, and the numerical solution that is implemented combines both boundary and interior elements in the discretization of the continuum.
TL;DR: Using the Lagrangian multiplier technique, an analysis was developed to compute the natural frequencies and mode shapes of clamped orthotropic laminated plates using a higher-order plate theory as mentioned in this paper.
Abstract: Using the Lagrangian multiplier technique, an analysis was developed to compute the natural frequencies and mode shapes of clamped orthotropic laminated plates. Transverse shear deformation effects were included using a higher-order plate theory. Predictions made with the developed analysis demonstrated excellent agreement with the available experimental test results and other analytical solutions. The validated free vibration analysis has also been used to develop an analysis to predict the dynamic response of clamped orthotropic plates subjected to low-velocity impact by a hard object.
TL;DR: In this article, the deformation of an angle-ply laminated plate under transverse loading is analyzed using the bending theory of laminated plates presented by Ren, which is suitable not only for cylindrical bending but also for general bending problems.
TL;DR: In this paper, the mode approximation is modified by assuming that points on the plate surface move in a direction which is instantaneously normal to the current plate surface, which gives good predictions of the transverse displacement, and quite good estimates of in-plane strains.
TL;DR: In this article, the finite element method is used to model the noise transmission through unstiffened and stiffened laminated composite panels of finite size into a closed cavity, and the model is then used to calculate the noise reduction of the panel.
TL;DR: In this article, the classic Kirchhoff plate theory is formulated through integral representation decomposing the biharmonic field equation in two coupled harmonic equations Two domain integrals appear, one inherent to the problem and the other due to the previous decomposition.
01 Jan 1987
TL;DR: The development of consistent refined theories of anisotropic plates (and shells) which discard the Kirchhoff hypothesis has attracted increasing attention during recent years as discussed by the authors, outside the purely heuristic interest the advent of the new exotic materials such as the advanced composites, has generated the greatest stimulus for such interest.
Abstract: The development of consistent refined theories of anisotropic plates (and shells) which discard the Kirchhoff hypothesis has attracted increasing attention during recent years. Outside the purely heuristic interest the advent of the new exotic materials, such as the advanced composites, has generated the greatest stimulus for such interest.
TL;DR: In this article, the effect of free vibration of prismatic plate structures of laminated composite material and having diaphragm end supports is considered using the finite strip method, and the results demonstrate the good convergence characteristics of the finite-strip approach and reveal the relative efficiency of particular economisation schemes.
TL;DR: In this article, a shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented.
01 Jan 1987
TL;DR: In this article, a preliminary study is made of the effectiveness of cubic spline functions when used in potential energy-based analyses of symmetrically-laminated, composite rectangular plates having orthotropic or anisotropic material properties.
Abstract: A preliminary study is made of the effectiveness of cubic spline functions when used in potential-energy-based analyses of symmetrically-laminated, composite rectangular plates having orthotropic or anisotropic material properties. The problem under consideration is the determination of laminate natural frequencies and a first-order shear deformation plate theory is used. The analysis procedures employed are the Rayleigh-Ritz and finite strip methods. The numerical results presented show that the use of cubic spline functions is efficient for moderately-thick laminates and is particularly promising for anisotropic material However, for truly thin laminates the efficiency is reduced considerably.