Showing papers on "Plate theory published in 1984"
TL;DR: In this paper, a higher-order shear deformation theory of laminated composite plates is developed, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
Abstract: A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.
3,504 citations
TL;DR: In this paper, a higher-order shear deformation theory of plates accounting for the von Karman strain was presented, which contains the same dependent unknowns as in the Hencky-Mindlin type first-order deformation theories and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate.
695 citations
TL;DR: A brief review of developments in the field of plate finite elements is presented in this article, followed by an extensive tabular listing of plate bending elements and their applications in the literature.
159 citations
TL;DR: In this paper, the plate theory was extended to laminates and closed-form solutions of this theory, as well as those of Reissner-Mindlin plate theory with appropriate shear correction, Seide's discrete-layer plate theory, and the higher-order theory of Lo et al. were all compared with Pagano's elasticity-theory solution for the cases of cylindrical bending of a single orthotropic layer and a symmetric cross-ply (0°/90°/0°) laminate consisting of three equal-thickness layers
152 citations
TL;DR: In this paper, the classical plate theory of Kirchhoff is the leading term of the outer expansion solution (in a small thickness parameter) for the linear elasto-statics of thin, flat, isotropic bodies.
Abstract: Friedrichs and Dressler and Gol'denveiser and Kolos have independently shown that the classical plate theory of Kirchhoff is the leading term of the outer expansion solution (in a small thickness parameter) for the linear elasto-statics of thin, flat, isotropic bodies. As expected, neither this leading term nor the full outer solution alone is able to satisfy arbitrarily prescribed edge conditions. On the other hand, the inner solution, which is significant only near the edge, is determined by a sequence of boundary value problems which are very difficult to solve, nearly as difficult as the original problem. For stress edge-data, St. Venant's principle may be invoked to generate a set of stress boundary conditions for the classical plate theory as well as for some higher order terms in the outer expansion without any reference to the inner solution. Attempts in the literature to derive the corresponding boundary conditions for displacement edge-data have not been successful.
148 citations
TL;DR: In this article, it was shown that above the coincidence condition, when acoustic wenumber exceeds plate wavenumber, the radiation resistance is area dependent as before, and that over a wide range of parameters, radiation resistance effectively doubles in going from freely hinged edges to clamped edges.
Abstract: Detailed calculations have been given earlier for the radiation resistance, at high modal numbers, of a panel whose edges are freely hinged. The present paper deals with the more realistic case where the plate is subject at its edges to a restoring couple proportional to its angular displacement. It is shown that above the coincidence condition, when acoustic wavenumber exceeds plate wavenumber, the radiation resistance is area dependent as before. Below coincidence the radiation resistance can be determined by solving appropriate semi-infinite or quarter-infinite plate problems, and it is shown that over a wide range of parameters the radiation resistance effectively doubles in going from freely hinged edges to clamped edges.
62 citations
TL;DR: In this article, an improved analytical procedure has been developed that allows for an efficient solution of the finite plate noise transmission problem, where the plate is modeled with classical thin plate theory and is assumed to be simply supported on all four sides.
Abstract: An improved analytical procedure has been developed that allows for an efficient solution of the finite plate noise transmission problem. The plate is modeled with classical thin plate theory and is assumed to be simply supported on all four sides. The incident acoustic pressure is modeled as a plane wave impinging on the plate at an arbitrary angle of incidence. Assuming the radiation damping is negligible compared to the structural damping, the incident, reflected, and transmitted pressures are approximated by the blocked pressure which allows the plate vibrations to be calculated by a normal‐mode approach. A Green's function integral equation is used to link the plate vibrations to the transmitted farfield sound waves. The incident and transmitted acoustic powers are calculated by integrating the incident and transmitted intensities over their appropriate areas, and transmission loss is calculated from the ratio of incident to transmitted acoustic powers. The result is a versatile research and engineer...
53 citations
TL;DR: In this paper, a general buckling theory for fiber-reinforced composite laminated plates was developed using the Theorem of Minimum Potential Energy, and the Rayleigh-Ritz method was employed in the solution of the governing equations for specific boundary conditions.
Abstract: Linear viscoelasticity theory was used in the formulation of a general buckling theory for fiber-reinforced composite laminated plates. The theory includes the effects of transverse shear and normal deformation (TSD and TND, respectively) and bending-extensional coupling of time-dependen t buckling response. Anisotropic viscoelastic constants were determined using the Tsai-Halpin equations, assuming elastic fiber properties in combination with a power law viscoelastic model for the matrix properties. The governing equations of plate buckling were developed using the Theorem of Minimum Potential Energy, and the Rayleigh-Ritz method was employed in the solution of the governing equations for specific boundary conditions. Results are presented comparing viscoelastic solutions based on classical analysis, analysis including TSD effects, and analysis including both TSD and TND effects for simply supported plate subjected to inplane compressive loading a aT
51 citations
TL;DR: In this paper, the flexural vibration analysis of rectangular Mindlin plates using the collocation method is described, and the results obtained by the present method are compared with published results for plates with uniform thickness and two opposite edges simply supported.
50 citations
50 citations
TL;DR: In this article, a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated rectangular plates are described and compared with those obtained by a shear deformable plate theory.
TL;DR: In this paper, an antisymmetrically laminated angle-ply plate is optimized with the objectives of maximizing the fundamental eigenfrequency and the distance between two consecutive natural frequencies.
TL;DR: In this article, a theory of plaques minces physiquement et cinematiquement non lineaire is presented, and a concept deformation effective for simplifying the theory is introduced.
Abstract: On developpe une theorie des plaques minces physiquement et cinematiquement non lineaire. On l'utilise pour caracteriser le comportement de materiaux elastiques pour des deformations arbitraires en etirement et flexion. On introduit un concept de deformation effective pour simplifier la theorie et on l'applique a la caracterisation du papier
TL;DR: In this paper, the results of a three-dimensional, geometrically nonlinear, finite-element analysis of the bending of cross-ply laminated anisotropic composite plates are presented.
TL;DR: In this paper, the authors deal with Reissner's plate theory and present two solution techniques which avoid some inherent difficulties of the conventional approach, such as the need for accurate evaluation of singular integrals.
TL;DR: An expression for the strain energy of plates, which includes a term for transverse shear deformation and which is expressed in terms of the total transverse displacement and the displacement due to bending alone, is presented in this paper.
TL;DR: In this paper, a theory of plates is developed that retains the simplicity of Reissner's theory, yet provides reliable threedimensional information for stresses and displacements, accounting for all major influences in a rational manner.
Abstract: A theory of plates is developed that retains the simplicity of Reissner's theory, yet provides reliable threedimensional information for stresses and displacements. It accounts for all major influences in a rational manner. Reissner's equations are obtained from the new equations for isotropic materials by averaging displacement variables over the plate thickness. Application of the theory to a benchmark problem demonstrates its capability to predict stresses with precision even for very thick plates.
TL;DR: In this article, the authors discuss the large deflection bending behavior of a plate subjected to bending moments along two opposite edges and free on the other two opposite sides, and show that when the applied moments become large, the classical saddle shape disappears and the plate flattens laterally to become more cylindrical in nature.
TL;DR: In this article, the fundamental aspects of the boundary element method of the Kirchhoff theory of thin plate flexure are given, and the direct boundary integral equation method with higher conforming properties are used for several computational examples.
TL;DR: In this paper, a mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated.
TL;DR: Hybrid SemiLoof elements for plates and shells were developed in this article based on modified Hu-Washizu principle and the equilibrium equations were satisfied through the introduction of internal displacement parameters as Lagrange multipliers.
14 May 1984
TL;DR: In this paper, a simple technique was developed for calculating the strain energy release rate, G, for delamination around an open hole in a laminate, where discrete locations around the hole boundary were modeled as straight edges, with the ply orientations rotated by an appropriate angle.
Abstract: A simple technique was developed for calculating the strain-energy-release rate, G, for delamination around an open hole in a laminate. Discrete locations around the hole boundary were modeled as straight edges, with the ply orientations rotated by an appropriate angle. The circumferential strain, calculated from an elasticity solution, was substituted into a simple equation, derived from the rule of mixtures and laminated plate theory, to generate G distributions around the hole boundary. These G distributions were plotted for delamination in each unique interface of two quasi-isotropic laminates to identify critical regions for delamination onset at the hole boundary. Previous work had indicated that delamination onset in brittle epoxy composites under static loading was controlled by the critical mode I G component. In order to compare to existing experimental data, distributions of approximate interlaminar normal stresses, a,,, at the hole boundary were generated from a simple analysis based on laminated plate theory. Then, a quasi-3D finite-element analysis was performed in the regions that had both high G values and tensile ozz stresses to calculate the various G components due to interlaminar tension and shear (GI, GII, and GIII). Static delamination onset strains were predicted at locations where GI was a maximum and were compared to measured values for T300/ 5208 laminates. Curves relating interlaminar GIc to delamination onset strains were drawn to evaluate the influence of a tough matrix on laminates with open holes.
TL;DR: A boundary-integral equation method for bending of thin orthotropic linear elastic plates with polygonal planform under quasistatic pressure loading is presented in this paper, where a change from Huber's differential equation for the deflection to the simpler biharmonic equation of Kirchoff's isotropic plate theory by means of a linear transformation of the plate domain renders a non-classical boundary value problem.
TL;DR: In this paper, a triangular bending finite element is formulated by using the singular solutions, for point loads, of the plate bending equation, which can be used as a conventional triangular bending element for thin plate analysis.
Abstract: A triangular plate bending finite element is formulated by using the singular solutions, for point loads, of the plate bending equation. The element can be used as a conventional triangular bending element for thin plate analysis. Numerical results are given for both classical plate bending and mode III fracture mechanics problems.
TL;DR: In this paper, the dynamic characteristics of rotating and non-rotating practical bladed discs have been investigated by taking blade shear center effects into account, and it has been found that when these effects in the blade are high the bladed disc vibration characteristics can also be considerably changed.
TL;DR: In this article, a materially nonlinear analysis of laminated composite plates is presented, based on the Reissner-Mindlin type plate theory and a fully three-dimensional elasticity theory, which is used to analyze the bending of plates under transverse loads.
TL;DR: In this paper, the temperature distribution in the electroded quartz plate is obtained from the uncoupled heat conduction equation subject to appropriate initial and boundary conditions, and the time-dependent change in resonant frequency resulting from the biasing state is determined from an equation for the perturbation of the eigenfrequency due to a bias.
Abstract: The temperature distribution in the electroded quartz plate is obtained from the uncoupled heat conduction equation subject to appropriate initial and boundary conditions. The time‐dependent biasing state resulting from the transient temperature distribution is determined from the exact equations of static linear thermoelasticity for electrode films of zero thickness and from a system of approximate thermoelastic extensional plate equations for electrode films of finite thickness. The time‐dependent change in resonant frequency resulting from the biasing state is determined from an equation for the perturbation of the eigenfrequency due to a bias. Results are presented for a number of thermally compensated as well as uncompensated cuts of quartz for some physically meaningful temperature inputs. In particular the calculations show that in thermally compensated cuts with electrodes of finite thickness, the frequency initially shifts considerably beyond the equilibrium resonant frequency for the final uniform temperature state.
01 Mar 1984
TL;DR: In this paper, the postbuckling behavior of long rectangular isotropic and orthotropic plates is determined by assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations.
Abstract: The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.
TL;DR: In this paper, a technique is presented for the analysis of transversely loaded thin rectangular plates on Winkler foundations and is used in a parametric study of plate behaviour, based on Fourier series expansions.