Showing papers on "Bending of plates published in 2007"
TL;DR: In this paper, a non-local plate model based on Eringen's theory of nonlocal continuum mechanics is proposed, which allows for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures.
Abstract: A non-local plate model is proposed based on Eringen's theory of non-local continuum mechanics. The basic equations for the non-local Kirchhoff and the Mindlin plate theories are derived. These non-local plate theories allow for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures. As illustrative examples, the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non-local solutions are discussed in relation to their corresponding local solutions.
270 citations
TL;DR: In this article, the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow was analyzed for two boundary conditions: clamped-free and pinned-free.
250 citations
TL;DR: In this article, a non-local plate theory was proposed for axisymmetric bending of micro/nanoscale circular plates. But the nonlocal theory only allows for small scale effects and does not consider the effects of small scale on nonlocal solutions.
Abstract: Axisymmetric bending of micro/nanoscale circular plates is studied using a nonlocal plate theory. The nonlocal theory allows for small scale effects. The governing equations and boundary conditions are derived for the aforementioned problem. By using a variable transformation technique, exact nonlocal solutions for axisymmetric bending of circular plates under general loading are obtained. A detailed examination of the effects of small scale on nonlocal solutions is carried out using uniformly loaded circular plates with either clamped or simply-supported edges. When compared with local plate theory, the nonlocal solutions show larger deflections, moments and shear force and lower bending stiffness.
189 citations
TL;DR: In this article, the observed range in slab dip and the observed trends between slab dip with convergence velocity, subducting plate age, and subduction duration can be reproduced without trench motion (i.e., slab roll-back) for locations away from slab edges.
Abstract: Several models have been proposed to relate slab geometry to parameters such as plate velocity or plate age. However, studies on the observed relationships between slab geometry and a wide range of subduction parameters show that there is not a simple global relationship between slab geometry and any one of these other subduction parameters for all subduction zones. Numerical and laboratory models of subduction provide a method to explore the relative importance of different physical processes in determining subduction dynamics. Employing 2-D numerical models with a viscosity structure constrained by laboratory experiments for the deformation of olivine, we show that the observed range in slab dip and the observed trends between slab dip and convergence velocity, subducting plate age, and subduction duration can be reproduced without trench motion (i.e., slab roll-back) for locations away from slab edges. Successful models include a stiff slab that is 100–1000 times more viscous than previous estimates from models of plate bending, the geoid, and global plate motions. We find that slab dip in the upper mantle depends primarily on slab strength and plate boundary coupling, with a small dependence on subducting plate age. Once the slab sinks into the lower mantle the primary processes controlling slab evolution are (1) the ability of the stiff slab to transmit stresses up dip, (2) resistance to slab descent into the higher-viscosity lower mantle, and (3) subduction-induced flow in the mantle-wedge corner.
175 citations
TL;DR: In this paper, the effect of stand-off distance and charge mass on the response of fully clamped circular mild steel plates, of radius 53mm, subjected to blast loads travelling along tubular structures is reported.
164 citations
TL;DR: In this paper, an improved simple third-order shear deformation theory for the analysis of shear flexible plates is presented, which is composed of three parts: the simple thirdorder kinematics of displacements reduced from the higher-order displacement field derived previously by the author; a system of 10th-order differential equilibrium equations in terms of the three generalized displacements of bending plates; five boundary conditions at each edge of plate boundaries.
160 citations
TL;DR: In this article, the authors present an experimental study on plate end debonding failures in FRP-plated RC beams, which was conducted to develop a better understanding of the behavior and failure mechanisms for the subsequent development of a predictive model.
154 citations
TL;DR: In this paper, the authors used Radial basis functions (RBF) for constructing trial functions, while a spline function was used as the weighting function over a local subdomain.
137 citations
TL;DR: In this article, a simple, rationally-based predictive model for plate end debonding failures is presented, which relates the debonding failure load to the shear capacity of the beam and a number of well-defined parameters.
111 citations
TL;DR: In this article, the post-buckling response of a functionally graded material plate, subjected to thermal and mechanical loadings, is obtained analytically, using fast converging finite double Chebyshev polynomials.
109 citations
TL;DR: In this paper, a nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented.
Abstract: Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Karman's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.
TL;DR: Adjustive bending of the plates, in the surgical operation, may be an important cause of fracture of the reconstruction plates, because of generated residual stresses, which affect the mean stress in fatigue loading.
Abstract: Purpose
The purpose of this study was to identify reasons for fracture of titanium mandibular reconstruction plates, when used to bridge lateral mandibular defects after ablative tumor surgery.
Materials and Methods
Sixteen titanium reconstruction plates from sheep mandibles were examined to identify reasons for the plate fractures. The broken plates and the seemingly unbroken plates were examined separately. The plates were removed from the mandibular bone and inspected by dye penetrant examination, metallography, optical microscope, scanning electron microscope, and energy dispersive X-ray spectrometer. Furthermore, axial load fatigue tests were performed in two different environments, air and physiologic salt solution, 0.9% NaCl, to compare titanium behavior in air and the human body.
Results
The site of crack initiation was the inner curvature of the reconstruction plate, and the cracks initiated as a result of stress concentration in the shoulder fillet of the plate. The cracks grew in a cyclic manner under masticatory loading of the mandible and the plate. The plate fracture occurred by means of fatigue. The corrosive environment did not affect the failure of the titanium plate, and the fracture was not caused by hydrogen embrittlement. The results revealed that the fatigue properties of the plates may have been impaired by the residual stresses generated in plate bending.
Conclusions
Adjustive bending of the plates, in the surgical operation, may thus be an important cause of fracture of the reconstruction plates, because of generated residual stresses, which affect the mean stress in fatigue loading. To make the plates function without failure the plates should match closely with the three-dimensional shape of the mandible, to avoid any bending in the operative phase. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2007
TL;DR: In this article, a new symplectic elasticity approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and elasticity which have long been bottlenecks in the history of elasticity.
TL;DR: A particular discontinuous Galerkin finite element formulation for the simulation of Kirchhoff plates is presented in this article, which is rotation-free and utilises standard C 0 Lagrange finite element basis functions, with the required continuity imposed in a weak sense across element boundaries.
TL;DR: In this paper, a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads is presented for nonlinear thermal bending analysis.
Abstract: Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads Heat conduction and temperature-dependent material properties are both taken into account The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E Z The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis
TL;DR: In this paper, a wave-based prediction technique was proposed to push up the frequency limit of the finite element method for convex plate bending problems through an enhanced computational efficiency, and the beneficial convergence rate of the wave based method was verified for various validation examples, including the most commonly encountered boundary conditions.
TL;DR: In this article, a closed-form solution of the plate response was derived using an energy-approach to determine the variation of plate stiffness and maximum plate deflection due to changing the web angle.
Abstract: termsA44 andA55 werecalculatedusinganenergyapproach.Usingtheshear-deformableplatetheory,aclosed-form solution of the plate response was derived. The variation of plate stiffness and maximum plate deflection due to changing the web angle are discussed. The calculated results, which require significantly less computational effort and time, agree well with the three-dimensional finite element analysis. This study indicates that panels with rectangular webs resulted in a weak extensional, bending, and A55 stiffness and that the center plate deflection was minimum for a triangular corrugated core. The micromechanical analysis procedures developed in this study were used to determine the stresses in each component of the sandwich panel (face and web) due to a uniform pressure load.
TL;DR: In this article, the elastic bending of unstiffened and stiffened corrugated plates is studied, and a mesh-free Galerkin method is presented for the analyses, where the stiffness matrix is obtained by superimposing the strain energy of the orthotropic plate and the beams.
TL;DR: In this paper, a geometrically nonlinear analysis of stiffened and un-stiffened corrugated plates using a mesh-free Galerkin method that is based on the first-order shear deformation theory is presented.
TL;DR: A local a posteriori error indicator for the well known Morley element for the Kirchhoff plate bending problem is presented and is proven to be both reliable and efficient.
Abstract: A local a posteriori error indicator for the well known Morley element for the Kirchhoff plate bending problem is presented. The error indicator is proven to be both reliable and efficient. The technique applied is general and it is shown to have also other applications.
TL;DR: In this article, an analytical model estimate of the bending angle about the y-axis is constructed based on the theories of heat transfer and the mechanics of elastoplasticity.
Abstract: To obtain further insight into the deformation of a plate in the laser forming process, the temperature gradient mechanism (TGM) is studied. Through the investigation, it can be found that, under the processing conditions of TGM, the plate not only bends about the x -axis but also about the y -axis. An analytical model estimate of the bending angle about the y -axis is constructed based on the theories of heat transfer and the mechanics of elastoplasticity. Numerical simulations are carried out to investigate the deformation of the plate about the y -axis by choosing the different process parameters. The analytically based estimate is used to suggest suitable starting values for the simulation process of calculated results. The study of the bending about the y-axis may describe more fully the deformation of a plate, which is helpful in high-precision forming.
TL;DR: In this paper, the authors used finite element computations to model coating delamination under contact loading and found that shear cracks may nucleate just outside the contact area if the indentation depth or load exceeds a critical value.
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TL;DR: By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed in this paper, which combines the accuracy of B-spline functions approximation and various waveletbased elements for structural analysis.
Abstract: By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms in finite element space via the corresponding two-dimensional C1 type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle. BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element.
TL;DR: In this article, an enhanced first-order plate theory based on the mixed variational theorem (EFSDTM) developed in this paper is presented for predicting displacements and stresses for laminated and sandwich plates.
TL;DR: In this article, a point-driven, infinite fluid-loaded, laminated composite plate which is reinforced by doubly periodic parallel stiffeners is investigated theoretically and the Fourier transform is used for solving the responses of the plate and the stationary phase approximate is then employed to find an expression for the far field pressure.
TL;DR: In this paper, the authors performed a geo-metrically nonlinear analysis of Reissner-Mindlin plate by using a meshless collocation method and the use of the smooth radial basis functions (RBFs) gave an advantage to evaluate higher order derivatives of the solution at no cost on extra interpolation.
Abstract: In this paper, we perform a geo- metrically nonlinearanalysis of Reissner-Mindlin plate by using a meshless collocation method. The use of the smooth radial basis functions (RBFs) gives an advantage to evaluate higher order derivatives of the solution at no cost on extra-interpolation. Thecomputationalcost islow and requires neither the connectivity of mesh in the domain/boundary nor integrations of funda- mental/particular solutions. The coupled nonlin- ear terms in the equilibrium equations for both the plane stress and plate bending problems are treated as body forces. Two load increment schemes are developed to solve the nonlinear dif- ferential equations. Numerical verifications are given to demonstrate the efficiency and accuracy of the proposed method in comparing with exact solutionsand results from using thefinite element software (ABAQUS). Keyword: large deformation, Reissner-Mindlin plate theory, meshless collocation, radial basis functions.
TL;DR: In this article, a three-node triangular shell element is developed by combining the optimal membrane element and discrete Kirchhoff triangle (DKT) plate bending element, and is modified for laminated composite plates and shells so as to include the membrane-bending coupling effect.
Abstract: A new three-node triangular shell element is developed by combining the optimal membrane element and discrete Kirchhoff triangle (DKT) plate bending element, and is modified for laminated composite plates and shells so as to include the membrane-bending coupling effect. Using appropriate shape functions for the bending and membrane modes of the element, the 'inconsistent' stress stiffness matrix is formulated and the tangent stiffness matrix is determined. Non-linear analysis of thin-walled structures with geometric non-linearity is conducted using the corotational method. The new element is thoroughly tested by solving few popular benchmark problems. The results of the analysis are compared with those obtained using existing membrane elements.
TL;DR: In this article, a Navier-type method for finding the exact three-dimensional solution for isotropic thick and thin rectangular plates is presented, which uses the Mixed Form of Hooke's Law (MFHL) which leads one to write the boundary conditions on the top and bottom surfaces of the plate directly in terms of transverse stresses.
TL;DR: In this article, the Euler equations for the estimate of the energy are regarded as the equilibrium equations for thin prismatic elastic bodies, and they are solvable provided that the three-dimensional strain energy is strongly elliptic at equilibrium.
Abstract: Non-linear plate theory for thin prismatic elastic bodies is obtained by estimating the total three-dimensional strain energy generated in response to a given deformation in terms of the small plate thickness. The Euler equations for the estimate of the energy are regarded as the equilibrium equations for the thin plate. Included among them are algebraic formulae connecting the gradients of the midsurface deformation to the through-thickness derivatives of the three-dimensional deformation. These are solvable provided that the three-dimensional strain energy is strongly elliptic at equilibrium. This framework yields restrictions of the Kirchhoff–Love type that are usually imposed as constraints in alternative formulations. In the present approach they emerge as consequences of the stationarity of the energy without the need for any a priori restrictions on the three-dimensional deformation apart from a certain degree of differentiability in the direction normal to the plate.