Plate Deformation Theory Research Articles

Hygrothermal stress analysis of laminated composite porous plates

This paper presents the stress analysis of a composite laminated simply supported plate with porosity under hygrothermal rising. In the displacement-strain relation of the plate structure, the first shear plate deformation theory is used. Material properties of laminas are considered as orthotropic. Three different porosity distributions are used. In the solution process, the Navier method is implemented for simply supported laminated composite plate. Non-uniform temperature and moisture rising are considered for laminated plate with three laminas. In the numerical results, the stress distributions of the laminated plate are presented and discussed for different values of moisture, temperature, stacking sequence of laminas and orientation angle of layers. The numerical results show that the hygrothermal condition is very effective in the stress behavior of laminated plates.

Mechanical Reshaping of Inorganic Nanostructures with Weak Nanoscale Forces.

Inorganic nanomaterials are often depicted as rigid structures whose shape is permanent. However, forces that are ordinarily considered weak can exert sufficient stress at the nanoscale to drive mechanical deformation. Here, we leverage van der Waals (VdW) interactions to mechanically reshape inorganic nanostructures from planar to curvilinear. Modified plate deformation theory shows that high-aspect-ratio two-dimensional particles can be plastically deformed via VdW forces. Informed by this finding, silver nanoplates were deformed over spherical iron oxide template particles, resulting in distinctive bend contour patterns in bright-field (BF) transmission electron microscopy (TEM) images. High-resolution TEM images of deformed areas reveal the presence of highly strained bonds in the material. Finally, we show that the distance between two nearby template particles allows for the engineering of several distinct curvilinear morphologies. This work challenges the traditional view of nanoparticles as static objects and introduces methods for postsynthetic mechanical shape control.

A predictive critical flutter wind speed modeling for long-span bridges

In this article, a two-dimensional Lighthill aerodynamic model is first extended to three-dimensional space, and then combined with the larger Von Karman plate deformation theory, a model for predicting the critical flutter wind speeds of long-span bridges in the primary design is proposed. The predictions of the presented model are compared to the results of wind tunnel tests for five long-span bridges with different main girder section forms. After that, based on the proposed model, the effects of width to span ratio and thickness to span ratio on the critical flutter wind speeds of long-span bridges are investigated. The results show that the differences between the proposed model and wind tunnel tests are only 7%–14%. Therefore, the presented model can assess the flutter wind speed in preliminary design stages of a bridge. The results also reveal that width to span ratios between 1/30 and 1/10 and thickness to span ratios between 1/300 and 1/100 are optimal for long-span bridges.

Design of variable stiffness composite structures using lamination parameters with fiber steering constraint

In this study, a lamination parameter based optimization algorithm is developed in a finite element framework using classical plate deformation theory. The optimization reveals lamination parameter distribution over the plate which are then converted into fiber directions, stacking sequences and layer thicknesses by means of a material library. The optimum fiber angles in each ply are used to find continuous fiber angle distributions a using weighted residual method for the first time. The method uses finite element based least-squares and continuity constraint (LSC) to find a manufacturable design without making any preliminary assumption such as splines, stream functions, etc., for the fiber angle distributions. Penalty parameter is used to enforce a maximum limiting value for the fiber curvatures. The proposed method is applied to design for the minimum compliance in-plane and out-of-plane problems, and significant improvements are obtained in comparison to the literature findings.

Bending of a Thin Rectangular Isotropic Micropolar Plate

In this note, deflection of a thin rectangular isotropic micropolar plate is observed under the influence of transverse loading. From the properties of asymptotic solution, a set of hypotheses is considered and the corresponding governing equations of bending are derived. The solutions are validated by comparing the numerical results and with their counterparts reported in literature for classical Timoshenko plate theory and the Kirchhoff’s theory of plate deformation.

Buckling and free vibration analysis of piezoelectric laminated composite plates using various plate deformation theories

A finite strip method was developed for buckling and free vibration analysis of piezoelectric laminated composite plates based on various plate theories such as Zigzag, Refined plate and other higher order shear deformation theory by variation of transverse shear strains through plate thickness in the form of parabolic, sine and exponential. The plate edge conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the in–plane and out–of–plane deflection and rotation of the normal cross section of plates in transverse direction. Numerical results were obtained based on various shear deformation plate theories to verify the proposed method. The effects of length to thickness ratio and fiber orientation of cross–ply and angle–ply laminate were presented. Also, the effect of different electrical conditions on the critical buckling load under in–plane forces and strains is investigated and electrical buckling load and natural frequency of piezoelectric laminate composite plates are calculated through numerical examples. In addition, the new results on the effect of piezoelectric layers thickness, placement of piezoelectric layers and also the effect of length to thickness ratio in the interaction of biaxial in–plane loading on critical buckling load were studied.

On the optimal shape parameters of distinct versions of RBF meshless methods for the bending analysis of plates

This study intends to computationally analyze single-layer plates. Reissner–Mindlin plate deformation theory was combined with the radial basis function (RBF) meshless method. Considering the first order shear deformation theory, the RBF meshless method formulation for isotropic plates analysis is presented. According to the motion equations in terms of displacement for isotropic homogeneous laminates, non-zero laminate stiffness is determined. Transverse displacement results are evaluated for various thickness values where the plate is simply supported in all edges. In this work, it is also shown that Wendland's RBF formulation with optimal values of the shape parameter formulation using several mesh densities produces deflections of single-layer laminate plates agreeing well with analytical solutions. The obtained RBF solution proves that the supporting numerical methodology is efficient and robust.

An Optimized RBF Analysis of an Isotropic Mindlin Plate in Bending

This study focuses on the numerical analysis of an isotropic plate under a uniform distributed load. The problem is solved considering the Reissner-Mindlin plate deformation theory combined with a Radial Basis Function (RBF) meshless method. Thus, in this work, the RBF meshless method formulation for the analysis of thick isotropic plates assuming a first order shear deformation theory is shown with detail. Additionally, the essential boundary conditions, material properties and geometrical characteristics of the model are fully presented. In this work, the nonzero laminate stiffnesses are determined through equations of motion in terms of displacements for homogeneous laminates.The transverse displacement results are evaluated for various thickness values where the plate is simply supported in all edges. Additionally, the shape parameter governing the RBF formulation is optimized using several mesh densities. The obtained numerical results are compared to the exact analytical solution available in the literature. Accurate RBF solutions are obtained, supporting the efficiency of the numerical methodology.

Deformation Analysis for Hydrostatic Rotary Table of Heavy Duty CNC Machine Tool

The deformation of constant flow and closed type hydrostatic rotary table of heavy duty CNC machine tool has a great influence on the film thickness because of its large diameter, high load-bearing. According to the circular plate deformation theory of elasticity, differential equations of worktable deformation are derived in the simply supported conditions when bearing uniform force of different locations. Displacement curves of worktable are obtained. Force and deformation weaknesses of hydrostatic rotary table are found, which can provide theory basis for supporting location of heavy workpiece machining and whether oil film is failure or not.

J191022 長方形平板の熱座屈解析について

This report describes the outline of the thermal stress analysis of flat plate Especially, we describe the plate deformation theory under the Kirchhoff s hypothesis We derive the two differential equations One governs the out of plane deformation of the plate The equation contains the thermal moment term The other governs the in-plane deformation of the plate The two differential equations are independent Furthermore, the differential equation which governs the thermal buckling problem is derived Some simple thermal buckling problems are solved The analytically obtained solution is compared with the finite element method solution

Static and dynamic analysis of laminated plates based on an unconstrained third order theory and using a radial point interpolator meshless method

The Natural Neighbour Radial Point Interpolation Method (NNRPIM), an improved meshless method, is used in the numerical implementation of an Unconstrained Third-Order Plate Theory applied to laminates. The nodal connectivity and the node dependent integration background mesh are constructed resorting to the Voronoï tessellation and to the Delaunay triangulation. Within NNRPIM the obtained interpolation functions, constructed with the Radial Point Interpolators, pass through all nodes inside the influence-cell providing the interpolation functions with the delta Kronecker property. In order to prove the high accuracy and convergence rate of the proposed meshless method several well-known benchmark static and dynamic laminate examples are solved. The numerical results obtained with the NNRPIM are compared with the Unconstrained Third-Order Plate Theory exact solution, when available, and with exact solutions of other plate deformation theories.

Thermo-optic Effects of Bragg Grating Optical Temperature Sensor

This paper demonstrates a comparison of linear and nonlinear analyses for thermo-optic effects of optical temperature sensor based on the etched silica-based planar waveguide Bragg grating. Topics include theoretical analyses and experiment of the etched planar waveguide Bragg grating optical temperature sensor. Theoretical models with nonlinear than linear temperature effect for the grating response based on waveguide and plate deformation theories agree with experiments to within acceptable tolerance.

A higher order shear deformable finite element for homogeneous plates

A C 0 finite element is introduced for the analysis of thick plates with transverse shear and normal strain and nonlinear in-plane displacement distribution with respect to the plate thickness. The warping theory proposed by Hassis [1] is used for the equations governing the plate deformation. The analytical solutions of the plate deformation theory were compared with other higher-order theories and found to be predicting the thick plate behavior reasonably well. Based on this higher order shear deformation theory, an eight-node finite element is introduced for thick plates, and a computer program is developed. The warping functions used in the formulations presented simpler equations than the other higher order homogeneous models. The proposed element incorporates bending–stretching coupling via the additional terms introduced in the displacement field. Some example problems are solved and the results are compared with the exact and other mathematical solutions available in the literature. For comparison, both stress and displacement results are investigated. The results of the proposed element are found to be in good agreement with the literature.

Planar optical waveguide temperature sensor based on etched bragg gratings considering nonlinear thermo-optic effect

This paper demonstrates the development of optical temperature sensor based on the etched silica-based planar waveguide Bragg grating. Topics include design and fabrication of the etched planar waveguide Bragg grating optical temperature sensor. The typical bandwidth and reflectivity of the surface etched grating has been ∼0.2 nm and ∼9 %, respectively, at a wavelength of ∼1552 nm. The temperature-induced wavelength change is found to be slightly non-linear over ∼200 °C temperature range. Typically, the temperature-induced fractional Bragg wavelength shift measured in this experiment is 0.0132 nm/°C with linear curve fit. Theoretical models with nonlinear temperature effect for the grating response based on waveguide and plate deformation theories agree with experiments to within acceptable tolerance.

A HIGHER ORDER THEORY FOR STATIC–DYNAMIC ANALYSIS OF LAMINATED PLATES USING A WARPING MODEL

A higher order theory is developed to model the behaviour of laminated plates. This theory is based on a warping theory of plate deformation developed by Hassis [1]. Through comparison with elasticity solutions obtained with classical models [2–6] and the higher order theory of Lo et al.[7, 8], it is shown that the present theory correctly models effects not attainable by the low order theories.

A “WARPING-KIRCHHOFF” AND A “WARPING-MINDLIN” THEORY OF SHELL DEFORMATION

The warping high-order theory of plate deformation developed in reference [1] is extended here to shells. A theory of shell deformation is derived which accounts for the effects of transverse shear deformation and a non-linear distribution of the in-surface displacements with respect to the thickness co-ordinate. This theory uses the normal modes associated to the normal fibre (considered as a geometrical beam) as basis functions. Using only the rigid body modes, we find the classical theory and using the deformation normal modes, a high order theory is constructed. This theory is compared to other theories and the exact solution through an application to a particular problem of shells.

Un modèle de gauchissement des coques

ABSTRACT The warping high-order theory of plate deformation developed in [HAS 98] is extended here to shells. A theory of shell deformation is derived which accounts for the effects of transverse shear deformation and a non linear distribution of the in-surface displacements with respect to the thickness coordinate. This theory uses the normal modes associated to the normal fibre (considered such as a geometrical beam) as basis functions. Using only the rigid body modes, we find the classical theory and using the deformation normal modes, a high order theory is constructed. Our theory is compared with other theory and the exact solution through application to a particular problem of shells.

A ‘warping’ theory of plate deformation

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain and a non-linear distribution of the in-plane displacements with respect to the thickness coordinate. This theory uses the normal modes associated with the normal fibre (considered as a geometrical beam) as basic functions. Using only the rigid body modes, we find the classical theory and using the deformation normal modes, a high-order theory is constructed. Our theory is compared with lower-order plate theories, with higher-order theory and the exact solution through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. A circular plate submitted to in-plane forces is analysed. The present work involves homogeneous plates and can be extended to laminated plates.

A finite volume method for analysing the bending deformation of thick and thin plates

The formulation of a novel finite volume based procedure for determining deformations and moment distributions within transversely loaded plates is described in detail. The formulation employs the Mindlin theory of plate deformation. Transverse displacement and bending moment distributions are determined for a number of test problems. The effect of mesh refinement upon the accuracy of the displacement and moment fields is investigated. The finite volume procedure exhibits a number of interesting features; it is conservative in the sense that equilibrium is satisfied locally within each cell and across cell boundaries, it has the capacity to represent the behaviour of thick and thin plates and it is geometrically versatile because the cell shapes can take the form of multifaceted polygons.

Stress solution determination for high order plate theory

The high order theory of plate deformation developed in Ref.[1] and [2] is further examined herein. Specifically, stress solutions are given and evaluated against exact elasticity solutions under stringent short wave length load conditions. By the first method the stresses are evaluated directly from the resulting displacement solutions. In a more refined procedure, the transverse shear stresses and the transverse normal stress are evaluated by an alternate equilibrium method. The latter procedure is shown to be more accurate than the former.