Showing papers on "Bending of plates published in 2002"

Composite Materials: Design and Applications

Abstract: PART ONE PRINCIPLES OF CONSTRUCTION COMPOSITE MATERIALS, INTEREST AND PROPERTIES What is Composite Material Fibers and Matrix What can be Made Using Composite Materials? Typical Examples of Interest on the Use of Composite Materials Examples on Replacing Conventional Solutions with Composites Principal Physical Properties FABRICATION PROCESSES Molding Processes Other Forming Processes Practical Hints in the Manufacturing Processes PLY PROPERTIES Isotropy and Anisotropy Characteristics of the Reinforcement-Matrix Mixture Unidirectional Ply Woven Fabrics Mats and Reinforced Matrices Multidimensional Fabrics Metal Matrix Composites Tests SANDWICH STRUCTURES: What is a Sandwich Structure? Simplified Flexure A Few Special Aspects Fabrication and Design Problems Nondestructive Quality Control CONCEPTION AND DESIGN Design of a Composite Piece The Laminate Failure of Laminates Sizing of Laminates JOINING AND ASSEMBLY Riveting and Bolting Bonding Inserts COMPOSITE MATERIALS AND AEROSPACE CONSTRUCTION Aircraft Helicopters Propeller Blades for Airplanes Turbine Blades in Composites Space Applications COMPOSITE MATERIALS FOR OTHER APPLICATIONS: Composite Materials and the Manufacturing of Automobiles Composites in Naval Construction Sports and Recreation Other Applications PART TWO: MECHANICAL BEHAVIOR OF LAMINATED MATERIALS ANISOTROPIC ELASTIC MEDIA: Review of Notations Orthotropic Materials Transversely Isotropic Materials ELASTIC CONSTANTS OF UNIDIRECTIONAL COMPOSITES: Longitudinal Modulus Poisson Coefficient Transverse Modulus Shear Modulus Thermoelastic Properties ELASTIC CONSTANTS OF A PLY ALONG AN ARBITRARY DIRECTION: Compliance Coefficients Stiffness Coefficients Case of Thermomechanical Loading MECHANICAL BEHAVIOR OF THIN LAMINATED PLATES: Laminate with Miplane Symmetry Laminate without Miplane Symmetry PART THREE: JUSTIFICATIONS, COMPOSITE BEAMS, THICK PLATES ELASTIC COEFFICIENTS Elastic Coefficients in an Orthotropic Material Elastic Coefficients for a Transversely Isotropic Material Case of a Ply THE HILL-TSAI FRACTURE CRITERION: Isotropic Material: Von Mises Criterion Orthotropic Material: Hill-Tsai Criterion Evaluation of the Resistance of a Unidirectional Ply with Respect to the Direction of Loading COMPOSITE BEAMS IN FLEXURE: Flexure of Symmetric Beams with Isotropic Phases The Case of any Cross Section (Asymmetric) COMPOSITE BEAMS IN TORSION: Uniform Torsion Location of the Torsion Center FLEXURE OF THICK COMPOSITE PLATES: Preliminary Remarks Displacement Field Strains Constitutive Relations Equilibrium Equations Technical Formulation for Bending Examples PART FOUR: APPLICATIONS LEVEL 1 Simply Supported Sandwich Beam Poisson Coefficient of a Unidirectional Layer Helicopter Blade Transmission Shaft for Trucks Flywheel in Carbon/Epoxy Wing Tip Made of Carbon/Epoxy Carbon Fibers Coated with Nickel Tube Made of Glass/Epoxy Under Pressure Filament Wound Reservoir, Winding Angle Filament Wound Reservoir, Taking into Account the Heads Determination of the Volume Fraction of Fibers by Pyrolysis Lever Arm Made of Carbon/Peek Unidirectionals and Short Fibers Telegraphic Mast in Glass/Resin Unidirectional Ply of HR Carbon Manipulator Arm of Space Shuttle LEVEL 2 Sandwich Beam: Simplified Calculations of the Shear Coefficient Procedure for Calculation of a Laminate Kevlar/Epoxy Laminates: Evolution of Stiffness Depending on the Direction of the Load Residual Thermal Stresses Due to Curing of the Laminate Thermoelastic Behavior of a Tube Made of Filament Wound Glass/Polyester Polymeric Tube Loaded by Thermal Load and Creep First Ply Fracture of a Laminate Ultimate Fracture Optimum Laminate for Isotropic Stress State Laminate Made of Identical Layers of Balanced Fabric Wing Spar in Carbon/Epoxy Determination of the Elastic Characteristics of a Carbon/Epoxy Unidirectional Layer from Tensile Test Sail Boat Shell in Glass/Polyester Determination of the in-Plane Shear Modulus of a Balanced Fabric Ply Quasi-Isotropic Laminate Orthotropic Plate in Pure Torsion Plate made by Resin Transfer Molding (RTM) Thermoelastic Behavior of a Balanced Fabric Ply LEVEL 3 Cylindrical Bonding Double Bonded Joint Composite Beam with Two Layers Buckling of a Sandwich Beam Shear Due to Bending in a Sandwich Beam Column Made of Stretched Polymer Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading Bending of a Sandwich Plate Bending Vibration of a Sandwich Beam Appendix 1: Stresses in the Plies of a Laminate of Carbon/Epoxy Loaded in its Plane Appendix 2: Buckling of Orthotropic Structures Bibliography

Temperature Profile Influence on Layered Plates Response Considering Classical and Advanced Theories

Abstract: A study on the influence of the through-the-thickness temperature profile T(z) on the thermomechanical response of multilayered anisotropic thick and thin plates has been conducted. The heat conduction problem is solved, and the temperature variation T c (z) is then calculated. The governing thermomechanical equations of multilayered plates are written considering a large variety of classical and advanced or zigzag theories into account. The principle of virtual displacement and the Reissner mixed variational theorem are employed. Linear, up to fourth-order expansions in z are retained for the assumed transverse stress and displacement fields. As a result, more than 20 plate theories are compared. The numerical investigation is restricted to orthotropic layered plates with harmonic in-plane distribution of both thermal loadings and unknown variables. Four sample plate problems are treated that are related to plates made of isotropic and/or orthotropic layers that are loaded by different top-bottom plate surface temperature conditions. Comparison is made to results related to a linear profile T a (z), which is usually assumed in open literature. The following is concluded: Thick plates could exhibit a layerwise form temperature profile T c (z). T a (z) case is approached for thin plate geometries. The use of linear temperature profile leads to large errors in tracing the response of thick plate geometries. The accuracy of plate theories is affected to great extent by the form of temperature variation T(z). Refinements of classical plate theories can be meaningless unless the calculated T c (z) is introduced. The layerwise form of T c (z) would require layerwise assumptions for stresses and/or displacements. Plate theories that neglect transverse normal strains lead to very inaccurate results in both thick and thin plates analysis. At least a parabolic expansion for transverse displacement is required to capture transverse normal thermal strains that vary linearly along the plate thickness.

Flexural vibration of perforated plates and porous elastic materials under acoustic loading.

Abstract: This paper presents a method of theoretical treatment of acoustic coupling due to flexural vibration of perforated plates and plates of porous elastic materials. The analytical model is developed by introducing flow continuity at the plate surface in a spatially mean sense and air-solid interaction within the plate material. To demonstrate the method of application, some fundamental acoustic problems based on a classical thin-plate theory are analyzed and discussed in relation to the interactive effect of flexural vibration and plate permeability. For acoustic radiation from a vibrating plate excited by a harmonic point-force, the attenuation effect of power radiation appears at frequencies below the critical frequency of coincidence. In the problem of sound absorption of a perforated plate or a plate of porous elastic material backed by an air layer, as permeability decreases, the effect of plate vibration increases. For perforated absorber systems including plate vibration effects, the trend of variation from ordinary theory depends on plate thickness.

On consistent plate theories

Abstract: Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction.

Vibration damping shim structure

Abstract: A vibration damping shim structure is provided, which not only can sufficiently exert vibration damping effect in a wide range of temperatures, but also can prevent a squeal phenomenon particularly in low temperatures. A rubber coating layer (a1) is formed on one side of a first constraint plate (a2) of a metallic plate and a second constraint plate (a4) is stuck to the other side of the first constraint plate (a2) with a adhesive layer (a3) placed in-between. The ratio of the thickness of the first constraint plate (a2) to a sum total of the thickness of the back plate (b1) forming a disc brake B and the second constraint plate (a4) is taken as within 0.1 to 0.2, and the second constraint plate (a4) is used so as to be brought into contact with the back plate (b1).

Progressive Failure Analysis of Laminated Composite Plates by Finite Element Method

Abstract: The progressive failure analysis of laminated composite plates under transverse static loading has been carried out in linear and elastic range. The laminated composite plate has been modeled using eight noded isoparametric plate bending elements. The first order shear deformation theory has been applied and a shear correction factor is used. After the failure of the weakest ply, the stiffness is reduced by either fiber failure or matrix failure. The stiffness of failed lamina has been totally discarded and other existing laminae are considered to remain unchanged after the weakest ply failure. The strength of the laminate at the same point is evaluated again to see if the laminate can carry additional load. This ply-by-ply analysis progresses until the ultimate strength of the laminate is reached. The results in terms of first-ply failure load obtained in the present investigation have been compared with those available in published literature. A parametric study has been done on the progressive failure ...

A Green's function approach to the deflection of a FGM plate under transient thermal loading

Abstract: Green's function approach is adopted for analyzing the deflection and the transient temperature distribution of a plate made of functionally graded materials (FGMs). The governing equations for the deflection and the transient temperature are formulated into eigenvalue problems by using the eigenfunction expansion theory. Green's functions for solving the deflection and the transient temperature are obtained by using the Galerkin method and the laminate theory, respectively. The eigenfunctions of Green's function for the deflection are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the plate. The eigenfunctions of Green's function for the temperature are determined from the continuity conditions of the temperature and the heat flux at interfaces.

A new stiffened plate element for the analysis of arbitrary plates

Abstract: In spite of the large number of finite elements developed so far, most of these lack in generality, and are found to be inadequate and inefficient in some way or other, when it comes to analyzing plates of arbitrary geometrical configurations. So far the isoparametric element has been the most successful among available elements because of its ability to model a curved boundary successfully. However, the shear-locking problem inherent in the isoparametric element makes it unsuitable for analyzing thin plates of arbitrary shapes. Though research has been conducted using reduced integration and stabilization to overcome the problem, the formulations either do not converge to the correct solution in the thin-plate limit or they make the stiffness matrix a singular one. In this paper, a four-noded stiffened plate element is developed. This has the advantages and elegance of an isoparametric element in modelling arbitrary shaped plates, but without the disadvantage of shear-locking phenomena. Though this element is a high-order element, only the usual degrees of freedom have been considered, and performance is superior to that of the low-order ones. The stiffened plate element has the feature of accommodating the arbitrary shape of the plate geometry, and the stiffener modelling has been done in a general manner, with the stiffener lying anywhere with arbitrary orientation, and not necessarily following the nodal lines. The new element has been successfully used for the static, free vibration and stability analyses of arbitrary bare and stiffened plates. The results are found to agree quite satisfactorily with those of previous investigators.

Fixation stability of comminuted humeral shaft fractures: locked intramedullary nailing versus plate fixation.

Abstract: Background: This study compared the fixation stability of two treatments for humeral shaft fractures with segmental bone loss during cyclic, physiologic loading. Methods: Six matched pairs of human humeri received either a 10-hole broad dynamic compression plate or a locked antegrade inserted humeral nail applied to a humeral diaphyseal osteotomy with a 1.5-cm gap defect. The bone-implant humeral constructs were axially loaded for 10,000 cycles at 250 N and 500 N, with measurements of gap displacement and calculation of construct stiffness. The specimens were then loaded to failure. Results: Cyclic loading showed no difference between the two groups for average gap displacement or construct stiffness. The intramedullary nail constructs failed by humeral shaft splitting (n = 4) or head cut-out (n = 2) at an average of 958.3 N, whereas the plate constructs failed by humeral shaft splitting and screw pull-out (n = 3) or plate bending (n = 3) at an average of 641.7 N (p < 0.001). Conclusion: Although both methods offer similar fixation stability under physiologic loads, the higher load to failure demonstrated by intramedullary nail fixation may have implications for the patient with multiple injuries for whom partial weightbearing on the injured upper extremity may be necessary.

On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models

Abstract: We show that the Reissner-Mindlin plate bending model has a wider range of applicability than the Kirchho-Love model for the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the transverse direction, the Reissner-Mindlin model solution converges to the three-dimensional linear elasticity solution in the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear eect, the Kirchho-Love model fails.

Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory

Abstract: A finite element based on the efficient higher-order zig-zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig-zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig-zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher-order zig-zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three-dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd.

Hygrothermal Effects on the Nonlinear Bending of Shear Deformable Laminated Plates

Abstract: The influence of hygrothermal effects on the nonlinear bending of shear deformable laminated plates subjected to a uniform or sinusoidal load is investigated using a micro-to-micromechanical analytical model. The material properties of the composite are affected by the variation of temperature and mositure, and are based on a micromechanical model of a laminate. The governing equations of a laminated plate are based on Reddy's higher-order shear deformation plate theory with von Karman-type kinematic nonlinearity, and including hygrothermal effects. A perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates under different sets of environmental conditions. The results presented show the effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on the nonlinear bending behavior of the plate.

Flexural waves on narrow plates

Abstract: Flexural wave speeds on beams or plates depend upon the bending stiffnesses, which differ by a well‐known factor depending on the Poisson’s ratio. A quantitative analysis of a plate of finite lateral width displays the plate‐to‐beam transition, and permits asymptotic analysis that shows the dependence on the width. Orthotropic plates are analyzed using both the Kirchhoff and Kirchhoff–Rayleigh theories, and isotropic plates are considered for Mindlin’s theory with and without rotational inertia. A frequency dependent Young’s modulus for beams or strips of finite width is suggested, although the form of the correction to the modulus is not unique and depends on the theory used. The sign of the correction for the Kirchhoff theory is opposite to that for the Mindlin theory. These results indicate that the different plate and beam theories can produce quite distinct behavior. This divergence in predictions is further illustrated by comparison of the speeds for antisymmetric flexural modes on narrow plates. Th...

Application of the local boundary integral equation method to boundary-value problems

Abstract: A review of the meshless formulations based on local boundary integral equation (LBIE) methods is presented. Physical quantities are approximated by the moving least-squares method. A summary of recent developments in the application of the LBIE method to potential problems, elastostatics, elastodynamics, thermoelasticity, and plate bending problems is given. The efficiency and generality of the present formulation in a wide class of engineering problems are confirmed.

An improved four-node hybrid-mixed element based upon Mindlin's plate theory

Abstract: Based on the mixed shear projected (MiSP) approach (Reference [54]: Int J Numer Meth Engng 1998; 42:1149–1179), an enhanced bending approximation for homogeneous isotropic plates is presented Some hard benchmark tests, such as the skew plate (30°) problem, have often shown poor convergence when low-order elements (3- or 4-node element) are developed using linear approximations for kinematic variables To put right this weakness, we propose a high-order interpolation for rotational dofs which results in more rich bending curvatures The mid-side rotational nodes are eliminated using a combination of local discrete kinematic and constitutive Mindlin hypotheses The derived 4-node quadrilateral element, called MiSP4+, is free of shear locking and passes all patch tests for thick and thin plates in an arbitrary mesh Copyright © 2002 John Wiley & Sons, Ltd

Analysis of a Composite Piezoelectric Circular Plate With Initial Stresses for MEMS

Abstract: The paper presents a mechanical analysis of the multi-layer circular composite plate For MEMS devices Each layer of the plate is assumed to have different radius, material properties and initial stresses Governing equations for the composite plate are derived based on the classical laminated plate theory, and analytical soultions have been developed for static deflection of the initially stressed plate due to transverse pressure loading as well as for a given electric field in the piezoelectric layer A nonlinear finite elernent analysis of the plate is also performed The analytical result match the FE results for the range of parameters used in the microphone design The analytical model will be useful in the design and optimization of MEMS devices containing circular piezoelectric composite plates and diaphragmsCopyright © 2002 by ASME

Stiffened plate bending analysis by the boundary element method

Abstract: In this work, the plate bending formulation of the boundary element method (BEM) based on the Kirchhoff's hypothesis, is extended to the analysis of stiffened elements usually present in building floor structures. Particular integral representations are derived to take directly into account the interactions between the beams forming grid and surface elements. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composite structure as a single body. Two possible procedures are shown for dealing with plate domain stiffened by beams. In the first, the beam element is considered as a stiffer region requiring therefore the discretization of two internal lines with two unknowns per node. In the second scheme, the number of degrees of freedom along the interface is reduced by two by assuming that the cross-section motion is defined by three independent components only.