Stresses in Marine Propellers

The exact value of Sanders’ path-independent, energy-release rate integral I for an infinite, bent elastic slab containing an elliptic hole is shown to be approximated by its value from classical plate theory to within a relative error of O(h/c)F(e), where h is the thickness, c is the semimajor axis of the ellipse, and F is a function of the eccentricity e. This result is based on Golden’veiser’s analysis of three-dimensional edge effects in plates, as developed by van der Heijden. As the elliptic hole approaches a crack, F(e)~In (1−e). However, this limit is physically meaningless, because Golden’veiser’s analysis assumes that h is small compared to the minimum radius of curvature of the ellipse. Using Knowles and Wang’s analysis of the stresses in a cracked plate predicted by Reissner’s theory, we show that the relative error in computing I from classical plate theory is only O(h/c)In(h/c), where c is the semicrack length. Our results suggest that classical plate and shell theories are entirely adequate for predicting crack growth, within the limitations of applying any elastic theory to an inherently inelastic phenomenon.

General spline finite strip analysis for buckling and vibration of prismatic composite laminated plate and shell structures

The influence of boundary conditions and transverse shear on the vibration of angle-ply laminated plates, circular cylinders and cylindrical panels

In this paper, a new structural strain method is presented to extend the early structural stress based master S-N curve method to low cycle fatigue regime in which plastic deformation can be significant while an elastic core is still present. The method is formulated by taking advantage of elastically calculated mesh-insensitive structural stresses based on nodal forces available from finite element solutions. The structural strain definition is consistent with classical plate and shell theory in which a linear through-thickness deformation field is assumed a priori in both elastic and elastic-plastic regimes. With considerations of both yield and equilibrium conditions, the resulting structural strains are analytically solved if assuming elastic and perfectly plastic material behavior. The formulation can be readily extended to strain-hardening materials for which structural strains can be numerically calculated with ease. The method is shown effective in correlating low-cycle fatigue test data of various sources documented in the literature into a single narrow scatter band which is remarkable consistent with the scatter band of the existing master S-N curve adopted ASME B&PV Code since 2007. With this new method, some of the inconsistencies of the pseudo-elastic structural stress procedure in 2007 ASME Div 2 Code can now be eliminated, such as its use of Neuber’s rule in approximating structural strain beyond yield. More importantly, both low cycle and high cycle fatigue behaviors can now be treated in a unified manner. The earlier mesh-insensitive structural stress based master S-N curve method can now be viewed as an application of the structural strain method in high cycle regime, in which structural strains are linearly related to traction-based structural stresses according to Hook’s law. In low-cycle regime, the structural strain method characterizes fatigue damage directly in terms of structural strains that satisfy linear through-thickness deformation gradient assumption, material nonlinear behavior, and equilibrium conditions. The use of a pseudo-elastic structural stress definition is not fundamental, but merely a means to put low-cycle and high-cycle fatigue test data in a conventional stress-based S-N data representation which is typically preferred in engineering practice, than a strain-based representation.

Buckling behavior of functionally graded materials cylindrical shell under pure bending is studied in this paper. The stability equations of functionally graded materials cylindrical shell are derived using the classical plate and shell theory with Kirchhoff hypothesis, importing the bending boundary condition to obtain the critical buckling load. The result shows that the critical moment is linear with the radius, quadratic with the thickness and irrelevant with the length of the cylindrical shell. In addition, the critical moment is decreased by increasing the power law index of the material bulk, trending to a constant finally.

In the absence of analytical expressions for the equivalent circuit parameters it is difficult to calculate the optimal design parameters and dimensions and to chose suitable materials. The influence of coupling between flexural and extensional deformation and coupling between structure and acoustic volume on the dynamic response of piezoelectrically actuated flextensional transducer is analyzed using three analytical methods: classical plate theory, Mindlin plate theory, and simple variational procedure. The transducer design is based on a flextensional transducer that excites the axisymmetric resonant modes of a clamped circular plate. It is constructed by depositing a thin piezoelectric annular plate onto a thin, edge clamped, circular plate. An ac voltage is applied accross the piezoelectric material to set the compound membrane into flexural vibration. The devices have a range of operating resonance frequencies starting from 450 kHz up to 4.5 MHz. The device is manufactured by silicon surface micromachining and implemented in the form of two-dimensional arrays. Individual elements are made of thin silicon nitride membranes covered by a coating of piezoelectric zinc oxide. Classical thin plate theory, Mindlin plate theory, and variational methods are applied to derive two-dimensional plate equations for the transducer, and to calculate the coupled electromechanical field variables such as mechanical displacement. These methods use classical kinematic relations for a plate and a variational equation for the coupled electromechanical field to reduce three-dimensional field equations to two-dimensional plate equations. As a result, three different exact solutions to corresponding systems are obtained. An equivalent circuit of the transducer is also obtained from these solutions.

9 - Relationships between vibration frequencies of higher-order plate theories and classical thin plate theory

A finite element displacement model was utilized to predict the elastic behavior of a propeller blade having an arbitrary shape and subjected to prescribed loading. Solid elements in their general form were adapted. The use of curvilinear coordinates in element space provides a practical means for defining complex design surfaces and also provides an expedient method for stress calculations . The curved three-dimensional elements fit readily to a skewed geometry of curved boundary and their application to propeller problems is simple and straight-forward. The performance of the curved solid finite elements has been found to be excellent and the computed results, because of the general nature of the solid elements are assured to converge to the true solution . The high degree of accuracy obtained from a recent analysis of a full size propeller strongly suggests that the current development represents a realistic and reliable approach to the general solution of the propeller stress problem.

On the errors of and possible corrections to classical linear shell theory

Generalized displacements and the accuracy of classical plate theory

Preface. 1. Introduction. 1.1 Structural Elements. 1.2 Nonlinearities. 1.3 Composite Materials. 1.4 Damping. 1.5 Dynamic Characteristics of Linear Discrete Systems. 1.6 Dynamic Characteristics of Nonlinear Discrete Systems 1.7 Analyses of Linear Continuous Systems. 1.8 Analyses of Nonlinear Continuous Systems. 2. Elasticity. 2.1 Principles of Dynamics. 2.2 Strain--Displacement Relations. 2.3 Transformation of Strains and Stresses. 2.4 Stress--Strain Relations. 2.5 Governing Equations. 3. Strings and Cables. 3.1 Modeling of Taut Strings. 3.2 Reduction of String Model to Two Equations. 3.3 Nonlinear Response of Strings. 3.4 Modeling of Cables. 3.5 Reduction of Cable Model to Two Equations. 3.6 Natural Frequencies and Modes of Cables. 3.7 Discretization of the Cable Equations. 3.8 Single--Mode Response with Direct Approach. 3.9 Single--Mode Response with Discretization Approach. 3.10 Extensional Bars. 4. Beams. 4.1 Introduction. 4.2 Linear Euler--Bernoulli Beam Theory. 4.3 Linear Shear--Deformable Beam Theories. 4.4 Mathematics for Nonlinear Modeling. 4.5 Nonlinear 2--D Euler--Bernoulli Beam Theory. 4.6 Nonlinear 3--D Euler--Bernoulli Beam Theory. 4.7 Nonlinear 3--D Curved Beam Theory Accounting for Warpings. 5. Dynamics of Beams. 5.1 Parametrically Excited Cantilever Beams. 5.2 Transversely Excited Cantilever Beams. 5.3 Clamped--Clamped Buckled Beams. 5.4 Microbeams. 6. Surface Analysis. 6.1 Initial Curvatures. 6.2 Inplane Strains and Deformed Curvatures. 6.3 Orthogonal Virtual Rotations. 6.4 Variation of Curvatures. 6.5 Local Displacements and Jaumann Strains. 7. Plates. 7.1 Introduction. 7.2 Linear Classical Plate Theory. 7.3 Linear Shear--Deformable Plate Theories. 7.4 Nonlinear Classical Plate Theory. 7.5 Nonlinear Modeling of Rectangular Surfaces. 7.6 General Nonlinear Classical Plate Theory. 7.7 Nonlinear Shear--Deformable Plate Theory. 7.8 Nonlinear Layerwise Shear--Deformable Plate Theory. 8. Dynamics of Plates. 8.1 Linear Vibrations of Rectangular Plates. 8.2 Linear Vibrations of Membranes. 8.3 Linear Vibrations of Circular and Annular Plates. 8.4 Nonlinear Vibrations of Circular and Annular Plates. 8.5 Nonlinear Vibrations of Rotating Disks. 8.6 Nonlinear Vibrations of Near--Square Plates. 8.7 Micropumps. 8.8 Thermally Loaded Plates. 9. Shells. 9.1 Introduction. 9.2 Linear Classical Shell Theory. 9.3 Linear Shear--Deformable Shell Theories. 9.4 Nonlinear Classical Theory for Double--Curved Shells. 9.5 Nonlinear Shear--Deformable Theories for Circular Cylindrical Shells. 9.6 Nonlinear Layerwise Shear--Deformable Shell Theory. 9.7 Nonlinear Dynamics of Infinitely Long Circular Cylindrical Shells. 9.8 Nonlinear Dynamics of Axisymmetric Motion of Closed Spherical Shells. Bibliography. Subject Index.

International Journal of Computational Engineering ScienceVol. 04, No. 01, pp. 109-119 (2003) No AccessANALYTICAL DETERMINATION OF STRESS INTENSITY FACTOR FOR PLATE BENDING PROBLEMSLALITHA CHATTOPADHYAYLALITHA CHATTOPADHYAYAdvanced Research Group, Structures Division, National Aerospace Laboratories, P.O. Box 1779, Kodhihalli, Bangalore 560 017, India Search for more papers by this author https://doi.org/10.1142/S1465876303000776Cited by:3 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an isotropic elastic plate of constant thickness is examined. The plate containing cracks is infinite and its boundary is subjected to bending moment or twisting moment. Using classical plate theory and integral transform techniques, the general formulae for the bending moment, twisting moment and bending stress distribution in an elastic plate acted upon by moment forces and containing cracks located on a single line are derived. The solution is obtained in detail, for the case in which there is a single crack in an infinite plate and the bending stress intensity factor is determined in a closed form and the results are compared with those obtained from finite element analysis. Close agreements between the analytical solution, numerical solution and reference solution were found in all cases.Keywords:Stress intensity factorplatecrackbendingintegral transform References M. L. Williams, ASME J. Appl. Mech. 28, 78 (1961). Crossref, Google ScholarG. C. Sih, P. C. Paris and F. Erdogan, ASME J. Appl. Mech. 29, 306 (1962). Crossref, Google ScholarJ. K. Knowles and N. M. Wang, J. Math. Phys. 39, 223 (1960). Crossref, Google ScholarR. S. Alwar and K. N. Ramachandran, Eng. Fracture Mech. 17, 323 (1983), DOI: 10.1016/0013-7944(83)90083-8. Crossref, Google ScholarE. Reissner, Quart. Appl. Math. 5, 55 (1947). Crossref, Google ScholarM. J. Vizet al., Int. J. Fracture 72, 21 (1995). Crossref, Google ScholarA. Zucchini, C.-Y. Hui and A. T. Zehnder, Int. J. Fracture 104, 387 (2000), DOI: 10.1023/A:1007699314793. Crossref, Google Scholar S. P. Timoshenko , Theory of Plates and Shells ( McGraw Hill Book Company , Auckland , 1959 ) . Google Scholar I. N. Sneddon , Use of Integral Transforms ( McGraw Hill Book Company , New York , 1972 ) . Google ScholarE. F. Rybicki and M. F. Kanninen, Eng. Fracture Mech. 9, 931 (1977), DOI: 10.1016/0013-7944(77)90013-3. Crossref, Google Scholar Y. Murakami , Stress Intensity Factors Handbook 2 ( Pergamon Press , Oxford , 1987 ) . Google Scholar FiguresReferencesRelatedDetailsCited By 3Two-Dimensional Crack and Contact Problems – Transform MethodArabinda Roy and Rasajit Kumar Bera6 Dec 2019EXACT SOLUTION FOR BENDING OF AN ELASTIC PLATE CONTAINING A CRACK AND SUBJECTED TO A CONCENTRATED MOMENTLALITHA CHATTOPADHYAY, S. SRIDHARA MURTHY and S. VISWANATH20 November 2011 | International Journal of Computational Methods, Vol. 04, No. 02Analytical Solution for an Orthotropic Elastic Plate Containing CracksLalitha Chattopadhyay1 Aug 2005 | International Journal of Fracture, Vol. 134, No. 3-4 Recommended Vol. 04, No. 01 Metrics History Received 28 August 2002 Accepted 24 January 2003 KeywordsStress intensity factorplatecrackbendingintegral transformPDF download

The actuation phenomena of materials upon external stimulus have attracted much attention for the development of excellent sensors and devices. Herein, we present a smart Janus-faced film that exhibits novel behavior of reverse orthogonal actuation under high humidity and a positive actuation under low humidity, which is achieved by asymmetric polymer brushes on polydimethysiloxane as a substrate through surface-initiated atom transfer radical polymerization. The classical theory of plates and shells and finite element simulations are also applied to understand the orthogonal actuation mechanism of the actuator. This Janus-faced film can reversely grab objects rapidly under high humidity, which provides significant potential to design a more intelligent actuator. In addition, this film is highly sensitive to humidity that even the approaching finger can make it to bend, which is just like the actuation behavior of Mimosa pudica. Based on the above phenomena, we also design the sensing devices to realize the detection of humidity. Interestingly, the film intelligently identifies different solvents (e.g., water and ethanol). This work may demonstrate significant potential in smart surface modifications, flexible robots, bionic sensors, and other fields.

An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.

Analytical solution of stability of FG-CNTRC conical shells under external pressures