On Some Classes of Three-dimensional Dynamic Problems of Plates and Shells and an Asymptotic Method of Solving Them

2020 ◽  
pp. 1-14
Author(s):  
Lenser A. Aghalovyan
Keyword(s):  
Asymptotic Method ◽  
Three Dimensional ◽  
Dynamic Problems ◽  
Plates And Shells

scholarly journals On Asymptotic Theory of Beams, Plates and Shells

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
L.A. Aghalovyan ◽  
M.L. Aghalovyan
Keyword(s):  
Asymptotic Method ◽  
Asymptotic Theory ◽  
Dynamic Problems ◽  
Classic Theory ◽  
Plates And Shells

AbstractBases of asymptotic theory of beams, plates and shells are stated. The comparison with classic theory is conducted. New classes of thin bodies problems, for which hypotheses of classic theory are not applicable, are considered. By the asymptotic method effective solutions of these problems are obtained. The effectiveness of the asymptotic method for finding solutions of as static, as well as dynamic problems of beams, plates and shells is shown.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

2005 ◽  
Vol 58 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Alan T. Zehnder ◽  
Mark J. Viz
Keyword(s):  
Fracture Mechanics ◽  
Plate Theory ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Crack Tip ◽  
Thin Plates ◽  
Element Analysis ◽  
Crack Tip Fields ◽  
Plates And Shells ◽  
Membrane Bending

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

Computational Models for Sandwich Panels and Shells

1996 ◽  
Vol 49 (3) ◽  
pp. 155-199 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton ◽  
Charles W. Bert
Keyword(s):  
Computational Models ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Local Buckling ◽  
Sandwich Panels ◽  
Free Vibrations ◽  
Sandwich Plates ◽  
Material Parameters ◽  
Sandwich Plates And Shells ◽  
Plates And Shells

The focus of this review is on the hierarchy of computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters. The literature reviewed is devoted to the following application areas: heat transfer problems; thermal and mechanical stresses (including boundary layer and edge stresses); free vibrations and damping; transient dynamic response; bifurcation buckling, local buckling, face-sheet wrinkling and core crimping; large deflection and postbuckling problems; effects of discontinuities (eg, cutouts and stiffeners), and geometric changes (eg, tapered thickness); damage and failure of sandwich structures; experimental studies; optimization and design studies. Over 800 relevant references are cited in this review, and another 559 references are included in a supplemental bibliography for completeness. Extensive numerical results are presented for thermally stressed sandwich panels with composite face sheets showing the effects of variation in their geometric and material parameters on the accuracy of the free vibration response, and the sensitivity coefficients predicted by eight different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the analytic three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of sandwich plates and shells are outlined.

Computational Models for High-Temperature Multilayered Composite Plates and Shells

1992 ◽  
Vol 45 (10) ◽  
pp. 419-446 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton
Keyword(s):  
High Temperature ◽  
Computational Models ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Composite Plates ◽  
Effect Of Temperature ◽  
Temperature Sensitive ◽  
Composite Models ◽  
Sandwich Plates And Shells ◽  
Plates And Shells

The focus of this review is on the hierarchy of composite models, predictor-corrector procedures, the effect of temperature-dependence of material properties on the response, and the sensitivity of the thermomechanical response to variations in material parameters. The literature reviewed is devoted to the following eight application areas: Heat transfer; thermal stresses; curing, processing and residual stresses; bifurcation buckling; vibrations of heated plates and shells; large deflection and postbuckling problems; and sandwich plates and shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of temperature-sensitive angle-ply composite plates on the accuracy of thermal buckling response, and the sensitivity derivatives predicted by nine different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the exact three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of high-temperature multilayered composites are outlined.

Three-Dimensional Exact Analysis of Laminated Piezoelectric Plates and Shells

2013 ◽  
Vol 745 ◽  
pp. 1-12
Author(s):  
Gennady M. Kulikov ◽  
S.V. Plotnikova
Keyword(s):  
Exact Solutions ◽  
Chebyshev Polynomial ◽  
Three Dimensional ◽  
Middle Surface ◽  
New Method ◽  
Efficient Approach ◽  
Exact Analysis ◽  
Anisotropic Structures ◽  
Plates And Shells ◽  
Piezoelectric Plates

A paper focuses on the use of the efficient approach to three-dimensional (3D) exact solutions of electroelasticity for laminated piezoelectric plates and shells. This approach is based on the new method of sampling surfaces (SaS). We introduce inside the nth layer Ιn not equally spaced SaS parallel to the middle surface of the shell and choose displacements of these surfaces as basic shell variables. This permits the derivation of 3D exact solutions of electroelasticity for thick and thin laminated piezoelectric anisotropic structures with a specified accuracy using a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes.

Sign in / Sign up

Export Citation Format

Share Document