A New Theory of Elastic Sandwich Plates—One-Dimensional Case

1959 ◽  
Vol 26 (3) ◽  
pp. 415-421
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Infinite Plate ◽  
Theory Of Elasticity ◽  
Dimensional Case ◽  
Transverse Shear Deformation ◽  
Sandwich Plates ◽  
Rotatory Inertia ◽  
One Dimensional ◽  
The Core ◽  
The One ◽  
Final Equation

Abstract A new flexural theory of isotropic elastic sandwich plates is deduced from the theory of elasticity. The one-dimensional case is presented in this paper. The theory includes the effects of transverse-shear deformation and rotatory inertia in both the core and faces of the sandwich, and no limitation is imposed upon the magnitudes of the ratios between the thicknesses, material densities, and elastic constants of the core and faces of the sandwich. The method used is an extension of one due to Mindlin [1], and the results reduce to those of his for the corresponding homogeneous plates as special limiting cases. A final equation also may be simplified and reduced to the corresponding results of Reissner [2], Hoff [3], and Eringen [4] for the bending of ordinary sandwich plates that have thin faces. Results of the theory are applied to the problem of bending of a cantilever plate subjected to load at the unsupported end and to the problem of propagation of straight-crested waves in an infinite plate.

An Accurate Discrete Model for the Dynamics of Web-Core Sandwich Plates

2015 ◽  
Author(s):  
Anup Pydah
Keyword(s):  
Discrete Model ◽  
Vibrational Frequency ◽  
Transverse Shear Deformation ◽  
Sandwich Plates ◽  
Lateral Bending ◽  
One Dimensional ◽  
Simply Supported ◽  
The Core ◽  
Transverse Bending ◽  
The Face

An accurate discrete model is presented here for the dynamics of simply supported web-core sandwich plates using the elasticity approach. By modelling the face-plates as 3D solids and the core webs using a plane stress idealization for transverse bending and classical one-dimensional models for lateral bending and torsion, the non-classical effects of transverse shear deformation, thickness-stretch and rotary inertia are completely accounted for in both, the face-plates and webs. Vibrational frequency results obtained using this model are used to highlight the errors of the commonly used model based on the classical Kirchhoff hypothesis for the face-plates, indicating the importance of using refined theories for modelling the face-plates.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

Total progeny in a multitype critical age dependent branching process with immigration

1974 ◽  
Vol 11 (3) ◽  
pp. 458-470 ◽  
Author(s):  
Howard J. Weiner
Keyword(s):  
Limit Theorem ◽  
Branching Process ◽  
Cell Types ◽  
Dimensional Case ◽  
One Dimensional ◽  
Age Dependent ◽  
Total Progeny ◽  
Critical Age ◽  
The One ◽  
Branching Process With Immigration

In a multitype critical age dependent branching process with immigration, the numbers of cell types born by t, divided by t2, tends in law to a one-dimensional (degenerate) law whose Laplace transform is explicitily given. The method of proof makes a correspondence between the moments in the m-dimensional case and the one-dimensional case, for which the corresponding limit theorem is known. Other applications are given, a possible relaxation of moment assumptions, and extensions are indicated.

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