Two dimensional theory of stiffened plates

1950 ◽  
Vol 2 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Chang o’chou
Keyword(s):  
Differential Equation ◽  
Isotropic Plate ◽  
Complete Solution ◽  
Stiffened Plates ◽  
Two Dimensional ◽  
Stiffened Plate ◽  
Dimensional Theory ◽  
All Solutions

SummaryThe two-dimensional stiffened plate problem is completely governed by the fundamental differential equation(22)where k1 and k2 are two non-dimensional structural constants depending on the relative proportions of the reinforcing members.The complete solution is(25)This solution renders all solutions for the isotropic plate available for the stiffened plate also. The choice between the several types of solution available is governed by the same considerations as for the isotropic or unstiffened plate.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Numerical Investigation of Ultimate Strength of Stiffened Plates With Various Cross-Section Forms

2018 ◽  
Author(s):  
Huilong Ren ◽  
Yifu Liu ◽  
Chenfeng Li ◽  
Xin Zhang ◽  
Zhaonian Wu
Keyword(s):  
Aluminum Alloy ◽  
Ultimate Strength ◽  
Cross Section ◽  
High Performance ◽  
Lightweight Design ◽  
Offshore Structures ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Element Analysis ◽  
Hull Structure

There is an increasing interest in the lightweight design of ship and offshore structures, more specifically, choosing aluminum alloys or other lightweight high-performance materials to build structure components and ship equipments. Due to its better mechanical properties and easy assembly nature, extruded aluminum alloy stiffened plates are widely used in hull structures. When the load on the hull reaches a certain level during sailing, partial or overall instability of stiffened plate makes significant contribution in an event of collapse of the hull structure. It is very necessary to investigate the ultimate strength of aluminum alloy stiffened plate to ensure the ultimate bearing capacity of large aluminum alloy hull structure. Most of studies of the ultimate strength of stiffened plates deal with stiffened plates with T–shaped stiffeners. Stiffeners of other shapes have seldom been explored. In this research, the ultimate strength of six different cross–section aluminum alloy stiffened plates and one steel stiffened plate was studied based on the non–linear finite element analysis (FEA). Taking into account stiffness, weight and other issues, the new cross–section aluminum stiffener has finally been concluded for replacing the original steel stiffener in upper deck of a warship.

scholarly journals The Lagrangian Stability for a Class of Second-Order Quasi-Periodic Reversible Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Yanling Shi ◽  
Jia Li
Keyword(s):  
Differential Equation ◽  
Analytic Functions ◽  
Order Differential Equation ◽  
Reversible Systems ◽  
Invariant Curves ◽  
Real Analytic Functions ◽  
All Solutions ◽  
Small Twist Theorem ◽  
Real Analytic ◽  
Twist Theorem

We study the following two-order differential equation,(Φp(x'))'+f(x,t)Φp(x')+g(x,t)=0,whereΦp(s)=|s|(p-2)s,p>0.f(x,t)andg(x,t)are real analytic functions inxandt,2aπp-periodic inx, and quasi-periodic intwith frequencies(ω1,…,ωm). Under some odd-even property off(x,t)andg(x,t), we obtain the existence of invariant curves for the above equations by a variant of small twist theorem. Then all solutions for the above equations are bounded in the sense ofsupt∈R|x′(t)|<+∞.

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