The Elastic Half Plane Subjected to Surface Tractions With Random Magnitude or Separation

1960 ◽  
Vol 27 (4) ◽  
pp. 701-709 ◽  
Author(s):  
A. C. Eringen ◽  
J. W. Dunkin
Keyword(s):  
White Noise ◽  
Stress Tensor ◽  
Half Plane ◽  
Second Order ◽  
Concentrated Loads ◽  
Random Boundary ◽  
Concentrated Load ◽  
Random Intervals ◽  
Random Location ◽  
Elastostatic Problem

First and second-order moments of the stress tensor are obtained for the elastostatic problem concerning the half-plane subjected to random boundary tractions. The cases treated include the following types of applied surface tractions: (a) A purely random Gaussian load (white noise); (b) concentrated loads of random magnitudes separated by equal intervals; (c) a concentrated load acting at a random location; and (d) concentrated loads of equal magnitudes separated by random intervals.

The Stress Distributions Induced by Concentrated Loads Acting in Isotropic and Orthotropic Half Planes

1953 ◽  
Vol 20 (1) ◽  
pp. 82-86
Author(s):  
H. D. Conway
Keyword(s):  
Half Plane ◽  
Complex Variable ◽  
Integral Method ◽  
Fourier Integral ◽  
Straight Edge ◽  
Variable Method ◽  
Stress Distributions ◽  
Concentrated Loads ◽  
Concentrated Load ◽  
Method Of Solution

Abstract Using a Fourier integral method, the solution is obtained to an isotropic half plane subjected to a concentrated load acting at some distance from the straight edge. This problem was discussed previously by Melan, using a complex variable method of solution. The Fourier integral method is then extended to solve the corresponding problems of the orthotropic half plane.

Random exponential attractor for second-order nonautonomous stochastic lattice systems with multiplicative white noise

2019 ◽  
Vol 19 (06) ◽  
pp. 1950044
Author(s):  
Haijuan Su ◽  
Shengfan Zhou ◽  
Luyao Wu
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Systems ◽  
Random System ◽  
Multiplicative White Noise ◽  
Infinite Sequences

We studied the existence of a random exponential attractor in the weighted space of infinite sequences for second-order nonautonomous stochastic lattice system with linear multiplicative white noise. Firstly, we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences. Secondly, we transferred the second-order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein–Uhlenbeck process, whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Thirdly, we estimated the bound and tail of solutions for the random system. Fourthly, we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts, and carefully estimated the bound of the norm of each part and the expectations of some random variables. Finally, we obtained the existence of a random exponential attractor for the considered system.

scholarly journals A Hida–Malliavin white noise calculus approach to optimal control

2018 ◽  
Vol 21 (03) ◽  
pp. 1850014
Author(s):  
Nacira Agram ◽  
Bernt Øksendal
Keyword(s):  
Optimal Control ◽  
Diffusion Coefficient ◽  
White Noise ◽  
Backward Stochastic Differential Equation ◽  
Second Order ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Alternative Approach ◽  
Quadratic Optimal Control ◽  
White Noise Calculus

The classical maximum principle for optimal stochastic control states that if a control [Formula: see text] is optimal, then the corresponding Hamiltonian has a maximum at [Formula: see text]. The first proofs for this result assumed that the control did not enter the diffusion coefficient. Moreover, it was assumed that there were no jumps in the system. Subsequently, it was discovered by Shige Peng (still assuming no jumps) that one could also allow the diffusion coefficient to depend on the control, provided that the corresponding adjoint backward stochastic differential equation (BSDE) for the first-order derivative was extended to include an extra BSDE for the second-order derivatives. In this paper, we present an alternative approach based on Hida–Malliavin calculus and white noise theory. This enables us to handle the general case with jumps, allowing both the diffusion coefficient and the jump coefficient to depend on the control, and we do not need the extra BSDE with second-order derivatives. The result is illustrated by an example of a constrained linear-quadratic optimal control.

Response dynamics and receptive-field organization of catfish amacrine cells

1992 ◽  
Vol 67 (2) ◽  
pp. 430-442 ◽  
Author(s):  
H. M. Sakai ◽  
K. Naka
Keyword(s):  
Receptive Field ◽  
White Noise ◽  
Amacrine Cells ◽  
Second Order ◽  
Response Dynamics ◽  
Field Center ◽  
Mean Luminance ◽  
Nonlinear Components ◽  
Receptive Field Center ◽  
Dc Potentials

1. We have applied Wiener analysis to a study of response dynamics of N (sustained) and C (transient) amacrine cells. Stimuli were a spot and an annulus of light, the luminance of which was modulated by two independent white-noise signals. First- and second-order Wiener kernels were computed for each spot and annulus input. The analysis allowed us to separate a modulation response into its linear and nonlinear components, and into responses generated by a receptive-field center and its surround. 2. Organization of the receptive field of N amacrine cells consists of both linear and nonlinear components. The receptive field of linear components was center-surround concentric and opposite in polarity, whereas that of second-order nonlinear components was monotonic. 3. In NA (center-depolarizing) amacrine cells, the membrane DC potentials brought about by the mean luminance of a white-noise spot or a steady spot were depolarizations, whereas those brought about by the mean luminance of a white-noise annulus or a steady annulus were hyperpolarizations. In NB (center-hyperpolarizing) amacrine cells, this relationship was reversed. If both receptive-field center and surround were stimulated by a spot and annulus, membrane DC potentials became close to the dark level and the amplitude of modulation responses became larger. 4. The linear responses of a receptive-field center of an N amacrine cell, measured in terms of the first-order Wiener kernel, were facilitated if the surround was stimulated simultaneously. The amplitude of the kernel became larger, and its peak response time became shorter. The same facilitation occurred in the linear responses of a receptive-field surround if the center was stimulated simultaneously. 5. The second-order nonlinear responses were not usually generated in N amacrine cells if the stimulus was either a white-noise spot or a white-noise annulus alone. Significant second-order nonlinearity appeared if the other region of the receptive field was also stimulated. 6. Membrane DC potentials of C amacrine cells remained at the dark level with either a white-noise spot or a white-noise annulus. The cell responded only to modulations. 7. The major characteristics of center and surround responses of C amacrine cells could be approximated by second-order Wiener kernels of the same structure. The receptive field of second-order nonlinear components of C amacrine cells was monotonic.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Strengthening of Reinforced Concrete Beams Subjected to Concentrated Loads

2022 ◽  
Author(s):  
Paolo Foraboschi
Keyword(s):  
Reinforced Concrete ◽  
Carrying Capacity ◽  
Concrete Beams ◽  
Shear Capacity ◽  
Reinforced Concrete Beams ◽  
Load Carrying Capacity ◽  
Reinforced Concrete Structure ◽  
Concentrated Loads ◽  
Concentrated Load ◽  
Load Carrying

Renovation, restoration, remodeling, refurbishment, and retrofitting of build-ings often imply modifying the behavior of the structural system. Modification sometimes includes applying forces (i.e., concentrated loads) to beams that before were subjected to distributed loads only. For a reinforced concrete structure, the new condition causes a beam to bear a concentrated load with the crack pattern that was produced by the distributed loads that acted in the past. If the concentrated load is applied at or near the beam’s midspan, the new shear demand reaches the maximum around the midspan. But around the midspan, the cracks are vertical or quasi-vertical, and no inclined bar is present. So, the actual shear capacity around the midspan not only is low, but also can be substantially lower than the new demand. In order to bring the beam capacity up to the demand, fiber-reinforced-polymer composites can be used. This paper presents a design method to increase the concentrated load-carrying capacity of reinforced concrete beams whose load distribution has to be changed from distributed to concentrated, and an analytical model to pre-dict the concentrated load-carrying capacity of a beam in the strengthened state.

Diffraction by a half plane perpendicular to the distinguished axis of a gyrotropic medium (oblique incidence)

1981 ◽  
Vol 59 (3) ◽  
pp. 403-424 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Boundary Value ◽  
Diffraction Problem ◽  
Closed Form Solution ◽  
Second Order ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Electromagnetic Plane Wave

An exact, closed form solution is found for the following half plane diffraction problem. (I) The medium surrounding the half plane is gyrotropic. (II) The scattering half plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The direction of propagation of the incident electromagnetic plane wave is arbitrary (skew) with respect to the edge of the half plane. The result presented is a generalization of a solution for the same problem with incidence normal to the edge of the half plane (two-dimensional case).The fundamental, distinctive feature of the problem is that it constitutes a boundary value problem for a system of two coupled second order partial differential equations. All previously solved electromagnetic diffraction problems reduced to boundary value problems for either one or two uncoupled second order equations. (Exception: the two-dimensional case of the present problem.) The problem is formulated in terms of the (generalized) scalar Hertz potentials and leads to a set of two coupled Wiener–Hopf equations. This set, previously thought insoluble by quadratures, yields to the Wiener–Hopf–Hilbert method.The three-dimensional solution is synthesized from appropriate solutions to two-dimensional problems. Peculiar waves of ghost potentials, which correspond to zero electromagnetic fields play an essential role in this synthesis. The problem is two-moded: that is, superpositions of both ordinary and extraordinary waves are necessary for the spectral representation of the solution. An important simplifying feature of the problem is that the coupling of the modes is purely due to edge diffraction, there being no reflection coupling. The solution is simple in that the Fourier transforms of the potentials are just algebraic functions. Basic properties of the solution are briefly discussed.

Design of Laterally Loaded Plating—Concentrated Loads

1983 ◽  
Vol 27 (04) ◽  
pp. 252-264
Author(s):  
Owen Hughes
Keyword(s):  
Experimental Data ◽  
Load Parameter ◽  
Uniform Pressure ◽  
Concentrated Loads ◽  
Rigid Plastic ◽  
Concentrated Load ◽  
Load Effect ◽  
Permanent Set ◽  
Multiple Location ◽  
Single Location

In the design of plating subject to lateral loading, the principal load effect to be considered is the amount of permanent set, that is, the maximum permanent deflection in the center of each panel of plating bounded by the stiffeners and the crossbeams. The present paper is complementary to a previous paper [1]2 which dealt with uniform pressure loads. It first shows that for design purposes there are two types of concentrated loads, depending on the number of different locations in which they can occur; single location or multiple location. The hypothesis is then made that for multiple-location loads the eventual and stationary pattern of plasticity which is developed in the plating is very similar to that for uniform pressure loads, and hence the value of permanent set may be obtained by using the same formula as for uniform pressure loads, with a load parameter Q that is some multiple r of the load parameter for the concentrated load: 0 = rQP. The value of r is a function of the degree of concentration of the load and is almost independent of plate slenderness and aspect ratio. The general mathematical character of this function is established from first principles and from an analysis of the permanent set caused by a multiple-location point load acting on a long plate. The results of this theoretical analysis provide good support for the hypothesis, as do also the relatively limited experimental data which are available. The theory and the experimental data are combined to obtain a simple mathematical expression for r. A more precise expression can be obtained after further experiments have been performed with more highly concentrated loads. Single-location loads produce a different pattern of plasticity and require a different approach. A suitable design formula is developed herein by performing regression analysis on the data from a set of experiments performed with such loads. Both methods presented herein, one for multiple-location loads and the other for single-location loads, are valid for small and moderate values of permanent set and can be used for all static and quasistatic loads. Dynamic loads and applications involving large amounts of permanent set require formulas based on rigid-plastic theory. Such formulas are available for uniform pressure loads and were quoted in reference [1]. A formula for single-location loads has recently been derived by Kling [4] and is quoted herein.

Sign in / Sign up

Export Citation Format

Share Document