Creep Deflections and Stresses of Beam-Columns

1958 ◽  
Vol 25 (1) ◽  
pp. 75-78
Author(s):  
T. H. Lin
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Creep Strain ◽  
Green's Function ◽  
Lateral Load ◽  
Time Curve ◽  
Beam Columns ◽  
End Conditions ◽  
Integrating Factors

Abstract A method of calculating the creep deflections and stresses of a beam-column is shown. The differential equation of equilibrium in terms of creep strain is solved by the method of integrating factors with Green’s function. For restrained and built-in ends, the end moments are found from the end conditions. An illustrative example is given for a beam-column of an ideal H-section with built-in ends and subjected to uniform lateral load. The deflection-time curve and flange stresses at different instants are shown.

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.

An integral solution of the electromagnetic seismograph equation

1960 ◽  
Vol 50 (3) ◽  
pp. 461-465
Author(s):  
R. E. Ingram
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Integral Solution ◽  
Ground Movement ◽  
Ground Movements ◽  
Angular Movement ◽  
Electromagnetic Seismograph

ABSTRACT In investigating the response of an electromagnetic seismograph to various ground movements it is advantageous to have the solution of the differential equation as an integral. This is done by finding the Green's function, f(s), for the particular instrument. The angular movement of the galvanometer is then θ(t)=q∫0tf(s)x″(t−s)ds where x(t) is the ground movement and prime stands for the operator d/dt. It is sufficient to find one function, F(s), with dF/ds = f(s), to give the response to a displacement test, a tapping test, or a ground movement.

Green's function for a differential equation with a deviating argument

1975 ◽  
Vol 17 (3) ◽  
pp. 259-262
Author(s):  
I. N. Inozemtseva ◽  
Yu. V. Komlenko ◽  
S. A. Pak
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Deviating Argument

A Green's Function-Based Design for Deformation Control of a Microbeam With In-Domain Actuation

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Amir Badkoubeh ◽  
Guchuan Zhu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Control Design ◽  
Target System ◽  
Bernoulli Equation ◽  
Test Function ◽  
Deformation Control ◽  
Control Scheme

This paper presents a Green's function-based design for deformation control of a microbeam described by an Euler-Bernoulli equation with in-domain pointwise actuation. The Green's function is first used in control design to construct the test function that enables the solvability of a map between the original nonhomogeneous partial differential equation and a target system in standard boundary control form. Then a regularized Green's function is employed in motion planning, leading to a computationally tractable implementation of the control scheme combined by a single feedback stabilizing loop and feedforward controls. The viability and the applicability of the proposed approach are demonstrated through numerical simulations of a representative microbeam.

scholarly journals Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

2021 ◽  
Vol 6 (11) ◽  
pp. 12583-12598
Author(s):  
Limin Guo ◽  
◽  
Lishan Liu ◽  
Ying Wang ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Nonlinear Term ◽  
Iterative Schemes ◽  
Hadamard Fractional Differential Equations ◽  
Equation Boundary ◽  
Derivative Term ◽  
Fractional Differential

<abstract><p>In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.</p></abstract>

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