STATIC AND KINEMATIC ANALYSIS OF A PLANAR REGULAR BEAM TRUSS WITH A DOUBLE LATTICE

Stroitelʹnaâ mehanika i konstrukcii ◽

10.36622/vstu.2021.30.3.001 ◽

2021 ◽

pp. 7-14

Author(s):

М. Н. Кирсанов

Keyword(s):

Kinematic Analysis ◽

Horizontal Shift ◽

Lattice Type

Предлагается схема статически определимой регулярной балочной фермы решетчатого вида. Обнаружен и исследован случай кинематического вырождения конструкции от числа панелей. Для сосредоточенной и распределенной по нижнему поясу нагрузок методом индукции с привлечением системы символьной математики выводится зависимость прогиба фермы от числа ее панелей. Прогиб вычисляется по формуле Максвелла-Мора. Полученная зависимость имеет вид полинома по числу панелей с переменными, зависящими от четности числа панелей. Получена также формула зависимости величины горизонтального сдвига подвижной опоры. A scheme of a statically determinate regular girder truss of a lattice type is proposed. The case of kinematic degeneration of the structure from the number of panels is discovered and investigated. For concentrated and distributed loads over the lower belt, the dependence of the deflection of the truss on the number of its panels is derived by induction with the involvement of a system of symbolic mathematics. The deflection is calculated using the Maxwell - Mohr formula. The resulting dependence has the form of a polynomial in the number of panels with variables depending on the parity of the number of panels. A formula for the dependence of the magnitude of the horizontal shift of the movable support is also obtained.

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Kinematic Approximations in TED and RHEED Analysis of Reconstructed Surfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100135587 ◽

1990 ◽

Vol 48 (2) ◽

pp. 396-397

Author(s):

L. -M. Peng ◽

M. J. Whelan

Keyword(s):

Electron Diffraction ◽

Kinematic Analysis ◽

Incident Beam ◽

High Energy ◽

Energy Electron ◽

Great Success ◽

High Energy Electron ◽

Kinematic Approximation ◽

Reconstructed Surfaces

In recent years there has been a trend in the structure determination of reconstructed surfaces to use high energy electron diffraction techniques, and to employ a kinematic approximation in analyzing the intensities of surface superlattice reflections. Experimentally this is motivated by the great success of the determination of the dimer adatom stacking fault (DAS) structure of the Si(111) 7 × 7 reconstructed surface.While in the case of transmission electron diffraction (TED) the validity of the kinematic approximation has been examined by using multislice calculations for Si and certain incident beam directions, far less has been done in the reflection high energy electron diffraction (RHEED) case. In this paper we aim to provide a thorough Bloch wave analysis of the various diffraction processes involved, and to set criteria on the validity for the kinematic analysis of the intensities of the surface superlattice reflections.The validity of the kinematic analysis, being common to both the TED and RHEED case, relies primarily on two underlying observations, namely (l)the surface superlattice scattering in the selvedge is kinematically dominating, and (2)the superlattice diffracted beams are uncoupled from the fundamental diffracted beams within the bulk.

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