Analysis of rockbolt reinforcement of layered rock using beam equations

Rock Bolting ◽  
2021 ◽  
pp. 173-185
Author(s):  
Robert G. Jeffrey ◽  
Jaak J.K. Daemen
Keyword(s):  
Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 100
Author(s):  
Mohammadreza Amoozgar ◽  
Michael I. Friswell ◽  
Seyed Ahmad Fazelzadeh ◽  
Hamed Haddad Khodaparast ◽  
Abbas Mazidi ◽  
...  

In this paper, the effect of distributed electric propulsion on the aeroelastic stability of an electric aircraft wing was investigated. All the electric propulsors, which are of different properties, are attached to the wing of the aircraft in different positions. The wing structural dynamics was modelled by using geometrically exact beam equations, while the aerodynamic loads were simulated by using an unsteady aerodynamic theory. The electric propulsors were modelled by using a concentrated mass attached to the wing, and the motor’s thrust and angular momentum were taken into account. The thrust of each propulsor was modelled as a follower force acting exactly at the centre of gravity of the propulsor. The nonlinear aeroelastic governing equations were discretised using a time–space scheme, and the obtained results were verified against available results and very good agreement was observed. Two case studies were considered throughout the paper, resembling two flight conditions of the electric aircraft. The numerical results show that the tip propulsor thrust, mass, and angular momentum had the most impact on the aeroelastic stability of the wing. In addition, it was observed that the high-lift motors had a minimal effect on the aeroelastic stability of the wing.


Author(s):  
Joackim Bernier ◽  
Roberto Feola ◽  
Benoît Grébert ◽  
Felice Iandoli

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.


Nonlinearity ◽  
1993 ◽  
Vol 6 (3) ◽  
pp. 457-479 ◽  
Author(s):  
A Eden ◽  
A J Milani

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.


2011 ◽  
Vol 90-93 ◽  
pp. 2363-2371
Author(s):  
Bin Wei Xia ◽  
Ke Hu ◽  
Yi Yu Lu ◽  
Dan Li ◽  
Zu Yong Zhou

Physical models of layered rock mass with different dip angles are built by physical model test in accordance with the bias failure characteristics of surrounding rocks of layered rock mass in Gonghe Tunnel. Bias failure characteristics of surrounding rocks in thin-layered rock mass and influences of layered rock mass dip angle on stability of tunnel are studied. The research results show that failure characteristics of physical models generally coincide with those of surrounding rocks monitored from the tunnel site. The failure regions of surrounding rock perpendicular to the stratification planes are obviously larger than those parallel to. The stress distributions and failure characteristics in the surrounding rocks are similar to each physical model of different dip angles. The stress distributions and failure regions are all elliptic in shape, in which the major axis is in the direction perpendicular to the stratification planes while the minor axis is parallel to them. As a result, obvious bias failure of surrounding rocks has gradually formed. The physical model tests provide reliable basis for theoretical analysis on the failure mechanism of deep-buried layered rock mass.


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