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Implementing a soil stress-strain model with hysteretic damping in FLAC
Published in Christine Detournay, Roger Hart, FLAC and Numerical Modeling in Geomechanics, 2020
Finally, comments about damping are in order as some of the damping evident in Figures 7 and 8 is generated by high amplitude stress waves. Figure 5 and some of the curves in Figure 8, on the other hand, show that shear stresses which are quite modest with respect to the undrained shear strength of the soil, and representative of earthquake loading, produce soil response quite different from elastic behaviour. Reference to Figure 3 shows that for shear strain amplitudes as small as 0.01% the cyclic stress-strain response departs considerably from linear elastic. Furthermore, the damping calculations, both for gravity turn-on and shear stress wave propagation, indicate that eventually the soil motion degenerates to undamped small strain elastic oscillations. This means that practical application of the model will require the provision of extra damping.
Introduction
Published in Yossef H. Hatzor, Guowei Ma, Gen-hua Shi, Discontinuous Deformation Analysis in Rock Mechanics Practice, 2017
Yossef H. Hatzor, Guowei Ma, Gen-hua Shi
DDA is a fully dynamic method that uses inertia forces to determine the motion of block systems. The inertia forces are updated after each time step and are dependent on the block displacement in the previous time step. Consequently, sudden loading at the beginning of the analysis, whether by gravity or any other applied load, produces unwanted artificial accelerations and displacements that propagate throughout the time steps of the analysis. MacLaughlin and Sitar (1999) identified this problem and were the first to propose a static “gravity turn-on” phase which precedes the dynamic analysis, and added two extra iterations in each time step in order to guarantee accurate determination of the contact forces between blocks. They demonstrated the enhanced accuracy of this approach using the classic block on an inclined plane problem.
Elasto-plastic dynamic response of fill-type dams: Total stress and effective stress analyses
Published in Jean-Jacques Fry, Norihisa Matsumoto, Validation of Dynamic Analyses of Dams and Their Equipment, 2018
In this case, material constants employed for analyses are same as previous shaking table test analyses, but the constant for shear modulus is used GE = 900.0 the Equation (11). Both three dimensional and two dimensional analyses, initial stresses are computed by applying gravity turn on analysis and the vertical stress smaller than 2.0 kN/cm2 is set to 2.0 kN/cm2 for excluding minus stress. The shear modulus estimated by using the Equation (11) and damping ratio (Rayleigh parameters for mass is 0.05 and for stiffness is zero) are constant during the dynamic computation. Figure 12 shows the three dimensional mesh and Figure 17 shows two dimensional mesh.
Design framework for optimizing waypoints of vehicle trajectory considering terminal velocity and impact angle constraints
Published in Engineering Optimization, 2022
Youngil Kim, Namhoon Cho, Jongho Park, Youdan Kim
The first waypoint is selected to reduce the influences of the initial conditions and to facilitate the manoeuvring of the missile beyond the burn-out point. It is known that, by performing a gravity turn, the angle of attack is kept near zero, beneficially minimizing the energy wasted due to the induced drag (Callaway 2004). In this regard, the proposed framework employs a gravity turn to determine the first waypoint that comes immediately after the boosting stage.