Geometric Nonlinear Dynamic Analysis of Tapered Steel Members

2020 ◽  
Author(s):  
Yasir F. Al-Lebban
Keyword(s):  
Dynamic Analysis ◽  
Mass Matrix ◽  
Nonlinear Dynamic Analysis ◽  
Axial Deformation ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Geometric Nonlinear ◽  
Steel Members ◽  
Mass Matrices

In this study, a theoretical analysis is presented for estimating the in-plane geometric nonlinear elastic stability behavior of steel members with tapered elements under dynamic loads. Beam-column approach is adopted for modeling the structural members as beam-column elements. The formulation is based on the Eulerian description taking into consideration the influence of axial force on bending stiffness. The changes in member chord length due to axial deformation and flexural bowing are also considered. In the dynamic analysis, the system mass properties have been represented using both lumped and consistent mass matrices. The consistent mass matrix is derived in three components: translational, rotational, and axial inertia. The formulation of the mass matrices in local and global coordinate systems of tapered members, which incorporates geometric nonlinearity, has been presented. A parametric study is conducted to examine the effects of number of tapered elements, tapering the prismatic members, time step size, and tapering ratio.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

On the Influence of Inflow Model Selection for Time-Domain Tiltrotor Aeroelastic Analysis

2021 ◽  
Author(s):  
Ethan Corle ◽  
Matthew Floros ◽  
Sven Schmitz
Keyword(s):  
Experimental Data ◽  
Particle Method ◽  
Comprehensive Analysis ◽  
Solution Stability ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Vortex Particle Method ◽  
Whirl Flutter ◽  
Vortex Particle

The methods of using the viscous vortex particle method, dynamic inflow, and uniform inflow to conduct whirl-flutter stability analysis are evaluated on a four-bladed, soft-inplane tiltrotor model using the Rotorcraft Comprehensive Analysis System. For the first time, coupled transient simulations between comprehensive analysis and a vortex particle method inflow model are used to predict whirl-flutter stability. Resolution studies are performed for both spatial and temporal resolution in the transient solution. Stability in transient analysis is noted to be influenced by both. As the particle resolution is refined, a reduction in simulation time-step size must also be performed. An azimuthal time step size of 0.3 deg is used to consider a range of particle resolutions to understand the influence on whirl-flutter stability predictions. Comparisons are made between uniform inflow, dynamic inflow, and the vortex particle method with respect to prediction capabilities when compared to wing beam-bending frequency and damping experimental data. Challenges in assessing the most accurate inflow model are noted due to uncertainty in experimental data; however, a consistent trend of increasing damping with additional levels of fidelity in the inflow model is observed. Excellent correlation is observed between the dynamic inflow predictions and the vortex particle method predictions in which the wing is not part of the inflow model, indicating that the dynamic inflow model is adequate for capturing damping due to the induced velocity on the rotor disk. Additional damping is noted in the full vortex particle method model, with the wing included, which is attributed to either an interactional aerodynamic effect between the rotor and the wing or a more accurate representation of the unsteady loading on the wing due to induced velocities.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Numerical Simulation of Proppant Transport in Hydraulically Fractured Reservoirs

2021 ◽  
Author(s):  
Seyhan Emre Gorucu ◽  
Vijay Shrivastava ◽  
Long X. Nghiem
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Fractured Reservoirs ◽  
Injection Timing ◽  
Fracture Permeability ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Proppant Transport ◽  
Fracture Closure

Abstract An existing equation-of-state compositional simulator is extended to include proppant transport. The simulator determines the final location of the proppant after fracture closure, which allows the computation of the permeability along the hydraulic fracture. The simulation then continues until the end of the production. During hydraulic fracturing, proppant is injected in the reservoir along with water and additives like polymers. Hydraulic fracture gets created due to change in stress caused by the high injection pressure. Once the fracture opens, the bulk slurry moves along the hydraulic fracture. Proppant moves at a different speed than the bulk slurry and sinks down by gravity. While the proppant flows along the fracture, some of the slurry leaks off into the matrix. As the fracture closes after injection stops, the proppant becomes immobile. The immobilized proppant prevents the fracture from closing and thus keeps the permeability of the fracture high. All the above phenomena are modelled effectively in this new implementation. Coupled geomechanics simulation is used to model opening and closure of the fracture following geomechanics criteria. Proppant retardation, gravitational settling and fluid leak-off are modeled with the appropriate equations. The propped fracture permeability is a function of the concentration of immobilized proppant. The developed proppant simulation feature is computationally stable and efficient. The time step size during the settling adapts to the settling velocity of the proppants. It is found that the final location of the proppants is highly dependent on its volumetric concentration and slurry viscosity due to retardation and settling effects. As the location and the concentration of the proppants determine the final fracture permeability, the additional feature is expected to correctly identify the stimulated region. In this paper, the theory and the model formulation are presented along with a few key examples. The simulation can be used to design and optimize the amount of proppant and additives, injection timing, pressure, and well parameters required for successful hydraulic fracturing.

scholarly journals Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh
Keyword(s):  
Stokes Equations ◽  
Field Application ◽  
Benchmark Problems ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Time Step Size ◽  
Saint Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

scholarly journals Wavelet-based Decomposition of Ground Acceleration for Efficient Calculation of Seismic Response in Elastoplastic Structures

2020 ◽  
Author(s):  
Reza Kamgar ◽  
Noorollah Majidi ◽  
Ali Heidari
Keyword(s):  
Wavelet Transform ◽  
Dynamic Analysis ◽  
Continuous Wavelet Transform ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Continuous Wavelet ◽  
Frequency Content ◽  
Time Step ◽  
Integration Schemes ◽  
The Waves

The nonlinear dynamic analysis provides a more accurate simulation of the structural behavior against earthquakes. On the other hand, this analysis method is time-consuming since the time-step integration schemes are used to calculate the responses of the structure. Wavelet transform is also considered as one of the strong computing tools in studying the properties of the waves. The continuous wavelet transform is a time-frequency study and examines the frequency content of the waves while, the discrete wavelet transform is used to reduce sampling data and also to eliminate the noise of the waves. In this paper, the discrete and continuous wavelet transforms are used to reduce the wave sampling and therefore to reduce the required time for analysis. In this regard, eight near- and far- field earthquakes are studied. The frequency content of the earthquake is investigated by the Fourier spectrum and the continuous wavelet transform. The results show that the first five frequencies for the main earthquakes are similar to those values of earthquakes obtained by wavelet transform. Besides, it is shown that using wavelet transform for the main and decomposed earthquakes indicates that the duration of strong ground motion and the time of dominant frequency occur approximately in the same domain. Finally, it is concluded that the required calculation time reduces to about 80 % with an error less than 6 % when the main earthquake is decomposed by wavelet transform and the approximation waves are used in the nonlinear dynamic analysis.

scholarly journals The Significance of Time Step Size in Simulating the Thermal Performance of Buildings

2015 ◽  
Vol 5 (6) ◽  
pp. 1-12 ◽  
Author(s):  
Aiman Albatayneh ◽  
Dariusz Alterman ◽  
Adrian Page ◽  
Behdad Moghtaderi
Keyword(s):  
Thermal Performance ◽  
Step Size ◽  
Time Step ◽  
Time Step Size

scholarly journals Effect of Time Step Size in MM5 Simulations of a Mesoscale Convective System

2001 ◽  
Vol 129 (3) ◽  
pp. 502-516 ◽  
Author(s):  
Mei Xu ◽  
Jian-Wen Bao ◽  
Thomas T. Warner ◽  
David J. Stensrud
Keyword(s):  
Mesoscale Convective System ◽  
Convective System ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Mesoscale Convective
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