scholarly journals ANALYSIS OF THE CONSERVATIVE SMOOTHING EFFECT ON THE ACCURACY OF DYNAMIC ELASTIC-PLASTIC SPHERICAL SHELLS BUCKLING NUMERICAL SIMULATION

2019 ◽  
Vol 81 (4) ◽  
pp. 475-488
Author(s):  
A.V. Demareva
Keyword(s):  
Experimental Data ◽  
Spherical Shell ◽  
Numerical Solution ◽  
Initial Conditions ◽  
Local Coordinate System ◽  
Isotropic Hardening ◽  
System Of Equations ◽  
State Equations ◽  
Defining System ◽  
Smoothing Procedure

Large changes of a lead spherical shell enclosed in an aluminum spacesuit under the action of an overload pulse are considered. The defining system of equations is formulated in Lagrange variables in a two-dimensional (axisymmetric) formulation. Strain and stress rates are determined in the local coordinate system. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with isotropic hardening are used as state equations. The contact interaction of the shell and the spacesuit is modeled by non-penetration conditions taking into account friction. The numerical solution of the problem under given boundary and initial conditions is based on the finite element method moment scheme and the explicit time integration “cross” type scheme. 4-node isoparametric finite elements with bilinear form functions are used to discretize the defining system of equations for spatial variables. To suppress the numerical solution high-frequency oscillations, the procedure of nodal displacements rates conservative smoothing is used. As shown by the results of numerical research spherical shell in the process of intensive dynamic loading undergoes large deformation and rotation angles as a rigid whole. The calculation results reliability is confirmed by a good correspondence to the experimental data. The influence of conservative smoothing procedure and moment components of deformations and stresses on the solution accuracy is analyzed. It is shown that without conservative smoothing procedure using, the shape of the spherical shell buckling obtained in the calculation does not correspond to the experimental data. Neglect of the moment components of strains and stresses leads to the development of instability of the “hourglass” type.

scholarly journals ANALYSIS OF THE CONSERVATIVE SMOOTHING EFFECT ON THE ACCURACY OF DYNAMIC ELASTIC-PLASTIC SPHERICAL SHELLS BUCKLING NUMERICAL SIMULATION

2019 ◽  
Vol 81 (4) ◽  
pp. 474-487
Author(s):  
A.V. Demareva
Keyword(s):  
Experimental Data ◽  
Spherical Shell ◽  
Numerical Solution ◽  
Initial Conditions ◽  
Local Coordinate System ◽  
Isotropic Hardening ◽  
System Of Equations ◽  
State Equations ◽  
Defining System ◽  
Smoothing Procedure

Large changes of a lead spherical shell enclosed in an aluminum spacesuit under the action of an overload pulse are considered. The defining system of equations is formulated in Lagrange variables in a two-dimensional (axisymmetric) formulation. Strain and stress rates are determined in the local coordinate system. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with isotropic hardening are used as state equations. The contact interaction of the shell and the spacesuit is modeled by non-penetration conditions taking into account friction. The numerical solution of the problem under given boundary and initial conditions is based on the finite element method moment scheme and the explicit time integration “cross” type scheme. 4-node isoparametric finite elements with bilinear form functions are used to discretize the defining system of equations for spatial variables. To suppress the numerical solution high-frequency oscillations, the procedure of nodal displacements rates conservative smoothing is used. As shown by the results of numerical research spherical shell in the process of intensive dynamic loading undergoes large deformation and rotation angles as a rigid whole. The calculation results reliability is confirmed by a good correspondence to the experimental data. The influence of conservative smoothing procedure and moment components of deformations and stresses on the solution accuracy is analyzed. It is shown that without conservative smoothing procedure using, the shape of the spherical shell buckling obtained in the calculation does not correspond to the experimental data. Neglect of the moment components of strains and stresses leads to the development of instability of the “hourglass” type.

scholarly journals ANALYSIS OF FINITE ELEMENT SOLUTION CONSERVATIVE SMOOTHING INFLUENCE ON THE ZERO ENERGY MODES SUPPRESSION

2021 ◽  
Vol 83 (1) ◽  
pp. 101-110
Author(s):  
A.I. Kibets ◽  
M.V. Bezhentseva
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Numerical Solution ◽  
Integration Scheme ◽  
System Of Equations ◽  
Zero Energy ◽  
Nodal Displacement ◽  
Finite Element Grid ◽  
Defining System ◽  
Smoothing Procedure

The problem of high-speed penetration of a non-deformable cylinder into a steel plate is considered. The defining system of equations is formulated in Lagrange variables in a three-dimensional formulation. The equation of motion is derived from virtual work capacities balance. Kinematic relations are recorded in the metric of the current state. The relations of the flow theory with kinematic and isotropic hardening are used as equations of state. The contact interaction of the cylinder and the plate is modeled by non-penetration conditions. The numerical solution of the problem under given boundary and initial conditions is based on the moment scheme of the finite element method and “cross” type explicit time integration scheme. To discretize the defining system of equations with respect to spatial variables, 8-node isoparametric finite elements with multilinear form functions are used. To suppress the high-frequency oscillations of the numerical solution, the procedure of nodal displacement velocities conservative smoothing is used. The smoothing algorithm is based on the momentum conservation law, focused on finite element grids consisting of blocks that are mutually unambiguously mapped to a unit cube. To analyze the nodal displacement velocities monotonicity, the numerical solution splitting in the directions of the finite element grid lines is used. As the results of computer modeling have shown, the finite elements of the plate are exposed large deformations and rotation angles as a rigid whole during local intense dynamic loading. The conservative smoothing procedure influence on the numerical solution stability is analyzed. It is shown that in the problem under consideration, without applying the conservative smoothing procedure, zero-energy modes develop in the contact zone in the finite-element grid of the plate (an hourglass-type instability) and the collision process cannot be modeled before the cylinder rebounds.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

Motion of a Large Dusty Buoyant Thermal With a Vortex Ring

1978 ◽  
Vol 45 (4) ◽  
pp. 711-716 ◽  
Author(s):  
Stephen S.-H. Chang
Keyword(s):  
Numerical Solution ◽  
Vortex Ring ◽  
Excellent Agreement ◽  
Spherical Particles ◽  
System Of Equations ◽  
Inhomogeneous Atmosphere

This paper presents a method for computing the motion and decay of a large dusty, buoyant thermal (cloud) carried by a vortex ring generated from a strong near ground explosion and ascending in an inhomogeneous atmosphere. A system of equations is derived describing the motion of the vortex ring, the thermal, and the pollutants which consist of numerous solid spherical particles. The interior properties and the trajectories of the thermal and the pollutants are obtained. The numerical solution for the thermal trajectory is in excellent agreement with experiment.

scholarly journals Simultaneous Parameters Identifiability and Estimation of anE. coliMetabolic Network Model

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Kese Pontes Freitas Alberton ◽  
André Luís Alberton ◽  
Jimena Andrea Di Maggio ◽  
Vanina Gisela Estrada ◽  
María Soledad Díaz ◽  
...  
Keyword(s):  
Experimental Data ◽  
Escherichia Coli ◽  
Metabolic Networks ◽  
Initial Conditions ◽  
Model Fit ◽  
Real Problem ◽  
Kinetic Rates ◽  
K 12 ◽  
Procedure Model

This work proposes a procedure for simultaneous parameters identifiability and estimation in metabolic networks in order to overcome difficulties associated with lack of experimental data and large number of parameters, a common scenario in the modeling of such systems. As case study, the complex real problem of parameters identifiability of theEscherichia coliK-12 W3110 dynamic model was investigated, composed by 18 differential ordinary equations and 35 kinetic rates, containing 125 parameters. With the procedure, model fit was improved for most of the measured metabolites, achieving 58 parameters estimated, including 5 unknown initial conditions. The results indicate that simultaneous parameters identifiability and estimation approach in metabolic networks is appealing, since model fit to the most of measured metabolites was possible even when important measures of intracellular metabolites and good initial estimates of parameters are not available.

Usage of composite kernel in the SPH method for simulating the movement of granular materials

2021 ◽  
pp. 50-61
Author(s):  
Игорь Иванович Потапов ◽  
Ольга Владимировна Решетникова
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Granular Medium ◽  
Mass Conservation ◽  
New Combination ◽  
Computational Domain ◽  
Sph Method ◽  
Classical Motion ◽  
Smoothing Kernel ◽  
Composite Kernel

В работе для моделирования движения сыпучей среды используется метод сглаженных частиц. Для аппроксимации искомых функций предложено новое составное ядро малой связности. Основой для разработки ядра послужило требование к условию о сохранении плотности единичной SPH-частицы. Выполнение данного условия позволяет правильно моделировать поле плотности на границах расчетной области, а также в случаях структурных изменений каркаса гранулированных частиц сыпучей среды. Из анализа решения задачи гидростатики методом SPH получена оценка значения масштаба сглаживающей длины ядра для двумерного случая. Выполнен расчет процесса обрушения гранулированного “столба” и проведено сравнение полученных численных результатов моделирования с экспериментальными данными. The purpose of the study is to improve the practice of the SPH methodology which is applied for modelling of movement in the various media. The basis of the SPH-approximation of the function fields is formed by the forms of the smoothing kernel and its derivatives. Popular forms of smoothing kernels are characterized by the presence of significant fatal approximation errors when modelling granular media. Methodology. The state of granular medium is described by the classical motion and mass conservation equations. Each granule of the medium corresponds to a separate SPH particle. To approximate the density and pressure fields in the SPH particle, a new combination of the smoothing core and its first derivative forms is proposed. Results. The proposed new composite core fulfills the conditions of mass conservation and density recovery in the particle during SPH modeling. It is shown that the new composite core is characterized by a minimum error of pressure gradient approximation - about 2%. A new estimate for the velocity of propagation of an elastic wave in a medium, sufficient to obtain a correct numerical solution, is proposed. A comparative analysis of the obtained solutions with experimental data is made. Findings. The proposed composite shape of the smoothing kernel allows correct simulation of the motion of a granular medium by the SPH method. Its compactness (unit smoothing radius and unit smoothing length) makes it possible to correctly reconstruct the density field at the boundaries of the computational domain and in cases of structural changes in the framework of the granular medium. The numerical solution of the problem of the collapse of a column of granules obtained using the proposed composite core shows good agreement with experimental data.

Numerical Simulation of Instantaneous Flashing LPG Release

2011 ◽  
Vol 236-238 ◽  
pp. 2660-2663
Author(s):  
Xiao Liu ◽  
Wei Tan ◽  
Yu Bu ◽  
Yu Jin Liu ◽  
Ze Jun Wang
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Initial Conditions ◽  
Expansion Process ◽  
Two Phase ◽  
Open Environment ◽  
Mass And Heat Transfer ◽  
Rate Of Evaporation ◽  
Instantaneous Release ◽  
Dynamics Method

An accident instantaneous release of LPG can results in a rapidly expanding two-phase flammable cloud, which is the medium of potentially disastrous consequences. In this paper, CFD (Computational Fluid Dynamics) method was applied for instantaneous LPG release in an open environment in order to analysis the expansion process of two-phase cloud. The results from simulation are compared with the published experimental data to validate the model. Statistical analysis of experimental data is used to set the initial conditions and computational inlet in the model. The mass and heat transfer is calculated in eulerian-lagrangian method. The features in expansion process are studied by the analyses of the variation of size, temperature, volume averaged rate of evaporation of the cloud and entropy of the whole flow field.

scholarly journals Influence of Induction Hardening on Wear Resistance in Case of Rolling Contact

2016 ◽  
Vol 66 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Michal Šofer ◽  
Rostislav Fajkoš ◽  
Radim Halama
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Induction Hardening ◽  
Rolling Contact ◽  
Isotropic Hardening ◽  
Wear Model ◽  
Wear Rates ◽  
C Programming Language ◽  
Hardening Rule ◽  
C Programming

AbstractThe main aim of the presented paper is to show how heat treatment, in our case the induction hardening, will affect the wear rates as well as the ratcheting evolution process beneath the contact surface in the field of line rolling contact. Used wear model is based on shear band cracking mechanism [1] and non-linear kinematic and isotropic hardening rule of Chaboche and Lemaitre. The entire numerical simulations have been realized in the C# programming language. Results from numerical simulations are subsequently compared with experimental data.

Sign in / Sign up

Export Citation Format

Share Document