Solid-state explosion simulation in COMSOL Multiphysics

2019 ◽  
Vol 14 (4) ◽  
pp. 253-261
Author(s):  
A.V. Belov ◽  
O.V. Kopchenov ◽  
A.O. Skachkov ◽  
D.E. Ushakov
Keyword(s):  
Solid Mechanics ◽  
Equations Of Motion ◽  
Solid Material ◽  
Normal Pressure ◽  
Steel Grade ◽  
Blast Waves ◽  
Comsol Multiphysics ◽  
Initial Moment ◽  
Steel Tank ◽  
Solving Equations

In this work, the propagation of blast waves in a rock mass caused by a short-term load is considered. Such loads are typical in the construction of tunnels and other excavations using blasting. For modeling by the finite element method, the cross-platform software COMSOL Multiphysics 5.4 was used. The explosion is reproduced in a steel tank whose steel grade is EN 1.7220 4CrMo4. The medium in the tank has the properties of granite rock (Young’s modulus E = 50 GPa, Poisson’s ratio ν = 2/7, Density ρ = 2700 kg/m3 ). The sphere is also a body having the properties of granite. Set to clarify the geometry of the explosion and the area where the mesh is indicated. The tank has dimensions: 10.39 m in length and diameter 2.9 m. The wall thickness of the tank is 0.01 m. To model the explosion, the Solid Mechanics interface was used, located in the Structural Mechanics branch, based on solving equations of motion together with a model for solid material. Results such as displacement, stress, and strain are calculated. The force per unit volume (Fv) is specified by the normal pressure in the sphere. Also, the tensile strength was calculated for this steel grade: upon reaching a certain pressure in the tank (7.26 MPa), the simulation stops, and the system notifies at what point in time the destruction occurred. A Time Dependent Study is used. Seconds are used as a unit of time. The task is calculated from 0 seconds (initial moment of time) to 0.003 seconds (final moment of time) with a construction step of 0.00005.

Simulation-based assessment of coupled frequency response of magneto-electro-elastic auxetic multifunctional structures subjected to various electromagnetic circuits

2021 ◽  
pp. 146442072110219
Author(s):  
Vinyas Mahesh ◽  
Vishwas Mahesh ◽  
Dineshkumar Harursampath ◽  
Ahmed E Abouelregal
Keyword(s):  
Electric Fields ◽  
Solid Mechanics ◽  
Natural Frequencies ◽  
Comsol Multiphysics ◽  
Simulation Based ◽  
Electric And Magnetic Fields ◽  
Auxetic Structures ◽  
Triangular Elements ◽  
Benchmark Solutions ◽  
Free Vibration Response

This article deals with the modeling of magneto-electro-elastic auxetic structures and developing a methodology in COMSOL Multiphysics® to assess the free vibration response of such structures when subjected to various electromagnetic circuit conditions. The triple energy interaction between elastic, magnetic, and electric fields are established in the COMSOL Multiphysics® using structural mechanics and electromagnetic modules. The multiphase magneto-electro-elastic material with different percentages of piezoelectric and piezomagnetic phases are used as the material. In the solid mechanics module, the piezoelectric and piezomagnetic materials were created in stress-charge and stress-magnetization forms, respectively. The electric and magnetic fields are defined in COMSOL Multiphysics® through electromagnetic equations. Further, the customized controlled meshing constituted of free tetrahedral and triangular elements is adapted to trade-off between the accuracy and the computational expenses. The eigenvalue analysis is performed to obtain the natural frequencies of the MEE re-entrant auxetic structures. Also, the efficiency of smart auxetic structures over conventional honeycomb structures is presented throughout the manuscript. In addition, the discrepancy in the natural frequencies of the structures considering coupled and uncoupled state is also illustrated. It is believed that the modeling procedure and its outcomes serve as benchmark solutions for further design and analysis of smart auxetic magneto-electro-elastic structures.

Investigation of Sinkage and Trim by Ships in Shallow Water Based on Overset Grid

2015 ◽  
Vol 713-715 ◽  
pp. 2126-2132
Author(s):  
Da Ming Sun ◽  
Ji Yong Liu ◽  
Qing Wen Kong
Keyword(s):  
Shallow Water ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Overset Grid ◽  
Ship Hulls ◽  
Surface Ship ◽  
Solving Equations ◽  
Sinkage And Trim ◽  
Volume Method ◽  
Good Agreement

A study on the navigation behavior for ships in shallow water had been carried out on CFD. The problem of surface ship hulls free of sinkage and trim in shallow water is analyzed numerically by simultaneously solving equations of the Reynolds averaged Navier-Stokes (RANS). The computations, based on the single-phase level set and overset grid, are discretized by finite volume method (FVM). An earth-based reference system is used for the solution to the fluid flow, while a ship-based reference is used to compute the rigid-body equations of motion. A S60 CB=0.6 ship model is taken as an example to the numerical simulation. Numerical results of the sinkage and trim of the seven Froude Numbers (Fn=0.5~0.8) are compared against experimental data, which have a good agreement.

The Isobars in Boundary Layers at Supersonic Speeds

1968 ◽  
Vol 19 (2) ◽  
pp. 105-126 ◽  
Author(s):  
D. F. Myring ◽  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Equations Of Motion ◽  
Normal Pressure ◽  
Simple Extension ◽  
Pressure Gradients ◽  
Boundary Layer Flows ◽  
Hyperbolic Flow ◽  
The Individual ◽  
Momentum Integral

SummaryFor boundary layer flows over curved surfaces at moderately high supersonic speeds the existence of normal pressure gradients within the boundary layer becomes important even for small curvatures and they cannot be ignored. The describing equations are basically parabolic in form so that the simplifications inherent in hyperbolic flows would not at first sight seem to be relevant. However, the equations of motion for a two-dimensional, supersonic, rotational, viscous flow are analysed along the lines of a hyperbolic flow and the individual effects of viscosity and vorticity are examined with regard to the isobar distributions. It is found that these two properties have compensating effects and the experimental evidence presented confirms the conclusion that inside the boundary layer the isobars follow much the same rules as those which determine the isobars in the external hyperbolic flow. Since for turbulent boundary layers the fullness of the Mach number profile produces almost linear Mach lines in the boundary layer, this provides a simple extension to the methods of analysis, and the momentum integral equation is reformulated using a swept element bounded by linear isobars. The final equation is similar in form to the conventional one except that the momentum and displacement thicknesses are now defined by integrals along the swept isobars, and all normal pressure gradients due to centrifugal effects are accounted for.

Analysis on Response of Blades With Friction Damping Interconnection Using a New Friction Model

1997 ◽  
Author(s):  
Zili Xu ◽  
Xinyi Li ◽  
Qingji Meng
Keyword(s):  
Equations Of Motion ◽  
Static Friction ◽  
Normal Pressure ◽  
Friction Model ◽  
Force Frequency ◽  
Steam Turbines ◽  
Friction Damping ◽  
Blade Vibration ◽  
Blade System ◽  
The Difference

Blades with damper structures have been widely used in gas and steam turbines. Operation experience indicate that damper structures can reduce the dynamic stress of the blade effectively, so it is essential to predict the oscillating characteristics of damped blade accurately. In this paper, a modified Oden friction model, which can consider the difference between static friction and dynamic friction, for analyzing nonlinear friction damping, is presented and the dynamic equations of motion of blade system is given also. The response of blade group with 5 blades is analyzed using the model presented in this paper. Factors such as the placement of connectors, external exciting force frequency, and normal pressure that influence the blade vibration characteristic are studied. Some results available for reference have been obtained.

A simplified analysis of spherical and cylindrical blast waves

1961 ◽  
Vol 11 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Manfred P. Friedman
Keyword(s):  
Main Shock ◽  
Specific Problem ◽  
Equations Of Motion ◽  
Present Theory ◽  
Blast Waves ◽  
Secondary Shock ◽  
Shock Dynamics ◽  
Explicit Formulae ◽  
Simplified Analysis ◽  
Subsequent Motion

Investigations into the behaviour of the gas flowbehind spherical or cylindrical blasts have shown that secondary shocks arise within the original detonation gases. The secondary shock, at first weak, is carried outward with the expanding gases. Subsequently it strengthens and bends back toward the origin, arriving there with high intensity.By using some recently developed techniques in shock dynamics and extending them where necessary, a theory is developed by which the motion of the main shock wave, as well as the formation and subsequent motion of the secondary shock, are given by explicit formulae. In addition, a method for determining, also by explicit formulae, the location of the contact surface between the detonation gases and the outside atmosphere is given. The results of a specific problem, which has been solved by numerically integrating the total equations of motion, and has also been checked experimentally, are compared with the results of the present theory.

DECISION-MAKING IN A HYBRID TWO-STEP PROBLEM OF DYNAMIC CONTROL

2018 ◽  
pp. 415-423
Author(s):  
Anatolii Fedorovich Kleimenov
Keyword(s):  
Optimal Control ◽  
Equations Of Motion ◽  
Dynamic Control ◽  
Control Process ◽  
Fixed Time ◽  
Time Interval ◽  
Initial Moment ◽  
Fixed Amount ◽  
Controlled System ◽  
Abnormal Behaviors

The equations of motion of the controlled system in the two-step problem under consideration at a fixed time interval contain the controls of either one player or two players. In the first step (stage) of the controlled process (from the initial moment to a certain predetermined moment), only the first player controls the system, which solves the problem of optimal control with a given terminal functional. In the second step (stage) of the process, the first player decides whether the second player will participate in the control process for the remainder of the time, or not. It is assumed that for participation the second player must pay the first side payment in a fixed amount. If «yes», then a non-antagonistic positional differential game is played out, in which the Nash equilibrium is taken as the solution. In addition, players can use «abnormal» behaviors, which can allow players to increase their winnings. If « no », then until the end of the process continues to solve the problem optimal control.

scholarly journals The dynamical problem on acting concentrated load on the elastic quarter space

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 7-25
Author(s):  
A. A. Fesenko ◽  
K. S. Bondarenko
Keyword(s):  
Fourier Transforms ◽  
Equations Of Motion ◽  
Compressive Load ◽  
Integral Transforms ◽  
Dynamical Problem ◽  
Asymptotic Formulas ◽  
Initial Moment ◽  
Concentrated Load ◽  
Quarter Space ◽  
Matrix Differential

The wave field of an elastic quarter space is constructed when one face is rigidly fixed and a dynamic normal compressive load acts on the other along a rectangular section at the initial moment of time. Integral Laplace and Fourier transforms are applied sequentially to the equations of motion and boundary conditions in contrast to traditional approaches when integral transforms are applied to solutions' representations through harmonic functions. This leads to a one-dimensional vector homogeneous boundary value problem with respect to unknown displacement's transformants. The problem was solved using matrix differential calculus. The original displacement field was found after applying inverse integral transforms. For the case of stationary vibrations a method of calculating integrals in the solution in the near loading zone was indicated. For the analysis of oscillations in a remote zone the asymptotic formulas were constructed. The amplitude of vertical vibrations was investigated depending on the shape of the load section, natural frequencies of vibrations and the material of the medium.

Dynamic Response of Multi-Cylinder Engines As Spatial Elastic Linkage Systems

1996 ◽  
Author(s):  
Cemil Bagci ◽  
Siva K. Rajavenkateswaran
Keyword(s):  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Lumped Mass ◽  
Time Histories ◽  
Solving Equations ◽  
Finite Line ◽  
Exponential Method ◽  
Motion Effect ◽  
Industrial Use

Abstract Dynamics of multi-cylinder engines have been performed by the conventional methods using lumped pure torsional systems. This article offers a finite element method of performing elastodynamic analysis of multi-cylinder engines considering them as spatial linkage systems with true spatial geometries of the crankshaft and the linkage loops. An engine can have any number of cylinders with linear offsets and angular orientations relative to each other. A three-dimensional finite-line element with isoparametric joint irregularity freedoms is developed and used. Consistent or lumped mass systems can be used. Elastodynamics of engines is considered in two forms: (a) kinetoelastostatics (KES) where all forces and torques acting on the system are considered except the vibratory motion effect; (b) kinetoelastodynamics (KED) where the forced and damped equations of motion of the system are solved. Matrix exponential method of solving equations of KED motions are presented and used. It is proven to be a very efficient and stable technique for the solutions of large systems of linear and nonlinear differential equations of any order. After solving for the generalized coordinates, time histories of the neutral coordinate displacements, forces, moments, stresses, bearing forces, and generated torque are determined for as many work cycles as desired. A generalized computer program performing KED and KES studies of any multi-cylinder engine is made available for industrial use. KED and KES analyses of a four-cylinder automobile engine are performed.

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