Method of solving equations of motion of viscoelastic media

1975 ◽  
Vol 9 (3) ◽  
pp. 382-388
Author(s):  
I. G. Filippov
Keyword(s):  
Equations Of Motion ◽  
Viscoelastic Media ◽  
Solving Equations

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.

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.

What nature knows about solving equations of motion

1989 ◽  
Vol 57 (5) ◽  
pp. 435-438 ◽  
Author(s):  
G. Ares‐de‐Parga ◽  
M. A. Rosales
Keyword(s):  
Equations Of Motion ◽  
Solving Equations

Cylindrical and Spherical Shear Waves in Nonhomogeneous Isotropic Viscoelastic Media

1973 ◽  
Vol 51 (10) ◽  
pp. 1091-1097 ◽  
Author(s):  
T. Bryant Moodie
Keyword(s):  
Equations Of Motion ◽  
Shear Waves ◽  
Three Dimensions ◽  
Radial Coordinate ◽  
Shear Stresses ◽  
Progressive Wave ◽  
Elastic Solids ◽  
Linearized Equations ◽  
Viscoelastic Media ◽  
Isotropic Media

This paper is concerned with the propagation of viscoelastic shear waves in nonhomogeneous isotropic media. Herein we develop formal methods of solving the linearized equations of viscoelastodynamics in two and three dimensions for nonhomogeneous Maxwell solids whose properties depend continuously on a single radial coordinate. These methods are developed for the linearized equations of motion formulated in terms of shear stresses, and are based on Cooper's and Reiss' extension to linear homogeneous viscoelastic media of the Karal–Keller technique. Shearing stesses are applied to the boundaries of cylindrical and spherical openings in the viscoelastic media, and formal asymptotic wave front expansions of the solutions are obtained. In both cases a modulated progressive wave that propagates with variable velocity is obtained. The modulation depends on the moduli of rigidity and viscosity, whereas the velocity depends only on the modulus of rigidity. When the viscosity parameter in our Maxwell element tends to infinity, the results reduce to the known results for nonhomogeneous elastic solids.

An Integrated Parallelizable Algorithm for Computer Motion Simulation of Large-Sized Bio-Molecular Structures

2017 ◽  
Author(s):  
Shanzhong (Shawn) Duan
Keyword(s):  
Fast Multipole Method ◽  
Equations Of Motion ◽  
Molecular Structures ◽  
Motion Simulation ◽  
Fast Multipole ◽  
Molecular Method ◽  
Simulation Procedure ◽  
Solution Of Equations ◽  
Multipole Method ◽  
Solving Equations

In this paper, an integrated parallelizable algorithm is presented for computer simulation of dynamics of multibody molecular structures in polymers and biopolymers. The algorithm is developed according to an integrated O(N) simulation procedure developed by the author for calculating interatomic forces and forming/solving equations of motion for large-sized bio-molecular structures. Specifically, the simulation procedure is created via a proper integration between a parallelizable multibody molecular simulation method (PMMM) produced by the author and a parallelizable fast multipole method (PFMM). PFMM is utilized for calculation of atomic forces such as Van der Waals and Coulomb attractions between the atomics in the molecular structures. The parallelizable multibody molecular method is used for forming/solving equations of motion of large-sized molecular structures in polymers and biopolymers. Currently, the calculation of interatomic forces and formation/solution of equations of motion are treated separately by various procedures. For instance, Fast Multipole Method (FMM) and Cell Multipole Method (CMM) are applied for calculating interatomic forces only. Cartesian Coordinate Method (CCM) and Internal Coordinate Molecular Dynamics Method (ICMM) have been introduced independently for forming/solving equations of motion. Though formation and solution of equations of motions, and atomic force calculations are needed for same molecular structure, there is no direct conversation between two group methods. The proposed algorithm integrates multibody molecular method with fast multipole method in a parallel fashion so that both calculating atomic forces and forming/solving equations of motion can be carried out concurrently in a combined procedure. Computational loads associated with these two simulation tasks then can be divided among sub-chains, and each sub-chain is allocated to a processor on a parallel computing system via a proper integration between PFMM and PMMM. The algorithm can be used on both shared-memory and distributed-memory parallel computational systems. Compared with its counterpart of the integrated O(N) procedure developed by the author before, this algorithm has a computational complexity of O(logN) theoretically (N is number of subsets). The algorithm may find its applications for force calculation and motion simulation associated with large-sized molecular structures of polymers and biopolymers.

scholarly journals NONCOMMUTATIVE BRANES IN D-BRANE BACKGROUNDS

2002 ◽  
Vol 17 (31) ◽  
pp. 4733-4747 ◽  
Author(s):  
MASAKO ASANO
Keyword(s):  
Magnetic Moment ◽  
Effective Action ◽  
Equations Of Motion ◽  
Quantum Numbers ◽  
World Volume ◽  
Solving Equations ◽  
Moment Effect

We study Myers' world volume effective action of coincident D-branes. We investigate a system of N0D0-branes in the geometry of Dp-branes with p = 2 or p = 4. The choice of coordinates can make the action simplified and tractable. For p = 4, we show that a certain pointlike D0-brane configuration solving equations of motion of the action can expand to form a fuzzy two-sphere via magnetic moment effect without changing quantum numbers. We compare noncommutative D0-brane configurations with dual spherical D(6 - p)-brane systems. We also discuss the relation between these configurations and giant gravitons in 11 dimensions.

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.

scholarly journals THE CANONICAL STRUCTURE OF THE FIRST-ORDER EINSTEIN–HILBERT ACTION

2010 ◽  
Vol 25 (17) ◽  
pp. 3453-3480 ◽  
Author(s):  
D. G. C. MCKEON
Keyword(s):  
Phase Space ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Affine Connection ◽  
Canonical Structure ◽  
First Order ◽  
Order Form ◽  
Solving Equations ◽  
Hilbert Action

The Dirac constraint formalism is used to analyze the first-order form of the Einstein–Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d-3) degrees of freedom in phase space. The gauge invariance of the action is discussed, with special attention being paid to the gauge generators of Henneaux, Teitelboim and Zanelli and of Castellani.

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