A New Approach to Elastodynamic Response of Cylindrical Shell Based on Developed Solution Structure Theorem for Wave Equation

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Shugen Xu ◽  
Weiqiang Wang ◽  
Yuliang Cui ◽  
Yan Liu
Keyword(s):  
Wave Equation ◽  
Solution Structure ◽  
Structure Theorem ◽  
Dynamic Pressure ◽  
Structural Response ◽  
High Accuracy ◽  
New Approach ◽  
Elastodynamic Response ◽  
Detailed Derivation ◽  
Derivation Process

In this paper, a developed solution structure theorem has been provided. It can be used to solve the wave equation about the structural response of cylinder under the dynamic pressure. This new approach also can be used to solve a batch of partial differential equations having the similar form. A detailed derivation process has been given to show how the solution is obtained. Finally, a practical example is presented, and the finite element result is also provided to validate the accuracy of methodology proposed in this paper. The result shows that it has a high accuracy for solving the elastodynamic response of the cylinder.

A New Approach to Elastodynamic Response of Cylindrical Shell Based on Generalized Solution Structure Theorem for Wave Equation

2010 ◽  
Author(s):  
Shugen Xu ◽  
Weiqiang Wang ◽  
Yan Liu
Keyword(s):  
Wave Equation ◽  
Solution Structure ◽  
Structure Theorem ◽  
Dynamic Pressure ◽  
Structural Response ◽  
Generalized Solution ◽  
New Approach ◽  
Response Data ◽  
Elastodynamic Response ◽  
Detailed Derivation

In this paper, a generalized solution structure theorem has been provided. It can be use to solve the wave equation about the structural response of cylinder under the dynamic pressure. This new approach also can be used to solve a batch of partial differential equations with the similar form. A detailed derivation process has been given to show how the solution is obtained. Finally, a practical example is presented, and all the elastodynamic response data at any point during dynamic pressure can be acquired conveniently.

A New Method to the Elastodynamic Response of a Spherical Shell Under the Impact Load

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Shugen Xu ◽  
Yang Wei ◽  
Chong Wang ◽  
Weiqiang Wang
Keyword(s):  
Wave Equation ◽  
Dynamic Response ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Solution Structure ◽  
Structure Theorem ◽  
Impact Load ◽  
Structural Dynamic ◽  
Elastodynamic Response ◽  
The Impact

In this paper, a new methodology for solving response of a spherical shell based on developed solution structure theorem has been proposed. It can be used to solve the wave equation about the structural dynamic response of a spherical shell under the impact pressure. The proposed method can be used to solve a batch of partial differential equations having the similar governing equation with different initial and boundary conditions. A detailed solving procedure has been provided to show how to use this method correctly. Finally, a practical example is provided to show how to use the proposed method to solving the elastodynamic response of a spherical shell under inner impact load.

Finite Volume Method for Computation of Water Hammer in Conical Tubes

2014 ◽  
Vol 563 ◽  
pp. 266-269
Author(s):  
Xiu Long Zhao ◽  
Jian Zhang ◽  
De Shuang Yu
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
High Accuracy ◽  
Water Hammer ◽  
Simple Derivation ◽  
Conical Tube ◽  
Discrete Equations ◽  
Volume Method ◽  
Approximate Treatment ◽  
Derivation Process

The most traditional way to calculate water hammer in the conical tube is using some small discrete equivalent uniform tubes to replace it. this approximate treatment can not show the much accurate results of the conical tube,but also not reflect the actual physical discontinuities of the system.This paper use finite volume method to integrate water hammer equations in conical tubes on spatial and temporal scales.Compare the results of FVM discrete equations with MOC. Conclusion shows that: the new discrete equations not only has high accuracy and stability in the calculation of water hammer in conical tubes,but also has a simple derivation process and clear physical meanings.This method provides a new way of thinking in water hammer calculation of conical tubes.

scholarly journals High-accuracy equation of equinoxes and VLBI astrometric Modelling

1991 ◽  
Vol 131 ◽  
pp. 342-345
Author(s):  
A.M. Gontier ◽  
N. Capitaine
Keyword(s):  
High Accuracy ◽  
Classical Representation ◽  
New Approach ◽  
The Earth ◽  
Angle Of Rotation

AbstractIn the course of implementing the use of nonrotating origin (Guinot 1979) in astrometric VLBI, for the transformation between celestial and terrestrial frames, we have compared the new approach with the classical one. We have shown that a difference exists between the two procedures at a few milliarcsecond level; this difference is due to the terms generally neglected when considering the equation of equinoxes in the classical representation of the Earth angle of rotation.

Structural Response of Metal Crystallite with BCC Lattice on Atomic Level under Nanoindentation

2013 ◽  
Vol 592-593 ◽  
pp. 55-58 ◽  
Author(s):  
Dmitrij Sergeevich Kryzhevich ◽  
Aleksandr Vyacheslavovich Korhuganov ◽  
Konstantin Petrovich Zolnikov ◽  
Sergei Grigorievich Psakhye
Keyword(s):  
Molecular Dynamics ◽  
Structural Response ◽  
Data Interpretation ◽  
High Accuracy ◽  
Atomic Level ◽  
Structural Defects ◽  
Embedded Atom Method ◽  
Free Surfaces ◽  
Embedded Atom ◽  
Bcc Lattice

Molecular dynamics investigation of metal crystallite with bcc lattice under nanoindentation was carried out. Potentials of interatomic interactions were calculated on the base of the approximation of the embedded atom method. The potentials chosen make it possible to describe with a high accuracy the elastic and surface properties of the simulated metal and energy parameters of defects, which is important for solution of the task posed in the work. For clarity and simpler indentation data interpretation, an extended cylindrical indenter was used in the investigation and loading was realized by its lateral surface. The simulated crystallite had a parallelepiped shape. The loaded plane of crystallite was modeled as a free surface while the positions of atoms in the opposite plane of crystallite were fixed along the indentation direction. Other planes of crystallite were simulated as free surfaces. The indenter velocity varied from 5 to 25 m/s in different calculations. The loading of the model crystallite was realized at 300 K. Influence of interfaces (free surfaces and grain boundaries) on peculiarities of plastic deformation nucleation and interactions of generated structural defects with interfaces in simulated crystallite under nanoindentation were investigated.

scholarly journals Analytical Solution of Heat Conduction in a Symmetrical Cylinder Using the Solution Structure Theorem and Superposition Technique

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1522 ◽  
Author(s):  
Rasool Kalbasi ◽  
Seyed Mohammadhadi Alaeddin ◽  
Mohammad Akbari ◽  
Masoud Afrand
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Solution Structure ◽  
Structure Theorem ◽  
Initial Conditions ◽  
Hyperbolic Heat Conduction ◽  
Fourier Heat Conduction ◽  
Superposition Technique ◽  
Complex Origin

In this paper, non-Fourier heat conduction in a cylinder with non-homogeneous boundary conditions is analytically studied. A superposition approach combining with the solution structure theorems is used to get a solution for equation of hyperbolic heat conduction. In this solution, a complex origin problem is divided into, different, easier subproblems which can actually be integrated to take the solution of the first problem. The first problem is split into three sub-problems by setting the term of heat generation, the initial conditions, and the boundary condition with specified value in each sub-problem. This method provides a precise and convenient solution to the equation of non-Fourier heat conduction. The results show that at low times (t = 0.1) up to about r = 0.4, the contribution of T1 and T3 dominate compared to T2 contributing little to the overall temperature. But at r > 0.4, all three temperature components will have the same role and less impact on the overall temperature (T).

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