Dynamic Burst Pressure of Cylindrical Explosion Containment Vessels

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Zhanfeng Chen ◽  
Sunting Yan ◽  
Zhijiang Jin
Keyword(s):  
Numerical Solutions ◽  
Burst Pressure ◽  
Public Security ◽  
Nuclear Engineering ◽  
The Finite Element Method ◽  
Explosive Load ◽  
Internal Wall ◽  
Pressure Equation ◽  
Research Fields ◽  
Stress Function Method

Cylindrical explosion containment vessels (ECVs) are widely applied in transportation, nuclear engineering, public security, and scientific research fields to ensure the safety of the staff and equipment. In this paper, a cylindrical ECV model under a nonuniformly explosive load was established. The nonuniformly explosive load is simplified as parabolic pressure acting on the internal wall of the ECV. And then, based on the stress function method and boundary conditions, an analytical solution of the ECV subjected to the parabolic load was obtained. Next, the dynamic burst pressure equation of the ECV under the explosive load was obtained. In the end, the accuracy of the dynamic burst pressure equation was evaluated by comparing with the finite element method (FEM) under different pulse duration. The results demonstrated that the equation can accurately predict the dynamic burst pressure of the ECV. In addition, our researches can provide a benchmark for approximate or numerical solutions. It is rewarding to analyze the failure problem and evaluate the safety and integrity of the pipe and vessels under a nonuniformly explosive load.

scholarly journals Data Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network

2020 ◽  
Author(s):  
Qi Zhang ◽  
Yilin Chen ◽  
Ziyi Yang
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Data Driven ◽  
Attractive Alternative ◽  
The Finite Element Method ◽  
The Neural Network ◽  
Engineering Problems ◽  
Free Parameters

Deep learning has achieved remarkable success in diverse computer science applications, however, its use in other traditional engineering fields has emerged only recently. In this project, we solved several mechanics problems governed by differential equations, using physics informed neural networks (PINN). The PINN embeds the differential equations into the loss of the neural network using automatic differentiation. We present our developments in the context of solving two main classes of problems: data-driven solutions and data-driven discoveries, and we compare the results with either analytical solutions or numerical solutions using the finite element method. The remarkable achievements of the PINN model shown in this report suggest the bright prospect of the physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters. More broadly, this study shows that PINN provides an attractive alternative to solve traditional engineering problems.

Linearization of the finite element method for gradient flows by Newton’s method

2020 ◽  
Author(s):  
Georgios Akrivis ◽  
Buyang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Solutions ◽  
Resolvent Estimate ◽  
Optimal Order ◽  
Gradient Flows ◽  
The Finite Element Method ◽  
Element Method

Abstract The implicit Euler scheme for nonlinear partial differential equations of gradient flows is linearized by Newton’s method, discretized in space by the finite element method. With two Newton iterations at each time level, almost optimal order convergence of the numerical solutions is established in both the $L^q(\varOmega )$ and $W^{1,q}(\varOmega )$ norms. The proof is based on techniques utilizing the resolvent estimate of elliptic operators on $L^q(\varOmega )$ and the maximal $L^p$-regularity of fully discrete finite element solutions on $W^{-1,q}(\varOmega )$.

A Theoretical Formula for the Validity Limits of the Dipole Approximation for a Dielectric Mixture

2014 ◽  
Vol 906 ◽  
pp. 72-80
Author(s):  
Chang He Yang ◽  
Ding Long Cao ◽  
Lin Song Guo
Keyword(s):  
Finite Element Method ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Dipole Approximation ◽  
Empirical Method ◽  
Theoretical Formula ◽  
The Finite Element Method ◽  
Dielectric Mixture ◽  
Good Agreement ◽  
Dielectric Mismatch

A newly criterion for the validity limits of the dipole approximation for a dielectric mixture was presented, based on the comparison between the dipole approximation and the numerical solutions by the finite-element method (FEM). In terms of this criterion and the dipole-enhanced model, a simple theoretical formula for the validity limits was derived. This formula includes three variables: the dielectric mismatch, the volume fraction of particles and the precision. Its calculated results have a good agreement with the limits determined by the empirical method in the range of our interest, which indicates the theoretical formula is creditable. Using this formula, we can approximate the precision of the dipole approximation for an arbitrary dielectric mixture. And we found that the dipole approximation is acceptable with the precision equal to 30% when the dielectric mismatch is less than 2.3 (εi/ εe2.3) for the almost touching spheres.

Increasing the Solution Accuracy in the Numerical Modeling of Boundary Value Problems Using Finite Element Method Based on Hankel Shape Functions

2019 ◽  
Vol 11 (07) ◽  
pp. 1950062
Author(s):  
S. Farmani ◽  
M. Ghaeini-Hessaroeyeh ◽  
S. Hamzehei-Javaran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Element Approach ◽  
Solution Accuracy ◽  
Element Method

A new finite element approach is developed here for the modeling of boundary value problems. In the present model, the finite element method (FEM) is reformulated by new shape functions called spherical Hankel shape functions. The mentioned functions are derived from the first and second kind of Bessel functions that have the properties of both of them. These features provide an improvement in the solution accuracy with number of elements which are equal or lower than the ones used by the classic FEM. The efficiency and accuracy of the suggested model in the potential problems are examined by several numerical examples. Then, the obtained results are compared with the analytical and numerical solutions. The comparisons indicate the high accuracy of the present method.

An Elastic-Plastic Stress Analysis of the Specimen Used in the Torsional Kolsky Bar

1980 ◽  
Vol 47 (2) ◽  
pp. 278-282 ◽  
Author(s):  
Eric K. C. Leung
Keyword(s):  
Numerical Solutions ◽  
Elastic Stress ◽  
Dynamic Testing ◽  
Kolsky Bar ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Elastic Plastic ◽  
Applied Torque ◽  
Torsional Kolsky Bar ◽  
Tubular Specimens

This paper examines the stress concentration, the yielding process, and the growth of the elastic-plastic boundary as a function of applied torque in tubular specimens with a short thin-walled section. Although the analysis is entirely quasi-static, it can, under the proper circumstances, be applied to the deformation of short specimens as generally used for dynamic testing in the torsional Kolsky bar. In the analysis, the governing equations for both elastic and elastic-plastic analyses are presented, the latter taking into account work hardening. Numerical solutions of these equations employ the finite-element method. The elastic stress distribution in the specimen and the elastic-plastic enclaves are presented for various loading stages.

scholarly journals Finite element modeling of fluid flow in fractured porous media using unified approach

2020 ◽  
Vol 43 (1) ◽  
pp. 13-22
Author(s):  
Hai-Bang Ly ◽  
Hoang-Long Nguyen ◽  
Minh-Ngoc Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Fractured Porous Media ◽  
Flow In Porous Media ◽  
Soil Science ◽  
The Finite Element Method ◽  
Element Method

Understanding fluid flow in fractured porous media is of great importance in the fields of civil engineering in general or in soil science particular. This study is devoted to the development and validation of a numerical tool based on the use of the finite element method. To this aim, the problem of fluid flow in fractured porous media is considered as a problem of coupling free fluid and fluid flow in porous media or coupling of the Stokes and Darcy equations. The strong formulation of the problem is constructed, highlighting the condition at the free surface between the Stokes and Darcy regions, following by the variational formulation and numerical integration using the finite element method. Besides, the analytical solutions of the problem are constructed and compared with the numerical solutions given by the finite element approach. Both local properties and macroscopic responses of the two solutions are in excellent agreement, on condition that the porous media are sufficiently discretized by a certain level of finesse. The developed finite element tool of this study could pave the way to investigate many interesting flow problems in the field of soil science.

Use of the Finite-Element Method in the Solution of Diffusion-Convection Equations

1971 ◽  
Vol 11 (02) ◽  
pp. 139-144 ◽  
Author(s):  
Y.M. Shum
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Variational Principle ◽  
Numerical Solutions ◽  
Transient Heat Conduction ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Diffusion Convection ◽  
Element Method

Abstract A variational principle can be applied to the transient heat conduction equation with heat-flux boundary conditions. The finite-element method is employed to reduce the continuous spatial solution into a finite number of time-dependent unknowns. From previous work, it was demonstrated that the method can readily be applied to solve problems involving either linear or nonlinear boundary conditions, or both. In this paper, with a slight modification of the solution technique, the finite-element method is shown to be applicable to diffusion-convection equations. Consideration is given to a one-dimensional transport problem with dispersion in porous media. Results using the finite-element method are compared with several standard finite-difference numerical solutions. The finite-element method is shown to yield satisfactory solutions. Introduction The problem of finding suitable numerical approximations for equations describing the transport of heat (or mass) by conduction (or diffusion) and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusion-convection equations, arise in describing many diverse physical processes. Of particular interest to petroleum engineers is the classical equation describing the process by which one miscible fluid displaces another in a one-dimensional porous medium. Many authors have presented numerical solutions to this rather simple presented numerical solutions to this rather simple diffusion-convection problem using standard finite-difference methods, method of characteristics, and variational methods. In this paper another numerical method is employed. A finite-element method in conjunction with a variational principle for transient heat conduction analysis is briefly reviewed. It is appropriate here to mention the recent successful application of the finite-element method to solve transient heat conduction problems involving either linear, nonlinear, or both boundary conditions. The finite-element method was also applied to transient flow in porous media in a recent paper by Javandel and Witherspoon. Prime references for the method are the papers by Gurtin and Wilson and Nickell. With a slight modification of the solution procedure for treating the convective term as a source term in the transient heat conduction equation, the method can readily be used to obtain numerical solutions of the diffusion-convection equation. Consideration is given to a one-dimensional mass transport problem with dispersion in a porous medium. Results using the finite-element method yield satisfactory solutions comparable with those reported in the literature. A VARIATIONAL PRINCIPLE FOR TRANSIENT HEAT CONDUCTION AND THE FINITE-ELEMENT METHOD A variational principle can be generated for the transient conduction or diffusion equation. Wilson and Nickell, following Gurtin's discussion of variational principles for linear initial value problems, confirmed that the function of T(x, t) that problems, confirmed that the function of T(x, t) that leads to an extremum of the functional...........(1) is, at the same time, the solution to the transient heat conduction equation SPEJ P. 139

Comparison of Analytical Solutions with Finite Element Solutions for Ultimate Bearing Capacity of Strip Footings

2013 ◽  
Vol 353-356 ◽  
pp. 3294-3303
Author(s):  
Zi Hang Dai ◽  
Xiang Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bearing Capacity ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Slip Surface ◽  
Ultimate Bearing Capacity ◽  
The Finite Element Method ◽  
Strip Footings ◽  
Element Method

The finite element method is used to compute the ultimate bearing capacity of a fictitious strip footing resting on the surface of c-φ weightless soils and a real strip footing buried in the c-φ soils with weight. In order to compare the numerical solutions with analytical solutions, the mainly existing analytical methods are briefly introduced and analyzed. To ensure the precision, most of analytical solutions are obtained by the corresponding formulas rather than table look-up. The first example shows that for c-φ weightless soil, the ABAQUS finite element solution is almost identical to the Prandtls closed solutions. Up to date, though no closed analytical solution is obtained for strip footings buried in c-φ soils with weight, the numerical approximate solutions obtained by the finite element method should be the closest to the real solutions. Apparently, the slip surface disclosed by the finite element method looks like Meyerhofs slip surface, but there are still some differences between the two. For example, the former having an upwarping curve may be another log spiral line, which begins from the water level of footing base to ground surface rather than a straight line like the latter. And the latter is more contractive than the former. Just because these reasons, Meyerhofs ultimate bearing capacity is lower than that of the numerical solution. Comparison between analytical and numerical solutions indicates that they have relatively large gaps. Therefore, finite element method can be a feasible and reliable method for computations of ultimate bearing capacity of practical strip footings.

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