Super high pressure blocking in thick-wall spherical vessels

An analytical formula is obtained, which allows us to find the maximum pressure within a multilayer spherical vessel in the case of a linear decrease of pressure between the layers.     

离散多层绕带容器在爆炸载荷作用下动力响应的数值模拟研究

运用LS-DYNA3D对不同缠绕角度的离散多层绕带容器在内部中心爆炸载荷作用下的动力响应进行了数值模拟。模拟结果与实验结果、理论分析以及单层圆柱高压容器的动力响应作了比较。研究结果表明,内部中心爆炸载荷作用下,容器绕带层应力分布比较均匀;相同炸药当量条件下,缠绕角度越大,最外层绕带中心的最终位移越大。结果还表明,离散多层绕带容器具有只漏不爆的良好抗爆性能,是单层结构容器不具备的。计算结果可为构建爆炸容器的工程设计标准提供参考。     

Scaling law for the elastic response of spherical explosion-containment vessels

The substantial progress made in the development of portable, spherical explosion-containment vessels has led to its adoption for explosives-related transporting and manufacturing. A simple scaling law for engineering-design use has been obtained for the maximum first-cycle elastic-strain response to explosive loading by a centered, spherical charge of a representative high explosive known as Pentolite. Results from a computer program based on the work of Baker have been accurately fitted to a six-product power law that is a function of the density, elastic modulus, diameter, and thickness of the vessel and the weight of detonated explosive. Nonlinear and log-linear fits are compared and found to agree if the role of weighting factors is understood. An impulse approximation is used to indicate that the scaling-law parameters are reasonable.     

Laminar and turbulent burning velocities of propane in spherical vessels

Laminar and turbulent burning velocities of C₃H₈/air mixtures under moderately elevated temperature and pressure conditions have been determined experimentally using spherical combustion bombs. The results are reported here and the effects of temperature, pressure, turbulence intensity and stoichiometric ratio are included. The results obtained are compared with those of other researchers. The laminar burning velocity obtained from the pressure-time curves without compensation for the reaction zone thickness is lower than those determined using burners. A reaction zone thickness correction which reduces the difference is suggested and this relies on an assessment based on the different histories found experimentally when different initial temperatures were used for the isentrope through the standard state. For mixtures with initially low turbulence levels, both the turbulent burning velocity and the burning velocity ratio, turbulent to laminar, increase as the combustion progresses. The rate of increase becomes larger with increase in the initial and instantaneous turbulence intensity, temperature and stoichiometric ratio. Deviation from the Damköhler relationship is noted.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

离散多层厚壁爆炸容器抗爆炸性能试验研究

为了研究离散多层爆炸容器的动力响应和破坏特性,制造了尺寸和材料相同但钢带缠绕倾角不同的三台离散多层试验容器,并进行了一系列大药量的中心加载试验,测量了典型位置的应变。结果表明中心装药时三台试验容器的破坏都在爆心截面处,钢带缠绕倾角较小的容器能够承受更大炸药量的爆炸作用,容器具有较好的抗内爆炸性能。     

Thermo-magnetic analysis of thick-walled spherical pressure vessels made of functionally graded materials

This study presents an analytical solution of thermal and mechanical displacements, strains, and stresses for a thick-walled rotating spherical pressure vessel made of functionally graded materials(FGMs). The pressure vessel is subject to axisymmetric mechanical and thermal loadings within a uniform magnetic field. The material properties of the FGM are considered as the power-law distribution along the thickness. Navier's equation, which is a second-order ordinary differential equation, is derived from the mechanical equilibrium equation with the consideration of the thermal stresses and the Lorentz force resulting from the magnetic field. The distributions of the displacement,strains, and stresses are determined by the exact solution to Navier's equation. Numerical results clarify the influence of the thermal loading, magnetic field, non-homogeneity constant, internal pressure, and angular velocity on the magneto-thermo-elastic response of the functionally graded spherical vessel. It is observed that these parameters have remarkable effects on the distributions of radial displacement, radial and circumferential strains, and radial and circumferential stresses.     

A theoretical analysis of angular deformation and local stresses in spherical vessels

In this paper several geometrical relations of angular deformation and the analytical expressions of local stresses in spherical vessels are established with the analytical method. A concise and practical formula for calculating the stress concentration coefficient is derived, which shows that the stress concentration is related to angular deformation and increases with an increases of the square root of the ratio of radius to thickness.     

Elastic analysis of thick-walled pressurized spherical vessels coated with functionally graded materials

In recent years, functionally graded material (FGM) has been widely explored in coating technology amongst both academic and industry communities. FGM coatings are suitable substitutes for many typical conventional coatings which are susceptible to cracking, debonding and eventual functional failure due to the mismatch of material properties at the coating/substrate interface. In this study, a thick spherical pressure vessel with an inner FGM coating subjected to internal and external hydrostatic pressure is analyzed within the context of three-dimensional elasticity theory. Young’s modulus of the coating is assumed to vary linearly or exponentially through the thickness, while Poisson’s ratio is considered as constant. A comparative numerical study of FGM versus homogeneous coating is conducted for the case of vessel under internal pressure, and the dependence of stress and displacement fields on the type of coating is examined and discussed.     

Investigation of thermo-elasto-plastic behavior of thick-walled spherical vessels with inner functionally graded coatings

Having high corrosion and thermal resistance characteristics, Functionally Graded Materials have been found wide range of applications in engineering fields. The analytical elasto-plastic solution for spherical vessels composed of outer homogenous part and inner FG coating under combined pressure and thermal loading is presented in this paper. Furthermore, the loading conditions resulted into onset of yielding from inner radius and fully plastic vessel are obtained. Material constituents in both homogenous and FG parts are assumed to be aluminum and SiC as metal matrix and ceramic particles, respectively. Although the amount of SiC particles in the homogenous part of vessel is assumed to be constant, it is varying in the radial direction of FG part based on the power law function. The results concerning two types of vessels with harder and softer FG coatings are also compared with those from homogenous vessel. Moreover, two dimensional finite element model was applied to simulate the process while the results were considered to verify the accuracy of the analytical solution. Generally, the results demonstrate that coating and grading behavior can really affect the stress distribution and yield pattern in the homogenous vessel with an inner FG coating.     

Novel material tailoring method for internally pressurized FG spherical and cylindrical vessels

A new material tailoring method for spherical and cylindrical vessels made of functionally graded materials (FGMs) is presented. It is assumed that the FG material is composed of an Al–SiC metallic-matrix composite. A uniform ratio of in-plane shear stress to yield strength [\(\varphi \left( r \right) \)] is used as the design criterion to utilize the maximum capacity of the vessel. The aim is to find a distribution of SiC particles in the radial direction, i.e., \(f\left( r \right) \), that achieves a uniform index \(\varphi \left( r \right) =\hbox {const}.\) through the wall thickness of the internally pressurized spherical or cylindrical vessel. Both the Mori–Tanaka and rule-of-mixtures homogenization schemes are used to express the effective elastic module and Poisson’s ratio. Moreover, the strength of the composite is expressed based on the rule of mixtures. Besides, finite element simulation is carried out to verify the accuracy of the analytical solution. The effects of input parameters such as the internal pressure, strength of the SiC particles, ratio of in-plane shear stress to effective yield strength, and choice of homogenization scheme on the tailored distribution of the SiC volume fraction in the radial direction are also investigated.     

球形容器内气体的泄爆过程

为了得到球形容器内可燃气体的泄爆强度产生机理以及燃烧火焰与压力传播的基本规律,从流体力学和化学反应动力学守恒出发,采用-湍流模型和EBU-Arrhenius燃烧模型,利用SIMPLE算法对带泄爆导管的球形容器二维空间内甲烷-空气预混气体的泄爆过程内外场进行了数值计算,获得了气体燃烧过程中火焰和压力传播特性以及气体流动特性,能够比较清晰地反映泄爆的整个过程。研究表明,燃烧火焰在泄爆过程中发生湍流,传播得到了极大的加速,泄爆导管对于容器内的高压气体泄放有很大的约束作用。     

Stability of multilayered bodies

Mariupol' Metallurgical Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 2, pp. 88–93, February, 1990.     

Nonlinear analysis of multilayered shells

A large deformation theory for layered shells of arbitrarily varying thickness and using a piecewise smooth displacement field is developed. A system of layer coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells.     

Parallel folding in multilayered structures

A recent two-layer nonlinear model for parallel folding is extended to a full multilayer formulation for n identical layers. The general behaviour of the multilayer is characterized using a sinusoidal Galerkin approximation substituted into the linearized potential energy function and equations for the wavelength and critical load are found. Comparisons with experiments conducted on layers of paper constrained between two sheets of foam rubber show that the trend of the load-amplitude plots is in good agreement with that predicted. Excellent correlation is also achieved between the wavelengths calculated by the linearized buckling analysis and those seen experimentally.     

Instabilities in multilayered soft dielectrics

Experimental observations clearly show that the performance of dielectric elastomeric-based devices can be considerably improved using composite materials. A critical issue in the development of composite dielectric materials toward applications is the prediction of their failure mechanisms due to the applied electromechanical loads. In this paper we investigate analytically the influence of electromechanical finite deformations on the stability of multilayered soft dielectrics under plane-strain conditions. Four different criteria are considered: (i) loss of positive definiteness of the tangent electroelastic constitutive operator, (ii) existence of diffuse modes of bifurcation (microscopic modes), (iii) loss of strong ellipticity of the homogenized continuum (localized or macroscopic modes), and (iv) electric breakdown. While the formulation is developed for generic isotropic hyperelastic dielectrics, results are presented for the special class of ideal dielectrics incorporating a neo-Hookean elastic response. The effect of material properties and loading conditions is investigated, providing a detailed picture of the different possible failure modes.     

Theory of elasticity of a multilayered medium

Summary Though the basic equations of the linear theory of elasticity are well known, it is rather cumbersome to evaluate the exact state of stress and displacement for a multilayered medium. In this paper we discuss a formal solution based on integral transforms and matrix analysis. Essentially the problem is reduced to the evaluation of some basic matrices and thus the calculation takes place in a clearly arranged way. Here we restrict ourselves to plane elastic and isotropic layers and use cartesian coordinates.

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Zusammenfassung Obwohl die Grundgleichungen der linearen Elastizitätstheorie wohlbekannt sind, ist die Ermittlung des genauen Spannungs- und Verschiebungszustandes eines vielschichtigen Mediums ziemlich mühsam. In der vorliegenden Arbeit wird mithilfe von Integraltransformationen und der Matrizenrechnung eine formale Lösung entwickelt. Das Problem wird im wesentlichen auf die Bestimmung einiger Grundmatrizen zurückgeführt, die eine übersichtliche Berechnung gestattet. Die Untersuchung beschränkt sich auf ebene elastisch-isotrope Schichten, wobei kartesische Koordinaten verwendet werden.