ON THE FREE ENERGY AND VARIATIONAL THEOREN OF ELASTIC PROBLEM IN THERMAL SHOCK

In some investigations on variational principle for cou-pled thermoelastic problems,the free energy φ(e_(ij),θ) ,Wherethe state variables are elastic strain e_(ij) and temperatureincrement θ,is expressed asφ(e_(ij),θ)=λ/2e_(kk)e(ij) μe_(ki)e_(kj)-γe_(kk)θ-c/2ρθ~2/T_o (0.1)This expression is employed only under the condition of|θ|≤T_o (absolute temperature of reference)But the value of temperature increment is great, evengreater than T_o in thermal shock. And the material pro-perties (λ,μ,γ,c,etc.) will not remain constant,theyvary with θ.The expression of free energy for this con-dition is derived in this paper. Equation (0.1) is itsspecial case.Euler’s equations Will be nonlinear While this expres-sion of free energy has been introduced into variationaltheorem. In order to linearise, the time interval of ther-mal shock is divided into a number of time elements △t_k(△t_k=t_k-t_(k-1),k=1,2,…,n),Which are so small that the tempera-ture increment θ_k within it is very small,too.Thus,t     

THE EXPRESSION OF FREE ENERGY FOR THERMOELASTIC MATERIAL AND ITS RELATION TO THE VARIABLE MATERIAL COEFFICIENTS

The expression of free energy is expanded in a power series, in which there aren't any terms of order higher than third in the temperature increments θ~* and second in the strains γ_(ij) in this paper. The regular patterns of the material coefficients changing with temperature increments can be derived from this expression, These regulations accord with the experimental graph in references but the constants in the expression of free energy must be determined by experimental data. It is pointed out that the variable modulus of elasticity E and shearing modulus of elasticity G are independent of each other, but the rest of the coefficients are related to them.     

热弹性材料的自由能表达式及其与物性系数的关系*

本文中,自由能的表达式展开成幂级数,其中,温度增量θ*取到三阶,应变张量γ_ij只取到二阶.由这个表达式可以导出物性系数随温度增量的变化规律.这些规律与参考文献中的实验图线是相符的.不过,自由能表达式中的常数须由实验数据确定.文中指出,变化的弹性模量E和剪切弹性模量G是彼此独立的,而其它的物性系数则与它们相关.     

耦合热弹性平面问题的有限元法基本方程

本文在耦合热弹性问题变分原理的基础上,导出非定常温度场热弹性平面问题的有限元法基本方程.推导中,弹性平面划分为三节点三角形单元,时间过程划分为时间元,时间元中各变量(节点的位移和温度)随时间作线性变化.得出以各节点在每个瞬时(时间元的端点)的位移和温度为待定值的两组耦合的线性代数方程组,即基本方程.     

Calculation of coupled problem between temperature and phase transformation during gas quenching in high pressure

The gas quenching is a modern, effective processing technology. On the basis of nonlinear surface heat-transfer coefficient obtained by Cheng during the gas quenching, the coupled problem between temperature and phase transformation during gas quenching in high pressure was simulated by means of finite element method. In the numerical calculation, the thermal physical properties were treated as the functions of temperature and the volume fraction of phase constituents. In order to avoid effectual "oscillation" of the numerical solutions under smaller time step, the Norsette rational approximate method was used.     

耦合热弹塑性问题的泛函及其变分原理*

为用有限元法求解耦合热弹塑性问题,建立适当的泛函是有必要的.本文试图在K.N.Rysinko和E.I.Blinov提出的热弹塑性本构方程和热传导方程[1]的基础上,用泛函分析理论导出耦合热弹塑性问题的泛函.     

关于热冲击弹性问题的自由能及变分原理

在讨论耦合热弹性问题的变分原理的一些著作中,以弹性应变e_ij和温度变化值θ为状态参数的自由能φ(e_ij,θ)为自由能的这一表达式只适用于|θ|<0(绝对参考温度)的情况.在热冲击弹性问题中,温度变化值θ很大,甚至可以大过T₀同时,材料常数(λ,μ,γ,c等)随θ而发生变化,不再保持为常数.就这种情况,本文导出自由能的表达式.(0.1)式则为其特殊情况.将自由能的这一表达式引入变分原理,其欧拉方程将成为非线性.为了线性化,将热冲击作用的时间过程划分为若干足够小的时间元△t_k(△t_k=t_k-t_k-1,k=1,2,…,n).在△t_k中,温度变化θ_k很小,材料常数由t_k-1瞬时的温度场T_k-1=T_{x1,x2,x3,tk-1}确定,自由能φ_k可近似地采用(0.1)式的形式,从而得到变分原理的分段近似表达.     

可动边界上热冲击和机械冲击联合作用下圆筒的动态热应力

本文讨论了枪炮内弹道问题中的枪筒瞬态温度场和动态热应力问题.射击过程中弹头在枪筒内前进时,火药燃烧产生的高温和高压作用在弹头后面的圆筒内壁上.本文给出这种状态下圆筒热弹性问题的控制方程组,讨论了相应的泛函,给出有限元法的计算结果.     

有限长厚壁管在过冷沸腾状态下的热应力响应

在求得有限长厚壁管水淬时瞬态温度分布的基础上［１］，引入了包含相变的热弹塑性本构方程的增量形式．用有限元法求得了瞬态热应力和残余应力．对影响热应力和残余应力的各种因素进行了分析和讨论．