温度非线性热粘弹性问题的泛函及其变分原理

分析热粘弹性问题时,不应忽略温度对物性系数的影响。因此,本文在物性系数是温度的线性假设条件下,根据泛函分析理论,采用内积式与卷积双线性式相结合的方法,导出了包含所有边界条件,初始条件及热传导方程的拟静态耦合热粘弹性问题的泛函,并证明了与之相应的变分原理。     

On the boundary integral formulation of thermo-viscoelasticity theory

A formulation of the boundary integral equation method for generalized thermo-viscoelasticity is given. Fundamental solutions of the corresponding differential equations are obtained. An outline of the implementation of the boundary element method is discussed for the solution of the above boundary equations. Special emphasis is given to the representation of the primary fields, namely, temperature and displacement.     

模数对药柱热应力的影响

为获得药柱模数对发动机结构完整性的影响,针对某一典型火箭发动机常用的圆孔药柱和星孔药柱,建立温度冲击下的计算模型,基于推进剂材料的粘弹性本构关系,结合热流变简单材料的特性,对不同模数的圆孔药柱和星孔药柱受温度载荷的情况进行了数值计算,得到温度冲击载荷作用下药柱的实时温度场及应力、应变特性,分析了不同时刻药柱内不同位置处应力、应变特性,应力、应变随时间的变化规律及最大应力、应变随模数的变化关系.分析结果表明圆孔药柱和星孔药柱内的最大应力值都随模数呈指数形式增长,危险点分别在药柱内壁处和星尖圆弧过渡处,药柱内的应力变化速度均大于应变变化速度.     

Potential method in the theory of thermoviscoelastic mixtures

In this article, the linear theory of binary thermoviscoelastic mixtures is considered and the basic boundary value problems (BVPs) of steady vibrations are investigated. Namely, the fundamental solution of the system of equations of steady vibrations is constructed explicitly and its basic properties are established. Green’s second and third identities are obtained and the uniqueness theorems for classical solutions of the internal and external basic BVPs of steady vibrations are proved. The surface and volume potentials are constructed and their basic properties are given. The determinants of symbolic matrices are calculated explicitly. The BVPs are reduced to the always solvable singular integral equations for which Fredholm’s theorems are valid. Finally, the existence theorems for classical solutions of the internal and external BVPs of steady vibrations are proved by the potential method and the theory of singular integral equations.     

DISCONTINUITIES IN GENERALIZED THERMO-VISCOELASTICITY UNDER FOUR THEORIES

A model of the equations of generalized thermoviscoelasticity for isotropic media is given. The formulation is applied to the generalized thermoelasticity theories—Lord–Shulman, Green–Lindsay, and Chandrasekharaiah and Tzou—as well as to the dynamic coupled theory. The state-space approach is adopted for the solution of the one-dimensional problem of plane distribution of heat sources. The Laplace transform technique is used. The expansions of the stress component, the temperature increment, and the displacement, in Laplace transform domain, in power series, and the exact inversions for arbitrary time, are given. The jump discontinuities are calculated for the four theories and the kinematic conditions of compatibility are verified. Numerical results are given and illustrated graphically by employing the numerical method for the inversion of the Laplace transforms. Comparisons are made with the results predicted by the four theories.     

形状记忆纤维热粘弹性基体复合材料的力学行为

应用热粘弹性理论和Voigt混合律,在变温场中针对马氏体逆相变过程建立了NiTi形状记忆纤维热粘弹性基体复合材料的应力-应变关系,在逆相变过程和基体呈现热粘弹态阶段,由于基体松弛其模量减小,在跃阶拉应力的作用下,复合材料的压缩应变迅速增大,纤维回复应力先增大后减小;在跃阶拉应变的作用下,复合材料的应力增加先变缓然后加快直至稳定,较高的温度和材料参数对NiTi纤维热粘弹性基体复合材料的力学行为和纤维的作动性能有明显的影响.     

关于1—3维介质中调和热粘弹性波的理论研究

研究了一－三维介质中平面热粘弹性波的性质,给出了热粘弹性材料的本构关系。研究表明,波的衰减趋势与其传播方向是一致的,研究了具有自由表面的半平面波的传播规律,分析了反射波：Ｐ波、Ｓ波的特点。     

Thermomechanical behavior of a viscoelastic finite circular cylinder under harmonic deformations

A coupled thermomechanical behavior of a finite viscoelastic cylinder under harmonic kinematic excitation at its ends is investigated. The method of superposition is utilized to determine the stress-strain state of the cylinder. A refined asymptotic technique is developed to find the stress-strain state at each point of the body including the corner. Stiffness characteristics are examined over a broad range of cylinder-geometry parameters. By use of known stress components the function for the dissipation rate is constructed and the temperature field of vibration heating is calculated by solving the appropriate heat-conduction boundary-value problem. For the case of strong temperature dependence of loss modulus the phenomenon of thermal instability is examined.     

Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites

This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro–macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation.     

热粘弹性有限元法

本文依据变温下一般热粘弹性材料的蠕变型本构方程，通过对记忆积分的化简，推导出了变温粘弹性有限元方法的一般列式．它适用于各种热粘弹性材料在变温下的有限元计算。