微孔压电弹性动力学的能量原理

根据古典阴阳互补和现代对偶互补的基本思想,通过作者早已提出一条简单而统一的新途径,系统地建立了微孔压电弹性动力学的能量原理,给出一个重要的以卷积表示的积分关系式,可以认为,在力学上它是广义虚功原理的表式,从该式出发,不仅能得到微孔压电弹性动力学的虚功原理和互等定理,而且通过作者所给出的一系列广义Legendre变换,能系统地导出成互补关系的11类变量、9类变量、6类变量和3类变量简化Gurtin型变分原理的泛函,同时,通过这条新途径,还能清楚地阐明这些原理之间的内在联系。     

STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.     

Large deformation symmetrical elasticity problems solved by the variational method

In this paper,based on the mathematical theory of classical mechanics and Chen‘s theorem,the variational method is used in the study of large deformation symmetrical elasticity problems.The generalized variational principles of potential energy and complementary energy,based on the instantaneous configuration are obtained,and the equivalence between the two principles is proved.Besides,the generalized variational principles of dynamical problems based on the instantaneous configuration are also given.     

On some basic principles in dynamic theory of elastic materials with voids

According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author^[1], some basic principles in dynamic theory of elastic materials with voids can be established systematically. In this paper, an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field and two-field simplified Gurtin-type variational principles. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly. The project supported by the Foundation of Zhongshan University Advanced Research Center     

Energy principles in theory of elastic materials with voids

According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author^[1], various energy principles in theory of elastic materials with voids can be established systematically. In this paper, an important integral relation is given, which can be considered essentially as the generalized pr. inciple of virtual work. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem of work in theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field and two-field generalized variational principles, and the principle of minimum potential and complementary energies. Furthermore, with this appro ach, the intrinsic relationship among various principles can be explained clearly. The project supported by the National Natural Science Foundation of China     

A mathematical programming algorithm for limit analysis

This paper deals with the limit analyses of perfect rigid-plastic continua. Based on the kinematic theorem of the limit analysis theory, a mathematical programming finite element formula for determining the upper bound load multiplier has been established, and an iteration algorithm proposed accordingly. In this algorithm the plastic and rigid zones are distinguished for every iteration step, and the goal function is modified gradually. The difficulties caused by the nonsmoothness of the goal function are overcome. Some examples solved by this algorithm are presented. The project supported by National Natural Science Foundation of China.     

多孔材料塑性极限载荷及其破坏模式分析

运用塑性力学中的机动极限分析理论，研究韧性基体多孔材料的塑性极限承载能力和破坏模式。以多孔材料的细观结构为研究对象，将细观力学中的均匀化理论引入到塑性极限分析中，并结合有限元技术，建立细观结构极限载荷的一般计算格式，并提出相应的求解算法。数值算例表明：细观孔洞对材料的宏观强度影响明显；在单向拉伸作用下，孔洞呈现膨胀扩大规律；多孔材料破坏源于基体塑性区的贯通。     

Fractional order theory of thermoelasticity

In this work, a new theory of thermoelasticity is derived using the methodology of fractional calculus. The theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases. A uniqueness theorem for this model is proved. A variational principle and a reciprocity theorem are derived.     

带孔隙损伤的弹性固体的广义变分原理

应用弹性微结构理论,建立了具广义力场带孔隙损伤线弹性固体的基本模型．应用变积方法,同时分别建立了带孔隙损伤弹性固体四类和两类变量的广义变分原理,这些变分原理对应着带孔隙损伤弹性固体微分方程和初值边值条件．应用弹性微结构理论,建立了带孔隙损伤的弹性Timoshenko 梁的基本方程,得到带孔隙损伤的弹性Timoshenko 梁两类变量的广义变分原理．这些广义变分原理为近似求解带孔隙损伤的弹性问题提供了有效途径．     

Theorems on the limit analysis of finite deformation

A generalized variational principle (theorem 1) which is equivalent mathematically to the whole set of equations and conditions and must be satisfied by the limit analysis of finite deformation is proposed in this paper. It is also proved that the limit load deduced from theorem 1 will lie between the lower and upper bounds given by the bound theorems of finite deformation