LARGE AMPLITUDE VIBRATION OF CIRCULAR SANDWICH PLATE

ＬＡＲＧＥＡＭＰＬＩＴＵＤＥＶＩＢＲＡＴＩＯＮＯＦＣＩＲＣＵＬＡＲＳＡＮＤＷＩＣＨＰＬＡＴＥＳＤｕＧｕｏ－ｊｕｎ（杜国君）（ＮｏｒｉｈｅａｓｉＩｎｓｔｉｔｕｔｅｏｆＨｅａｖｙＭａｃｈｉｎｅｒｙ,Ｑｉｑｉｈａｒ）（ＲｅｃｅｉｖｅｄＪａｎ．２,１９９２,...     

A general solution and the application of space axisymmetric problem in piezoelectric material

ＡＧＥＮＥＲＡＬＳＯＬＵＴＩＯＮＡＮＤＴＨＥＡＰＰＬＩＣＡＴＩＯＮＯＦＳＰＡＣＥＡＸＩＳＹＭＭＥＴＲＩＣＰＲＯＢＬＥＭＩＮＰＩＥＺＯＥＬＥＣＴＲＩＣＭＡＴＥＲＩＡＬＷａｎｇＺｉ－ｋｕｎｇ（王子昆）ＣｈｅｎＧｅｎｇ－ｃｈａｏ（陈庚超）（ＸｉａｎＪｉａｏ...     

LARGE DEFLECTION PROBLEM OF THIN ORTHOTROPIC CIRCULAR PLATE ON ELASTIC FOUNDATION WITH VARIABLE THICKNESS UNDER UNIFORM PRESSURE

ＬＡＲＧＥＤＥＦＬＥＣＴＩＯＮＰＲＯＢＬＥＭＯＦＴＨＩＮＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＯＮＥＬＡＳＴＩＣＦＯＵＮＤＡＴＩＯＮＷＩＴＨＶＡＲＩＡＢＬＥＴＨＩＣＫＮＥＳＳＵＮＤＥＲＵＮＩＦＯＲＭＰＲＥＳＳＵＲＥ（王嘉新）（刘杰）ＬＡＲＧ...     

Bending problems of non-homogeneous cylindrical orthotropic circular plate

ＢＥＮＤＩＮＧＰＲＯＢＬＥＭＳＯＦＮＯＮ－ＨＯＭＯＧＥＮＥＯＵＳＣＹＬＩＮＤＲＩＣＡＬＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＱｉｎＳｈｅｎｇ－ｌｉ（秦圣立）（ＱｕｆｕＮｏｒｍａｌＵｎｉｃｅｒｓｉｔｙ,Ｑｕｆｕ,Ｓｈａｎｄｏｎｇ）（Ｒｅｃｅｉ...     

THE ANALYTICAL STUDY ON THE LASER INDUCED REVERSE－PLUGGING EFFECT BY USING THE CLASSICAL ELASTIC PLATE THEORY（Ⅰ）－TEMPERATURE FIELDS

ＴＨＥＡＮＡＬＹＴＩＣＡＬＳＴＵＤＹＯＮＴＨＥＬＡＳＥＲＩＮＤＵＣＥＤＲＥＶＥＲＳＥ－ＰＬＵＧＧＩＮＧＥＦＦＥＣＴＢＹＵＳＩＮＧＴＨＥＣＬＡＳＳＩＣＡＬＥＬＡＳＴＩＣＰＬＡＴＥＴＨＥＯＲＹ（Ⅰ）－ＴＥＭＰＥＲＡＴＵＲＥＦＩＥＬＤＳＺｈｏｕＹｉｃｈｕｎ...     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

ＴＨＥＰＲＯＢＬＥＭＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＵＮＳＹＭＭＥＴＲＩＣＡＬ．ＢＥＮＤＩＮＧＦＯＲＣＹＬＩＮＤＲＩＣＡＬＬＹＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥ（ＩＩ）ＨｕａｎｇＪｉａｙｉｎ（黄家寅）;ＱｉｎＳｈｅｎｇｌｉ（秦圣立）;Ｘｉ...     

THE ANALYTICAL STUDY ON THE LASER INDUCED REVERSE－PLUGGING EFFECT BY USING THE CLASSICAL EIASTIC PLATE THEORY（I）─TEMPERATURE FIELDS

ＴＨＥＡＮＡＬＹＴＩＣＡＬＳＴＵＤＹＯＮＴＨＥＬＡＳＥＲＩＮＤＵＣＥＤＲＥＶＥＲＳＥ－ＰＬＵＧＧＩＮＧＥＦＦＥＣＴＢＹＵＳＩＮＧＴＨＥＣＬＡＳＳＩＣＡＬＥＩＡＳＴＩＣＰＬＡＴＥＴＨＥＯＲＹ（Ｉ）─ＴＥＭＰＥＲＡＴＵＲＥＦＩＥＬＤＳＺｈｏｕＹｉｃｈｕｎ...     

THE LAGRANGE DYNAMIC EQUATIONS OF MULTI－RIGIDBODY SYSTEMS WITH EXTERNAL SHOCKS

ＴＨＥＬＡＧＲＡＮＧＥＤＹＮＡＭＩＣＥＱＵＡＴＩＯＮＳＯＦＭＵＬＴＩ－ＲＩＧＩＤＢＯＤＹＳＹＳＴＥＭＳＷＩＴＨＥＸＴＥＲＮＡＬＳＨＯＣＫＳ￥ＺｈａｎｇＤｉｎｇｇｕｏ（章定国）（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏ...     

DOUBLE HIGH ORDER S－BREAKING BIFURCATION POINTS AND THEIR NUMERICAL DETERMINATION

ＤＯＵＢＬＥＨＩＧＨＯＲＤＥＲＳ－ＢＲＥＡＫＩＮＧＢＩＦＵＲＣＡＴＩＯＮＰＯＩＮＴＳＡＮＤＴＨＥＩＲＮＵＭＥＲＩＣＡＬＤＥＴＥＲＭＩＮＡＴＩＯＮ￥(杨忠华，叶瑞松)ＹａｎｇＺｈｏｎｇｈｕａ；（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｈａｎｇｈ...     

SPATIAL－TEMPORAL DISCRETE COORDINATION OF FEM AND DIRECT INTEGRAL METHOD FOR TRANSIENT DYNAMIC PROBLEMS

ＳＰＡＴＩＡＬ－ＴＥＭＰＯＲＡＬＤＩＳＣＲＥＴＥＣＯＯＲＤＩＮＡＴＩＯＮＯＦＦＥＭＡＮＤＤＩＲＥＣＴＩＮＴＥＧＲＡＬＭＥＴＨＯＤＦＯＲＴＲＡＮＳＩＥＮＴＤＹＮＡＭＩＣＰＲＯＢＬＥＭＳＷａｎｇＨｕａｉ－ｚｈｏｎｇ（王怀忠）（ＳｈａｎｇｈａｉＵｎｉｖｅｒ...     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

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.     

刚塑性广义变分不等原理及其在平面应变分析中的应用

首先利用Lagrangian乘子法，从势能角度出发构造了考虑摩擦效应这一能导致变分不等形式的广义能量泛函，把一般的有条件的变分原理化为无条件的变分原理唯一确定，得出了各Lagrangian乘子所代表的物理意义。建立了刚塑性理论中的Coulomb摩擦约束的广义变分不等原理。而后基于退化的摩擦约束广义变分等式原理，对长矩形板镦粗进行了塑性加工工步分析，所得结果与经典上限法结果相吻合。     

A method for establishing generalized variational principle

A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu ’s generalized variational principle and the Hu’s generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potenlial energy and the correct proofs of these two generaleed variational principles are given. It is also proved that this is wrong if one beleives that σ_ij, e_ij and ui are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained.     

分析力学初值问题的一种变分原理形式

明确了分析力学初值问题的控制方程,按照广义力和广义位移之间的对应关系,将 各控制方程卷乘上相应的虚量,代数相加,进而在 原空间中建立了分析力学初值问题的一种变分原理形式,即建立了分析力学初值问题的卷积 型变分原理和卷积型广义变分原理. 推导了分析力学初值问题卷积型变分原理和卷积型广义 变分原理的驻值条件. 在建立分析力学初值问题的一种变分原理形式的同时, 将变积方法推广为卷变积方法.     

Generalized H-η-accretive operators in Banach spaces with application to variational inclusions

In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.     

More generalized hybrid variational principle and corresponding finite element model

According to recent studies of the generalized variational principle by Professor Chien Weizang, the more generalized hybrid variational principle for finite element method is given, from which a new kind of the generalized hybrid element model is etablished.Using the thin plate bending element with varying thickness as an example, we compare various hybrid elements based on different generalized variational principles.     

Variational principles in elasticity with nonlinear stress-strain relation

Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1] (1979), [6] (1980), [2,3] (1983) and [4,5] (1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems.     

相空间中非保守系统的Herglotz广义变分原理及其Noether定理

与经典变分原理相比,基于由微分方程定义的作用量的Herglotz广义变分原理给出了非保守动力学系统的一个变分描述,它不仅能够描述所有采用经典变分原理能够描述的动力学过程,而且能够应用于经典变分原理不能适用的非保守或耗散系统.将Herglotz广义变分原理拓展到相空间,研究相空间中非保守力学系统的Herglotz广义变分原理与Noether定理及其逆定理.首先,提出相空间中Herglotz广义变分原理,给出相空间中非保守系统的变分描述,导出相应的Hamilton正则方程;其次,基于非等时变分与等时变分之间的关系,导出相空间中Hamilton-Herglotz作用量变分的两个基本公式;再次,给出Noether对称变换的定义和判据,提出并证明相空间中非保守系统基于Herglotz变分问题的Noether定理及其逆定理,揭示了相空间中力学系统的Noether对称性与守恒量之间的内在联系.在经典条件下,Herglotz广义变分原理退化为经典变分原理,与之相应的相空间中的Noether定理退化为经典Hamilton系统的Noether定理.文末以著名的Emden方程和平方阻尼振子为例说明上述方法和结果的有效性.     

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．