应用数学和力学

1993 Vol. 14, No. 1

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Pansystems Philosophy, Pansystems Mathematics(PPPM) and Applications to APTEM: Affairology, Physics, Technology: Medicine and Strategics(Ⅰ)

Wu Xue-mou

1993, 14(1): 1-8.

Abstract(1943) PDF(868)

Abstract:
A new type of philosophy and mathematics from the pansytems view isintroduced here, including the 7 philosophic theories(7PT) and related mathematic researches. Many second/third philosophies are developed within pansvstems framework and related applications to APTMS.

KKM Technique and Its Applications

Zhang Shi-sheng, Ma Yi-hai

1993, 14(1): 9-18.

Abstract(2773) PDF(467)

Abstract:
In this paper, the Knaster-Kitrattnvski-Maiurkiewic: technique(KKM technique, in short) is presented. By using this technique a new alternative theorem ami a new coincidence theorem are estahlished. The results obtained in this paper unify and generalize the corresponding results in the recent works^{[2,10,11,15,16]}.

Hamiltonian System and Simpletic Geometry in Mechanics of Materials(Ⅲ)——Flexure and Free Vibration of Plates

Ouyang Hua-jiang, Zhong Wan-xie

1993, 14(1): 19-23.

Abstract(2771) PDF(520)

Abstract:
The methodology presented in Part I is employed to deal with flexure and free vibration of anisotropic plates.

Anisotropic Plastic Fields at a Rapidly Propagating Plane-Stress Crack-Tip

Lin Bai-song

1993, 14(1): 25-38.

Abstract(1949) PDF(467)

Abstract:
Under the condition that all the stress components at a crack-tip are the functions of θonly, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z.

An Approximate Analytical Solution of the Laminar Boundary Layer Equations

Yuan Yi-wu

1993, 14(1): 39-40.

Abstract(2140) PDF(697)

Abstract:
Using the pressure gradient as the new variable instead of. the ordinary longitudinal coordinate x, Liu transformed the ordinary laminar boundary equations into a new form. On this base Liu obtained the frictional stress factor by using the graphical method.In this paper the same variable replacement as in [1] is used and an approximate analytical solution of the laminar boundary layer equations by the series method is obtained. The author also obtains a formula of frictional stress factor. For the case of the main function without the term of constant, the author makes a further simplification. The error of the frictional stress factor obtained by the author is still less than 10%, compared with that of [1].

Infinite Spline Boundary Element Method and Its Application to Structure-Foundation Interaction

Wang You-cheng, Wang Zhang-hu

1993, 14(1): 51-58.

Abstract(1788) PDF(501)

Abstract:
In view of the infinity behaviors of 3-D Kelvin solution, we constructed an infinite spline boundary element which has fine precision in the analysis of the half space foundation subjected to uniform pressure on the circular domain. We also analysed a square plate resting on elastic half space foundation. The results indicate that this model not only fits for the coupled analysis of foundation and structures but also has the advantage of fewer degrees of freedom and fine precision.

Existence and Stability of Common Fixed Points for Systems of Mappings

Shao Yong-heng

1993, 14(1): 59-68.

Abstract(1687) PDF(508)

Abstract:
In this paper, we establish some common fixed point theorems and stability theorems of the sets of common fixed points for the systems of set-valued and single-valued nonlinear contractive type mappings in a finite Cartesian product of metric spaces.

Generalized Multivariate Ridge Regression Estimate and Criteria Q(c)for Choosing Matrix K

Chen Shi-ji, Zeng Zhi-bin

1993, 14(1): 69-78.

Abstract(1929) PDF(575)

Abstract:
When multicollinearity is present in a set of the regression variables, the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper, generalized ridge estimate β^*(K) of the regression coefficient β=vec(B) is considered in multivaiale linear regression model. The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K. Moreover, it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses. In order to overcome these weaknesses, a new family of criteria Q(c) is adpoted which includes the criterion MSE and criterion LS as its special case. The good properties of the criteria Q(c) are proved and discussed from theoretical point of view. The statistical meaning of the scale c is explained and the methods of determining c are also given.

The Strain Energy Density Ratio Criterion for Predicting Cracking Direction in Composite Materials

Zhang Shuang-yin, Cai Liang-wu

1993, 14(1): 79-87.

Abstract(2243) PDF(515)

Abstract:
The strain energy density ratio criterion for predicting cracking direction in composite materials is proposed. The Tsai-Hill criterion and Norris criterion of composite materials are extended to predict the cracking direction in composites. The three criteria are used to analyse the crack propagation problem of the unidirectional fibre composite sheet with various fibre directions. The predicted results are compared with those of the existing normal stress ratio criterion and strain energy density criterion.

The Asymptotic Stability of the Linear Discrete Large Scale Systems

Hu Chao-yuang

1993, 14(1): 89-94.

Abstract(2089) PDF(492)

Abstract:
In this paper, we directly use the tirear norm Liapunov function to investigate the stability of the linear discrete large-scale systems and obtain some criteria for the asymptotic stability of such a system.