UZAWA TYPE ALGORITHM BASED ON DUAL MIXED VARIATIONAL FORMULATION

ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｔｈｅｓｏｌｕｔｉｏｎｏｆｔｈｅｅｌａｓｔｉｃｐｒｏｂｌｅｍ ,ｔｈｅｍｏｓｔｉｍｐｏｒｔａｎｔａｄｖａｎｔａｇｅｏｆｔｈｅｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｓｌｉｅｓｉｎｔｈｅｃｏｍｐｕｔｉｎｇｏｆｓｔｒｅｓｓａｎｄｄｉｓｐｌａｃｅｍｅｎｔａｎｄｓｏｏｎｓｉｍｕｌｔａｎｅｏｕｓｌｙ .Ｆｏｒｔｈｅｃｏｎｔａｃｔｐｒｏｂｌｅｍｉｎｅｌａｓｔｉｃｉｔｙ ,ａｎｅｗｄｕａｌｍｉｘｅｄｖａｒｉａｔｉｏｎａｌｆｏｒｍｕｌａｔｉｏｎａｎｄｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎ…     

THE AXISYMMETRIC MIXED BOUNDARY-VALUE PROBLEM OF THE VERTICAL VIBRATION OF A RIGID FOUNDATIONON SATURATED LAYERED SOIL SUBGRADE

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｅｌａｓｔｉｃｈａｌｆ＿ｓｐａｃｅｔｈｅｏｒｙｏｆｆｏｕｎｄａｔｉｏｎｖｉｂｒａｔｉｏｎａｎｄｔｈｅｓｔｕｄｙｏｆｓｏｉｌ＿ｓｔｒｕｃｔｕｒｅｉｎｔｅｒａｃｔｉｏｎｐｒｏｂｌｅｍｈａｖｅｂｅｅｎｔｈｅｓｕｂｊｅｃｔｏｆｉｎｔｅｎｓｉｖｅｒｅｓｅａｒｃｈｉｎｔｈｅｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ .ＳｉｎｃｅＬｕｃｏｅｔａｌ.[1]ｓｕｍｍａｒｉｚｅｄｔｈｅｖｉｂｒａｔｉｏｎｏｆａｃｉｒｃｕｌａｒｒｉｇｉｄｆｏｕｎｄａｔｉｏｎｒｅｓｔｉｎｇｏｎａｎｅｌａｓｔｉｃｈａｌｆ＿ｓ…     

STABILITY CRITERIA IN TERMS OF TWO MEASURES FOR DELAY DIFFERENTIAL EQUATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｗｅｋｎｏｗ ,ｉｎｔｈｅｉｎｖｅｓｔｉｇａｔｉｏｎｏｆｔｈｅｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｆｏｒｎｏｎｌｉｎｅａｒｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ,ｔｈｅｍｅｔｈｏｄｏｆｖａｒｉａｔｉｏｎｏｆｐａｒａｍｅｔｅｒｓｉｓａｎｅｆｆｅｃｔｉｖｅｔｏｏｌｉｎｔｈｅｃａｓｅｔｈａｔｔｈｅｃｏｒｒｅｓｐｏｎｄｉｎｇｕｎｐｅｒｔｕｒｂｅｄｔｅｒｍｓａｒｅｌｉｎｅａｒｏｒｏｆｃｅｒｔａｉｎｓｍｏｏｔｈｎｅｓｓｔｈｏｕｇｈｔｈｅｙａｒｅｎｏｎｌｉｎｅａｒ.Ｏｎｔｈｅ…     

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional three-dimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.     

DYNAMIC BEHAVIOR OF TWO PARALLEL SYMMETRY CRACKS IN MAGNETO-ELECTRO-ELASTIC COMPOSITES UNDER HARMONIC ANTI-PLANE WAVES

The dynamic behavior of two parallel symmetry cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied by Schmidt method. By using the Fourier transform, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surface were expanded in a series of Jacobi polynomials. The relations among the electric filed, the magnetic flux and the stress field were obtained. From the results, it can be obtained that the singular stresses in piezoelectric/piezomagnetic materials carry the same forms as those in a general elastic material for the dynamic anti-plane shear fracture problem. The shielding effect of two parallel cracks was also discussed.     

FLOQUET STABILITY ANALYSIS OF TWO-LAYER FLOWS IN VERTICAL PIPE WITH PERIODIC FLUCTUATION

Based on linear stability theory, parametric resonance phenomenon of a liquid-gas cylindrical flow in a vertical pipe with periodic fluctuation was discussed with the help of Floquet theory and Chebyshev spectral collocation method. The effects of different physical parameters were investigated on the properties of parametric resonance and the stability characteristics of flow field.     

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.     

Analysis of nonlinear dynamic stability of liquid-converying pipes

Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different. Foundation items: the National Natural Science Foundation of China (50079007); the Hydraulic Science Foundation of China Hydraulic Ministry (SZ9830); the Natural Science Foundation of Yunnan Provicce (98E003G) Biographies: ZHANG Li-xiang (1959−) HUANG Wen-hu (1926−)     

Biology,Buddhism, and AI: Care as the Driver of Intelligence

Intelligence is a central feature of human beings’ primary and interpersonal experience. Understanding how intelligence originated and scaled during evolution is a key challenge for modern biology. Some of the most important approaches to understanding intelligence are the ongoing efforts to build new intelligences in computer science (AI) and bioengineering. However, progress has been stymied by a lack of multidisciplinary consensus on what is central about intelligence regardless of the details of its material composition or origin (evolved vs. engineered). We show that Buddhist concepts offer a unique perspective and facilitate a consilience of biology, cognitive science, and computer science toward understanding intelligence in truly diverse embodiments. In coming decades, chimeric and bioengineering technologies will produce a wide variety of novel beings that look nothing like familiar natural life forms; how shall we gauge their moral responsibility and our own moral obligations toward them, without the familiar touchstones of standard evolved forms as comparison? Such decisions cannot be based on what the agent is made of or how much design vs. natural evolution was involved in their origin. We propose that the scope of our potential relationship with, and so also our moral duty toward, any being can be considered in the light of Care—a robust, practical, and dynamic lynchpin that formalizes the concepts of goal-directedness, stress, and the scaling of intelligence; it provides a rubric that, unlike other current concepts, is likely to not only survive but thrive in the coming advances of AI and bioengineering. We review relevant concepts in basal cognition and Buddhist thought, focusing on the size of an agent’s goal space (its cognitive light cone) as an invariant that tightly links intelligence and compassion. Implications range across interpersonal psychology, regenerative medicine, and machine learning. The Bodhisattva’s vow (“for the sake of all sentient life, I shall achieve awakening”) is a practical design principle for advancing intelligence in our novel creations and in ourselves.