Response of Uncertain Nonlinear Vibration Systems with 2D Matrix Functions

This paper extends the response of uncertain nonlinear vibration systems to vector-valued and matrix-valued functions. Random variables and system derivatives are conveniently arranged into 2D matrices. The method is based on a second order expansion of the governing equations and matrix calculus, Kronecker algebra are used in the mathematical development. The results derived are easily amenable to computational procedures.     

软土地基变形的混沌性与承载力识别

本文以混沌理论为基础, 分析了软土地基变形的混沌性态, 并采用映射函数f(x)=ax²+c来拟合软土地基的沉降-载荷曲线。根据映射函数的不动点, 对软土地基加固前后的承载力进行了识别, 并与按相对变形值确定的承载力进行了比较。     

层间剪切带粒度分形几何特征及工程地质意义

本文对分形几何方法表征土的粒度组成加以了补充, 并用它来描述和表征层间剪切带的粒度组成, 据此将其划分为五个类型。在此基础上较为深入地阐述了其工程地质意义, 并着重讨论了用它来识别层间剪切带所遭受的构造变形破坏程度、演化阶段问题等。     

智能岩石力学及其内容

本文针对岩石力学研究中目前存在的问题和信息时代的要求, 提出了21世纪的智能岩石力学的新思想和研究内容。它是综合现有各种行之有效的方法, 系统研究岩石工程问题, 提高岩石力学解决复杂问题的准确性。     

The use of possibility theory in the definition of fuzzy Pareto-optimality

Pareto-optimality conditions are crucial when dealing with classic multi-objective optimization problems. Extensions of these conditions to the fuzzy domain have been discussed and addressed in recent literature. This work presents a novel approach based on the definition of a fuzzily ordered set with a view to generating the necessary conditions for the Pareto-optimality of candidate solutions in the fuzzy domain. Making use of the conditions generated, one can characterize fuzzy efficient solutions by means of carefully chosen mono-objective problems and Karush-Kuhn-Tucker conditions to fuzzy non-dominated solutions. The uncertainties are inserted into the formulation of the studied fuzzy multi-objective optimization problem by means of fuzzy coefficients in the objective function. Some numerical examples are analytically solved to illustrate the efficiency of the proposed approach.     

Dynamic extension problems concerning asymmetrical mode III crack

By application of the method of complex variable function, dynamic extension problems on the surfaces of asymmetrical mode III crack subjected to shear loads were researched. Universal expressions of analytical solutions were attained by the approaches of self-similar functions. The problems considered can be facilely transformed into Riemann–Hilbert problems in terms of this technique, and analytical solutions of the stress, the displacement and dynamic stress intensity factor under the actions of unlike loads P and Pt located at the origin of the coordinates respectively, were acquired. In the light of corresponding material properties, the variable rule of dynamic stress intensity factor was depicted very well. By those solutions gained and superposition principle, the solutions of discretionarily intricate problems can be obtained.     

Fracture dynamics problem on mode I semi-infinite crack

By means of the theory of complex functions, fracture dynamics problems concerning mode I semi-infinite crack were studied. Analytical solutions of stress, displacement and dynamic stress intensity factor under the action of moving increasing loads Pt ³/x ³, Px ³/t ², respectively, are very easily obtained using the ways of self-similar functions. The correlative closed solutions are attained based on the Riemann–Hilbert problems.