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The proofs rely on the NashMoser implicit function theory and variational methods.


In the quasistationary approximation, an analytical solution of the problem representable in the form of an implicit function is obtained.


Relation between an implicit function and solutions of a singularly perturbed equation


Implicit function theorem for cosymmetric equations


Converse implicit function theorem for dynamical systems with cosymmetry

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 To analyze the timehistory reliability of aseismatic structures, an algorithm based on the genetic simulated annealing and timehistory methods was proposed on the basis of the characteristic of structural performance functions for the timehistory reliability of aseismatic structures, i.e. they are implicit functions with strong nonlinearity. This algorithm can reflect the randomness of structural parameters and earthquake motions and the effects of an earthquake action and static loads. Furthermore, timehistory... To analyze the timehistory reliability of aseismatic structures, an algorithm based on the genetic simulated annealing and timehistory methods was proposed on the basis of the characteristic of structural performance functions for the timehistory reliability of aseismatic structures, i.e. they are implicit functions with strong nonlinearity. This algorithm can reflect the randomness of structural parameters and earthquake motions and the effects of an earthquake action and static loads. Furthermore, timehistory reliability index of aseismatic structures at any time in the process of an earthquake can be got by using the algorithm. As an example, the timehistory reliability of storydrift capacity for a threestory reinforced concrete (RC) frame respectively under frequent and strong earthquakes was analyzed using the algorithm and the Monte Carlo method, and the result shows the effectiveness of the algorithm.  针对抗震结构时程可靠度分析中功能函数为非线性程度较高的隐式函数的特点,将遗传模拟退火算法与时程分析法相结合,建立了抗震结构时程可靠度分析的遗传模拟退火算法.该算法可以充分考虑结构参数和地震动的双重随机性,可确定任意时刻结构的时程可靠指标.用此方法及MonteCarlo法分析了分别受大震和小震作用的三质点钢筋混凝土结构的时程可靠度,结果表明了该方法的有效性.  In order to set a strength capacity calculation method suitable to any section,analytical algorithm derived from classical teaching materials has been changed for numerical algorithm.Based on the characteristics of numerical calculation,division lines method is introduced,which is usually used in bridgeelectronic computation to calculate section geometry properties,and numerical algorithm on strength capacity calculation of concrete member is put forward.In the numerical algorithm,calculation formulas are expressed... In order to set a strength capacity calculation method suitable to any section,analytical algorithm derived from classical teaching materials has been changed for numerical algorithm.Based on the characteristics of numerical calculation,division lines method is introduced,which is usually used in bridgeelectronic computation to calculate section geometry properties,and numerical algorithm on strength capacity calculation of concrete member is put forward.In the numerical algorithm,calculation formulas are expressed in implicit function,with which calculation is uncorrelated with member section shape.The corresponding programs are expressed with UML model to testify the accuracy and practice of algorithm presented.The numerical algorithm is suitable to any shape of member sections in strength capacity calculation.  目的为建立适合于任意截面的正截面承载力计算方法,将原有的解析算法改为数值算法.方法根据数值计算的特点,引入桥梁电算中计算截面性质惯用的截线法,提出了混凝土构件正截面承载力的数值算法.结果数值算法在正截面承载力计算列式中,混凝土截面几何性质项表达为受压区高度的隐式函数,使得表达式与截面形式无关.结论与解析算法比较,数值算法计算流程简洁,适合程序实现,计算结果更为精确.  The formula for analyzing the slope stability based on the Sarma model was deduced and the iteration method for determining the implicit stability coefficient was studied.The finite element numerical simulation in classical response surface method was substituted by iterative calculation of implicit stability coefficient of slope in Sarma model.Sampling rule of random variables in iterative calculation method of implicit stability coefficient obeys sampling rules of response surface method.An idea of classical... The formula for analyzing the slope stability based on the Sarma model was deduced and the iteration method for determining the implicit stability coefficient was studied.The finite element numerical simulation in classical response surface method was substituted by iterative calculation of implicit stability coefficient of slope in Sarma model.Sampling rule of random variables in iterative calculation method of implicit stability coefficient obeys sampling rules of response surface method.An idea of classical response surface method was combined with Sarma model and a new response surface method of slope stability reliability degree analysis was established.The new method was applied to analyze the stability of a slope and the procedure and calculation result were compared with those of MonteCarlo method.It is found that the calculation efficiency of the proposed method is much higher and the accuracy of calculation result is acceptable.  推导了边坡Sarma力学模式稳定性分析的有关公式,揭示了其稳定性系数是隐式函数的特点,研究了该隐式稳定性系数的迭代计算方法。针对Sarma模式和经典响应面法的特点,将响应面中的有限元数值模拟以Sarma模式中隐含稳定性系数的迭代方法代替,而隐含稳定性系数迭代计算过程中随机变量的抽样则遵从响应面中的规则,将传统的响应面思路与Sarma模式结合起来,形成了一种新的边坡稳定可靠性响应面分析方法。最后采用此方法分析了某一边坡工程的稳定可靠性,并把分析过程与结果与蒙特卡洛模拟法计算结果进行对照,表明该方法计算效率较高,原理简单,精度满足要求。   << 更多相关文摘 
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