Then combined with reliability computation , the stochastic finite element method is used to establish the relationship between the load effect ( stress or force ) and basic stochastic variable dealing with statistical features of variables 再與可靠度理論相結(jié)合,考慮變量的隨機(jī)特性,通過隨機(jī)有限元法建立荷載效應(yīng)(如應(yīng)力、內(nèi)力等)與基本隨機(jī)變量之間的關(guān)系。
The equation of the structural limiting state can be expressed : z = r - s , thereinto r and s respectively are structural resistance and load response expressed with stochastic variables , we ca 結(jié)構(gòu)的極限狀態(tài)方程可以表示為: z = r ? s ,其中r和s分別為用隨機(jī)變量表示的結(jié)構(gòu)的抗力和荷載響應(yīng),通過極限狀態(tài)方程就可以得出結(jié)構(gòu)的失效概率,或者是用可靠指標(biāo)表示的結(jié)構(gòu)的可靠度。
For the uncertain character of material function , the intensity of spray concrete and concrete lining is uncertain too . it can describe quality character better by probability model and statistic parameter of stochastic variable 由于材料性能具有不確定性,噴混凝土和二次襯砌的強(qiáng)度亦同樣具有不確定性,一般用隨機(jī)變量的概率模型和統(tǒng)計(jì)參數(shù)來描述,能更好地描述其質(zhì)量特征。
This paper proved that in the optimal models with stochastic variables , if the parameter estimation and the optimal solution are separated , the optimal result in practice is bound to be less than that in theory 摘要證明了在涉及隨機(jī)變量的最優(yōu)化模型中,如果將參數(shù)估計(jì)和最優(yōu)化求解過程分離,實(shí)際得到的最優(yōu)化結(jié)果必然低于理論值,即參數(shù)估計(jì)在最優(yōu)化模型中總是造成低效的結(jié)果。
A class of strong convergence theorem for an arbitrarily adapted stochastic sequence without the non - decrease condition was established by using the truncation method of stochastic variables and the stop time 摘要引入了隨機(jī)變量的截尾和停時(shí)的概念,在定理?xiàng)l件及其證明過程中適當(dāng)?shù)囟x隨機(jī)變量的截尾和停時(shí),并通過定義鞅差序列和利用鞅差序列的收斂定理,得到了一類關(guān)于任意隨機(jī)適應(yīng)序列的強(qiáng)收斂定理。
A necessary and sufficient condition with ergodic of 1 - order probability distribution function of stochastic process ( theorem 1 and corollary 1 ) and extended the general distribution theorem of stochastic variable under the case of weakly condition ( theorem2 ) are presented 摘要提出了隨機(jī)過程一階概率分布函數(shù)具有遍歷性的一個(gè)充分必要條件(定理1和推論1 ) ,并在較弱條件下,對(duì)一般的關(guān)于隨機(jī)變量函數(shù)分布定理作了進(jìn)一步的推廣(定理2 ) 。
Define a random route , which pass through all the grid node , on the condition of given n conditional datum , get a value on the first grid node from the conditional distribution of stochastic variable , add the new value into the conditional datum as a new conditional data . on the condition of current n + 1 conditional datum , get a new value from conditional distribution of stochastic variable on the next node again . then continue until all the nodes gets own value 定義一個(gè)經(jīng)過所有網(wǎng)格節(jié)點(diǎn)的隨機(jī)路徑,在給定n個(gè)條件數(shù)據(jù)的情況下,在第一個(gè)網(wǎng)格節(jié)點(diǎn)處從隨機(jī)變量的條件分布中抽取一個(gè)值,將這個(gè)新值加入到條件數(shù)據(jù)集中,在給定的n + 1個(gè)條件數(shù)據(jù)的情況下,在節(jié)點(diǎn)處從隨機(jī)變量的條件分布中抽取一個(gè)值,重新進(jìn)行,直到所有節(jié)點(diǎn)被模擬完為止。
It has shown by the uncertainty of the data of fatigue experimentation and the size deviation of machine accessory and structure component and the original defect of materials that all of the stress and intensity and the factors that affect them are stochastic variables , so we should deal with the problem of fatigue by the method of probability and statistics to making the engineering life deduced by fatigue intensity to be the reliable life under a certain probability 疲勞試驗(yàn)數(shù)據(jù)的離散性,零件和構(gòu)件加工允許的尺寸偏差,材料中分布的原始缺陷,以及受載零件危險(xiǎn)部位應(yīng)力響應(yīng)的分布特性等,都說明應(yīng)力和強(qiáng)度以及影響它們的因素都是隨機(jī)變量,它們有各自的分布形式,應(yīng)該用概率統(tǒng)計(jì)理論和方法來處理,才能使疲勞強(qiáng)度在工程中所確定的壽命,成為保證某一概率下的可靠壽命。
Based on the theory of stochastic finite element , the structural parameters of frame - shear structure including stiffness and mass and damping are simulated to be stochastic variables . by solving recurrence equation of stochastic finite element , the duration curve of mean value and standard deviation of seismic response can be obtained for every floor of frame - shear structure . an analysis is thus given to the effects of independent variation and simultaneous variation of structural parameters on the seismic dynamic response of frame - shear structure . as shown by the results , with regard to frame - shear structure , the effect of variation of strucural parameters on the change of mean value are chiefly the increase of standard deviation of response . variation of stiffness will cause the response of frame - shear structure to variate greatly ; variation of mass shows less effect ; and variation of damping shows insignificant effect . the effects of simultaneous variation of various structral parametres on seismic response are only slightly greater than the effect of stiffness variation alone 以隨機(jī)有限元理論為基礎(chǔ),將框剪結(jié)構(gòu)的剛度、質(zhì)量、阻尼等結(jié)構(gòu)參數(shù)為隨機(jī)變量.通過求解隨機(jī)有限元的遞推方程,得到框剪結(jié)構(gòu)各層的地震動(dòng)力響應(yīng)均值和標(biāo)準(zhǔn)差歷時(shí)曲線.分析結(jié)構(gòu)參數(shù)單獨(dú)變異,以及同時(shí)變異對(duì)框剪結(jié)構(gòu)地震響應(yīng)的影響.研究結(jié)果表明,對(duì)框剪結(jié)構(gòu)而言,結(jié)構(gòu)參數(shù)的變異對(duì)響應(yīng)的均值變化影響都不大,主要是增大響應(yīng)的標(biāo)準(zhǔn)差.剛度的變異性將引起框剪結(jié)構(gòu)的響應(yīng)發(fā)生大幅度變異,質(zhì)量的變異性影響稍小,阻尼的變異性影響不顯著.結(jié)構(gòu)各參數(shù)的同時(shí)變異,對(duì)框剪結(jié)構(gòu)地震響應(yīng)的影響,僅比剛度單獨(dú)變異的影響稍大