In the finite element method, one of the restrictions on the approximating functions is relaxed . 在有限單元方法中,放開了定近似函數(shù)的限制。
When adding an entropy function as regularizing term to the lagrangian function , we obtain a smooth approximate function for m ( x ) , which turns out to be the exponential penalty function 當(dāng)將熵函數(shù)作為正則項(xiàng)加到拉格朗日函數(shù)上,我們得到了逐點(diǎn)逼近于m ( x )的光滑函數(shù)。經(jīng)證明,該函數(shù)即為指數(shù)罰函數(shù)。
By constructing approximate functions and using prior estimate and conversion of variable , it is proved that the inverse problem has weak solution for given initial value , boundary value and the oil output 通過變量和函數(shù)變換,作逼近函數(shù)和估計(jì)等方法,證明了對給定的初邊值和石油產(chǎn)量,此反問題存在弱解。
Ph linearization method is employed to solve a nonlinear reynolds equation for a steady state and micro - scale flow field , and the approximate function expressions of gas dynamic pressure and velocity in the spiral groove are obtained 摘要應(yīng)用ph線性化方法、迭代法,近似求解了螺旋槽內(nèi)穩(wěn)態(tài)微尺度流動場的非線性雷諾方程,求得了氣體動壓和速度分布的解析解。
2 . for the problem with size , stress and displacement constraints , the stress constraint is transformed into movable lower bounds of sizes , the displacement constraint is transformed into an approximate function which explicitly includes design variables by using mohr integral theory . a mathematical programming model of the optimization problem is set up . the dual programming of the model is approached into a quadratic programming model 2 .對于尺寸、應(yīng)力和位移約束的問題,將應(yīng)力約束化為動態(tài)下限,用單位虛荷載方法將位移約束近似顯式化,構(gòu)造優(yōu)化問題的數(shù)學(xué)規(guī)劃模型,將其對偶規(guī)劃處理為二次規(guī)劃問題,采用lemke算法進(jìn)行求解,得到滿足尺寸、應(yīng)力和位移約束條件的截面最優(yōu)解。