finite series solution 中文意思是什麼
finite series solution
解釋
可限級數解-
The elastic foundation model is considered as two - parameter elastic foundation model and its effect to moderate - thick plates are taken into account by a set of governing differential equations. united with hu hai - chang ’ s function, least squares collocation weighted residual method which uses b - spline function as trial function is put forward for solving the bending problems. compare with the results of finite element method of lines, spline finite strip method, accurate solution of series etc. it is proved that the method in this article has adequate accuracy and practical feasibility
本文採用瑞斯納中厚板理論求解彈性地基板，建立雙參數地基與中厚板相互作用的控制微分方程，結合胡海昌的解耦函數，運用雙五次b樣條函數作為試函數的離散型最小二乘加權殘值法分析了雙參數地基上的中厚板的彎曲問題，並將結果與有限元線法、有限條法、級數精確解等進行比較，證明本文方法具有足夠的精確性與實際的可行性。 -
Using the complex potential method in the plane theory of elasticity of an anisotropic body, a series solution to the stress field of a finite plate containing multiple cracks subjected to arbitrary loads is obtained by means of the faber series expansion, and the stress intensity factors at the crack tips are calculated based on the theories of fracture mechanics. equivalence yield stress is introduced in order to consider the effects of the plastic zones, with which the strip yield criteria is developed in the article so that the effects of structural size and the crack interactions on the stress distribution can be considered accurately. the effects of plate size, crack size and crack distributions on the stress intensity factors as well as the residual strength of the plate are studied detailedly
採用各向異性體平面彈性理論中的復勢方法，以faber級數為工具，得到了含多裂紋有限大板在任意載荷作用下應力場的級數解，並應用斷裂力學方法確定裂紋尖端的應力強度因子；引入當量屈服應力考慮裂尖塑性區的影響，提出基於帶屈服準則的剩餘強度分析模型，能夠充分考慮結構尺寸和裂紋之間相互作用對應力場的影響；通過數值計算詳細討論了結構尺寸和裂紋之間位置關系對應力強度因子和結構剩餘強度的影響規律，得到了一系列對工程應用具有實用價值的結論。 -
Using the complex potential method in the plane theory of elasticity of an anisotropic body, the series solution of finite anisotropic thin plate containing an elliptical inclusion is proposed with the help of faber series. a hybrid element with an elliptical inclusion for anisotropic materials is obtained by using the hybrid variable principle, and the element efficiency is verified by numerical examples. the state of the damage is modeled by an elliptical soft inclusion, and using the point stress criterion based on characteristic curve and yamada - sun etc. criteria, the prediction of the strength of a composite laminate with damage is set up
首先基於經典層板理論，將復合材料層板的彈性問題化歸為均勻各向異性板來求解；採用各向異性體平面彈性理論中的復勢方法，以faber級數為工具，給出了有限大含橢圓核各向異性板彈性問題的級數解形式；利用雜交變分原理，成功導出含橢圓核各向異性板雜交應力有限元，並用算例驗證了該單元的可行性和有效性；採用含剛度折減橢圓形彈性核的沖擊損傷模型，引入基於特徵曲線和yamada - sun破壞準則的點應力判據，建立了含損傷復合材料層板剩餘強度的分析方法；通過數值計算詳細討論了各種幾何參數對損傷層板應力分佈、剩餘強度的影響，得到了一系列對工程應用具有實用價值的結論。 -
However, the simulated annealing algorithm will expand too much time to estimate the values of objective function when applied to aerodynamics optimizations. the way to remedy this problem in this dissertation is by improving the efficiency of optimizer and the cfd - solver. our cfd - solver is base on the modification to the proper orthogonal decomposition ( pod ) method that can produce a finite series of basis functions or modes through the solution of snapshots
但對于氣動外形優化設計問題來說，由於評估需要解決的問題的目標函數值需要多次調用流場解算器，會導致用模擬退火演算法進行優化設計的計算工作量過大，因此需要我們對流場解算器和優化方法兩個方面進行研究以尋找此問題的解決辦法。 -
By series of linear and nonlinear mechanical analysis of the road pavement, and together with series of plate - bearing test and stress test in place, we elicit that marshall mix design method is not fitful for asphalt pavement design. the mechanical property between the asphalt layers is a problem of contact. the contact nonlinear finite element method can get more credible solution than linear finite element method or layer theory does
通過對試驗段路面的線性、非線性力學計算和現場承載板試驗得出：馬歇爾試驗不能如實反映實際路面的受力性能；瀝青混凝土結構層之間通過接觸傳遞應力，接觸非線性模型比層狀彈性體系模型更符合實際，接觸非線性有限元計算結果可以較準確地反映實際路面的力學特性。 -
And then moving coordinate system is used to transform the solving problem into a " conjunction " problem. finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of infinite algebraic equations
利用移動坐標法將問題轉化為「契合」問題進行求解，最終歸結為一組無窮代數方程組並用截斷有限項的方法進行計算。 -
Secondly, the two - dimensional hotibc was applied to the anisotropic coated bor. solutions for bistatic rcs based on a planar hotibc solution were compared to the mom solution or the mie series solution in isotropic case. accuracy and limitations of hotibc imposed by the finite radii of curvature on the bor such as sphere, and discontinues surface curvature such as cone - sphere were investigated
計算過程和結果與矩量法進行比較，討論了高階張量阻抗邊界條件在表面曲率半徑連續和不連續的三維目標上的應用精度和應用條件； 6 、給出多層介質塗敷平面、球面和半球面結構雷達吸波材料優化設計的統一表達式。
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