[數] 有限元法；[數] 有限單元法
Stress of Al motorcycle wheel under the service condition was analyzed with finite element method (FEM).
用有限元法對服役狀态的摩托車鋁合金輪毂進行了應力分析。
The irregular distribution of the wave load along the erect riser makes the computation of equivalent wave nodal force difficult when applying Finite Element Method to analyze risers strength.
波浪荷載沿垂直立管的分布是不規則的，這對工程中用有限元法分析立管強度進行等效波浪結點力的計算帶來困難。
By using finite element method, the deformations of flat membrane mirror have been calculated.
運用有限元法對不同工況下平面薄膜反射鏡的變形進行了計算。
The influence is stu***d in this paper with nonlinear finite element method, as an example, for a high arch dam in design.
采用非線性有限單元法，以設計中的某高拱壩為例，分析建基面強度對壩體應力和變形的影響。
Then, the article derives finite element analysis equilibrium equation and element rigidity matrix in use of nonlinear finite element method.
然後運用非線性有限單元法推導了空間鉸接杆單元的剛度矩陣和平衡方程。
A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method.
本文結合有限元法和攝動法給出了一個确定薄闆在二重特征值處分支方向的方法。
In this paper, temperature and stress field on the bottom had been simulated using finite element method.
本文運用有限單元法，對鋼包底的溫度場和應力場進行了數值模拟。
The paper brings the conception of seepage force and use finite element method to analyze rock slope stability under rainfall, based on unsaturated earth drained shear strength theory.
本文以非飽和土抗剪強度理論為基礎，引入了滲透力的概念，利用有限單元法進行了降雨條件下岩質邊坡穩定性的分析。
The time domain finite difference and the finite element method are more convenient.
有限差分法和有限單元法在時間域裡更為方便。
Through the simplification of intensity with the finite element method of data. simulation and discuss both the difference.
經由簡化光強度搭配有限元素法所得到的數據，模拟并讨論兩者間的差異。
Using the finite element method to analyze the mixing chamber, the temperature distribution as well as the change situation.
利用有限元法對混煉過程中密煉室、膠料的溫度分布以及變化情況進行了分析。
The flow field and thermal environment of gap in solid rocket nozzle were simulated by finite element method.
用有限元素法數值模拟了固體火箭發動機噴管内縫隙的流場和熱環境。
By comparison, we calculate the same problem by finite element method.
作為比較，我們用有限元法計算了同一問題。
The calculated result is consistent with that by finite element method and transfer matrix method.
與“有限元法”和“傳遞矩陣法”的計算結果進行了對比，結果基本一緻。
The above-mentioned methods are combined to optimize the field of the breaker, and the calculation results are compared with the results calculated by finite element method.
本文将上述方法結合起來對斷路器的電場進行優化計算。并将計算結果與有限元法的計算結果進行了分析比較。
This article mainly introduces some similarities and differences between finite volume method and finite element method.
本文主要介紹有限體積法和有限元法之間的一些相同點和不同點。
It combines the merit of the finite element method with that of the finite difference method.
它可以吸收有限元法和有限差分法的一些重要思想與技巧。
The process can be simulated by finite element method theoretically, but reasonable result requires very small meshes.
有限元法理論上可對此進行仿真模拟，但合理的結果要求網格尺寸非常小。
Based on the finite element method, the maximum circumferential stress and stress intensity factor near the tip of mode I V-notch added coating are analyzed numerically.
基于有限元法，對添加塗層後的I型V形切口尖端附近的最大周向應力和應力強度因子進行了數值分析。
In addition, the coupling stiffness of the double rotors was successfully calculated with the finite element method.
文中還利用有限元法有效地解決了主軸雙轉子耦合剛度的計算問題。
We analysed the stress field and constrained force at attachment margin in human aortic valve by using finite element method.
本文用有限元法分析了人主動脈瓣在正常生理狀态下的應力場、附着緣的約束反力。
This paper analyzes the skid-mounted seawater purification equipment using classic mechanics and finite element method. On this basis, the system body is assessed for strength.
本文采用經典力學和有限元法對橇裝海水淨化設備進行了分析計算，在此基礎上對系統本體進行了強度評定。
First contact stress and deformation of parts which have normal shapes and ****** contacting status are calculated using Hertz formula and finite element method.
首先，運用了赫茲公式和有限元法對外形規則、接觸狀态簡單的零件進行接觸應力和接觸變形計算。
有限元方法（Finite Element Method, FEM）是一種用于求解複雜工程和物理問題的數值計算技術。其核心思想是将一個連續的、幾何形狀或邊界條件複雜的求解域（如機械零件、流體區域、電磁場空間等），離散化為有限數量、形狀簡單且相互連接的子區域（稱為“有限元”），然後在每個單元上構建近似的數學解，最後通過組合所有單元的解來逼近整個求解域的行為。
有限元方法的核心數學基礎是變分原理（如最小勢能原理、虛功原理）或加權殘值法（如伽遼金法）。它将描述物理現象的偏微分方程（控制方程）轉化為一個等價的積分形式，然後通過離散化求解該積分問題。例如，在結構力學中，基于最小勢能原理，FEM求解的最終方程形式通常為： $$ mathbf{K} mathbf{u} = mathbf{F} $$ 其中：
有限元方法（Finite Element Method, FEM）是一種廣泛應用于工程和物理學領域的數值分析技術，主要用于求解複雜的微分方程問題。其核心思想是将連續的求解區域離散化為有限個簡單幾何形狀的小單元（如三角形、四邊形或四面體），再通過數學方法構建近似解。以下是其關鍵要點：
以一維泊松方程為例： $$ -frac{du}{dx} = f(x) quad (0 < x < 1) $$ 通過伽遼金法離散後，單元剛度矩陣可表示為： $$ Ke = int{x_i}^{x_j} frac{dphi_i}{dx} frac{dphi_j}{dx} dx $$ 其中$phi_i$為形函數。
若需進一步了解具體算法或軟件實現，可結合實際案例深入探讨。
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