【文章內(nèi)容簡(jiǎn)介】 獨(dú)立的未知領(lǐng)域T(x，y)。4. 數(shù)值例子說(shuō)明我們的理論發(fā)展，在上一節(jié)中，通過(guò)數(shù)值例子。設(shè)k = 5W/m?C, Q = 10 W/m3 and H = 。表1:結(jié)果表表1給出了不同時(shí)段的邊界條件。第一裝置溫度欄的共同溫度為所有幾何分析模式(這不取決于插槽邊界條件及插槽幾何分析)。最后一欄是實(shí)際的裝置溫度所得的全功能模式(前幾何分析)，是列在這里比較前列的。在全部例子中，我們可以看到最后一欄則是介于第二和第三列。T Tdevice T對(duì)于絕緣插槽來(lái)說(shuō)，Dirichlet邊界條件指出，觀察到的各種預(yù)測(cè)為零。不同之處在于這個(gè)事實(shí):在第一個(gè)例子，一個(gè)零Neumann邊界條件的時(shí)段，導(dǎo)致一個(gè)自我平衡的特點(diǎn)，因此，其對(duì)裝置基本沒(méi)什么影響。另一方面，有Dirichlet邊界條件的插槽結(jié)果在一個(gè)非自我平衡的特點(diǎn)，其缺失可能導(dǎo)致器件溫度的大變化在。不過(guò)，固定非零槽溫度預(yù)測(cè)范圍為20度到0度。這可以歸因于插槽溫度接近于裝置的溫度，因此，將其刪除少了影響。的確，人們不難計(jì)算上限和下限的不同Dirichlet條件插槽。圖4說(shuō)明了變化的實(shí)際裝置的溫度和計(jì)算式。預(yù)測(cè)的上限和下限的實(shí)際溫度裝置表明理論是正確的。另外，跟預(yù)期結(jié)果一樣，限制槽溫度大約等于裝置的溫度。5. 快速分析設(shè)計(jì)的情景我們認(rèn)為對(duì)所提出的理論分析什么如果的設(shè)計(jì)方案，現(xiàn)在有著廣泛的影響。研究顯示設(shè)計(jì)如圖5，現(xiàn)在由兩個(gè)具有單一熱量能源的器件。如預(yù)期結(jié)果兩設(shè)備將不會(huì)有相同的平均溫度。由于其相對(duì)靠近熱源，該裝置的左邊將處在一個(gè)較高的溫度。圖4估計(jì)式versus插槽溫度圖圖5雙熱器座圖6正確特征可能性位置為了消除這種不平衡狀況，加上一個(gè)小孔，固定直徑。五個(gè)可能的位置見(jiàn)圖6。兩者的平均溫度在這兩個(gè)地區(qū)最低。強(qiáng)制進(jìn)行有限元分析每個(gè)配置。這是一個(gè)耗時(shí)的過(guò)程。另一種方法是把該孔作為一個(gè)特征，并研究其影響，作為后處理步驟。換言之，這是一個(gè)特殊的“幾何分析”例子，而擬議的方法同樣適用于這種情況。我們可以解決原始和伴隨矩陣的問(wèn)題，原來(lái)的配置(無(wú)孔)和使用的理論發(fā)展在前兩節(jié)學(xué)習(xí)效果加孔在每個(gè)位置是我們的目標(biāo)。目的是在平均溫度兩個(gè)裝置最大限度的差異。表2概括了利用這個(gè)理論和實(shí)際的價(jià)值。從上表可以看到，位置W是最佳地點(diǎn)，因?yàn)樗凶畹途殿A(yù)期目標(biāo)的功能。附錄II 外文文獻(xiàn)原文A formal theory for estimating defeaturing induced engineering analysis errorsSankara Hari Gopalakrishnan, Krishnan SureshDepartment of Mechanical Engineering, University of Wisconsin, Madison, WI 53706, United StatesReceived 13 January 2006。 accepted 30 September 2006AbstractDefeaturing is a popular CAD/CAE simplification technique that suppresses ‘small or irrelevant features’ within a CAD model to speedup downstream processes such as finite element analysis. Unfortunately, defeaturing inevitably leads to analysis errors that are not easily quantifiable within the current theoretical framework.In this paper, we provide a rigorous theory for swiftly puting such defeaturing induced engineering analysis errors. In particular, we focus on problems where the features being suppressed are cutouts of arbitrary shape and size within the body. The proposed theory exploits the adjoint formulation of boundary value problems to arrive at strict bounds on defeaturing induced analysis errors. The theory is illustrated through numerical examples.Keywords: Defeaturing。 Engineering analysis。 Error estimation。 CAD/CAE1. IntroductionMechanical artifacts typically contain numerous geometric features. However, not all features are critical during engineering analysis. Irrelevant features are often suppressed or ‘defeatured’, prior to analysis, leading to increased automation and putational speedup.For example, consider a brake rotor illustrated in Fig. 1(a). The rotor contains over 50 distinct ‘features’, but not all of these are relevant during, say, a thermal analysis. A defeatured brake rotor is illustrated in Fig. 1(b). While the finite element analysis of the fullfeatured model in Fig. 1(a) required over 150,000 degrees of freedom, the defeatured model in Fig. 1(b) required 25,000 DOF, leading to a significant putational speedup.Fig. 1. (a) A brake rotor and (b) its defeatured version.Besides an improvement in speed, there is usually an increased level of automation in that it is easier to automate finite element mesh generation of a defeatured ponent [1,2]. Memory requirements also decrease, while condition number of the discretized system improves。the latter plays an important role in iterative linear system solvers [3].Defeaturing, however, invariably results in an unknown ‘perturbation’ of the underlying field. The perturbation may be ‘small and localized’ or ‘large and spreadout’, depending on various factors. For example, in a thermal problem, suppose one deletes a feature。 the perturbation is localized provided: (1) the net heat flux on the boundary of the feature is zero, and (2) no new heat sources are created when the feature is suppressed。 see [4] for exceptions to these rules. Physical features that exhibit this property are called selfequilibrating [5]. Similarly results exist for structural problems.From a defeaturing perspective, such selfequilibrating features are not of concern if the features are far from the region of interest. However, one must be cautious if the features are close to the regions of interest.On the other hand, nonselfequilibrating features are of even higher concern. Their suppression can theoretically be felt everywhere within the system, and can thus pose a major challenge during analysis.Currently, there are no systematic procedures for estimating the potential impact of defeaturing in either of the above two cases. One must rely on engineering judgment and experience.In this paper, we develop a theory to estimate the impact of defeaturing on engineering analysis in an automated fashion. In particular, we focus on problems where the features being suppressed are cutouts of arbitrary shape and size within the body. Two mathematical concepts, namely adjoint formulation and monotonicity analysis, are bined into a unifying theory to address both selfequilibrating and nonselfequilibrating features. Numerical examples involving 2nd order scalar partial differential equations are provided to substantiate the theory.The remainder of the paper is organized as follows. In Section 2, we summarize prior work on defeaturing. In Section 3, we address defeaturing induced analysis errors, and discuss the proposed methodology. Results from numerical experiments are provided in Section 4. A byproduct of the proposed work on rapid design exploration is discussed in Section 5. Finally, conclusions and open issues are discussed in Section 6.2. Prior workThe defeaturing process can be categorized into three phases:Identification: what features should one suppress?Suppression: how does one suppress the feature in an automated and geometrically consistent manner?Analysis: what is the consequence of the suppression?The first phase has received extensive attention in the literature. For example, the size and relative location of a feature is often used as a metric in identification [2,6]. In addition, physically meani