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具有最佳超收敛阶的EEP法计算格式:Ⅲ数学证明 总被引:1,自引:0,他引:1
对一维C0问题的高次有限元后处理中超收敛计算的EEP(单元能量投影)法提出改进的最佳超收敛计算格式,即用m次单元对足够光滑问题的有限元解答,采用该格式计算的任一点的位移和应力都可以达到h2m阶的最佳超收敛结果。整个工作分为3个部分,分别给出算法公式、数值算例和数学证明。该文是系列工作的第三部分,对所提出的最佳的EEP超收敛格式给出数学证明。 相似文献
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该文对一维问题Ritz有限元后处理超收敛计算的EEP(单元能量投影)法简约格式给出误差估计的数学证明,即对足够光滑问题的(>1)次单元的有限元解答,采用EEP法简约格式计算得到的单元内任一点位移和应力(导数)超收敛解均可以达到的收敛阶,即位移比常规有限元解的收敛阶至少高一阶,而应力则至少高二阶。 相似文献
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二维有限元法(FEM)的超收敛计算,借助有限元线法(FEMOL)作为桥梁,分两步采用单元能量投影(EEP)法导出超收敛公式,初步形成“逐维离散、逐维恢复”的方案。然而这一思路直接应用于三维问题却遇到了困扰:一维问题的EEP解(位移和导数)均可达到相同的超收敛阶,而二维问题却难以做到。研究发现,为了得到三维问题的EEP超收敛位移,只需提供二维问题最低阶的超收敛位移即可。该文按此思路推导了非规则网格下三维六面体单元的EEP超收敛位移公式,给出了一个实施方案,并通过数值算例验证了此方案的有效性。 相似文献
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最近,袁驷等基于力学原理提出了一种一维有限元超收敛后处理计算格式,称为单元能量投影(EEP)法。大量数值例子显示:若真解充分光滑,对m次有限元解,EEP法后处理节点恢复导数具有h2m阶精度。首先利用限元超收敛理论中的一个基本估计式证明了线性元(m=1)节点恢复导数具有h2阶精度。另外,对EEP法高次元的内点计算公式提出了一点简化。 相似文献
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基于EEP (单元能量投影)超收敛计算的自适应有限元法,已对一系列问题取得成功,但其自适应特性尚缺乏相关研究。该文以二阶常微分方程为模型问题,同时考察基于EEP和SPR (超收敛分片恢复)超收敛解的自适应分析方法,与有限元最优网格进行了比较分析,进而提出反映自适应有限元收敛特性的估计式,并给出了自适应收敛率β的定义。该文给出的数值试验表明:采用m次单元,对于解答光滑的问题,SPR法与EEP法均可有效用于自适应求解,其位移可按最大模获得m+1的自适应收敛率;对于奇异因子为α(<1)的奇异问题,SPR法失效,而基于EEP法的自适应求解,其位移按最大模可获得m+α的自适应收敛率,远高于α的常规有限元收敛率。 相似文献
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Manufacturing defects in the membrane of MEMS (Micro-Electro-Mechanical-Systems) structures have a significant effect on the sensitivity and working range of the device. Thus, in optimizing the design of MEMS devices, it is essential that the effects of membrane defects (e.g., cracks) can be predicted in advance. Accordingly, this study proposes the detailed two-dimensional Infinite Element Method (IEM) formulation with Infinite Element (IE)-Finite Element (FE) coupling scheme for analyzing the out-of-plane vibration of isotropic MEMS membranes containing one or more tip cracks. In the proposed approach, a degenerative computation scheme is used to condense the multiple element layers of the IEM domain to a single layer with master nodes at the boundary only. The validity of the proposed algorithm is demonstrated by comparing the results obtained for the vibration of a rectangular membrane with the analytical solutions and the solutions obtained using the conventional Finite Element (FE) method, respectively. The validated IEM algorithm is then coupled with an FE scheme to analyze various cracked membrane vibration problems. The results show that the fundamental frequency of the membrane changes in accordance with the membrane thickness, but is unaffected by the number of cracks. However, it is shown that a change in the location of the cracks may cause a shift or rotation of the wave peaks of the structural mode shape. In general, the IEM algorithm presented in this paper provides a fast modeling, direct, and accurate tool to simulate the effects of cracks on the dynamic response of MEMS membranes. Furthermore, the algorithm can be easily integrated with experimental methods in order to test for the presence of cracks as part of the MEMS membrane quality control process. 相似文献
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Atomic force microscopy imaging of dipalmitoylphosphatidylcholine (DPPC)/dilauroylphosphatidylcholine (DLPC) monolayers deposited onto alkanethiol modified-gold surfaces by the Langmuir–Schaefer technique was used to investigate domain formation in a binary system where phase separation arises from a difference in the alkyl chain lengths of the lipids. We have established how the condensed domain structure (shape and size) in DPPC/DLPC monolayers depends on the surface pressure and lipid composition. The mixed monolayers exhibit a positive deviation from an ideal mixing behavior at surface pressures of 32 mN/m. Lateral compression to pressures greater than the liquid-expanded-to-liquid-condensed (LE-to-LC) phase transition pressure of the mixed monolayer (8–16 mN/m) induces extensive separation into condensed DPPC-rich domains and a fluid DLPC matrix. The condensed structures observed at a few milliNeutons per meter above the LE-to-LC transition pressure resemble those reported for pure DPPC monolayers in the LE/LC co-existence region. At a bilayer equivalence pressure of 32 mN/m and 20 °C, condensed domains exist between xDPPC 0.25 and 0.80, analogous to aqueous DPPC/DLPC dispersions. Compression from 32 to 40 mN/m results in either a striking distortion of the DPPC domain shape or a break-up of the microscopic DPPC domains into a network of nanoscopic islands (at higher DPPC mol fractions), possibly reflecting a critical mixing behavior. The results of this study provide a fundamental framework for understanding and controlling the formation of lateral domain structures in mixed phospholipid monolayers. 相似文献
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有限元后处理中超收敛计算的EEP(单元能量投影)法以及基于该法的自适应分析方法对线性ODE(常微分方程)问题的求解已经获得了全面成功,也推动了非线性ODE问题自适应求解的研究。经过研究,已经实现了一维有限元自适应分析技术从线性到非线性的跨越,该文意在对这方面的进展作一简要综述与报道。该文提出一种基于EEP法的一维非线性有限元自适应求解方法,其基本思想是通过线性化,将现有的线性问题自适应求解方法直接引入非线性问题求解,而无需单独建立非线性问题的超收敛计算公式和自适应算法,从而构成一个统一的、通用的非线性问题自适应求解算法。该文给出的数值算例表明所提出的算法高效、稳定、通用、可靠,解答可逐点按最大模度量满足用户给定的误差限,可作为先进高效的非线性ODE求解器的核心理论和算法。 相似文献