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首頁(yè)> 外文學(xué)位 >A new node-to-node approach to contact/impact problems for two dimensional elastic solids subject to finite deformation.
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A new node-to-node approach to contact/impact problems for two dimensional elastic solids subject to finite deformation.

機(jī)譯：一種新的節(jié)點(diǎn)到節(jié)點(diǎn)方法來解決二維彈性固體受到有限變形的接觸/碰撞問題。

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摘要

Contact analysis is an important branch of solid mechanics. Numerical simulation using the finite element method has become the dominant approach recently because of the high nonlinearity of contact problems. In the traditional Lagrangian description for solid mechanics, the numerical nodes are attached to the material particles, making it impossible to maintain node-to-node contact due to independent deformation. Various node-to-segment or segment-to-segment treatments are proposed to discretize the contact interface. But some issues still exist. Specifically, mesh distortion or element entanglement may be present if deformation is large.;A new node-to-node approach for 2D contact/impact problems subject to finite deformation is proposed in this dissertation to offer an alternative approach to these traditional methods, wherein node-to-node contact is maintained throughout the contact process. This method is based on the Arbitrary Lagrangian-Eulerian algorithm (ALE). One or both bodies in the two-body contact problem have an ALE mesh, which is independent of the material particles and has prescribed motion set to maintain node-to-node contact. The strategy of the ALE mesh motion has two steps: (1) to move nodes in the active set to maintain node-to-node contact (2) to smooth ALE mesh to improve mesh quality using the Laplacian or angle-based smoothing algorithm.;Problems of interest in this study are contact/impact problems wherein the implicit mid-point rule is used as the primary time stepping algorithm to find the solution incrementally. In order to conserve the system energy, the persistency condition is incorporated as the contact constraint. The augmented Lagrangian method is primarily used to apply contact constraints. Non-classical Coulomb friction laws are used where friction is present. Several quasi-static and impact examples are given to demonstrate the performance and validity of the new approach.
機(jī)譯：接觸分析是固體力學(xué)的重要分支。由于接觸問題的高度非線性，使用有限元方法進(jìn)行的數(shù)值模擬近來已成為主要方法。在傳統(tǒng)的拉格朗日固體力學(xué)描述中，數(shù)值節(jié)點(diǎn)附著在材料粒子上，由于獨(dú)立的變形，不可能保持節(jié)點(diǎn)間的接觸。提出了各種節(jié)點(diǎn)到段或段到段的處理來離散化接觸界面。但是仍然存在一些問題。具體來說，如果變形較大，則可能會(huì)出現(xiàn)網(wǎng)格變形或元素糾纏。本論文提出了一種用于二維接觸/碰撞問題的有限變形新的節(jié)點(diǎn)到節(jié)點(diǎn)方法，為這些傳統(tǒng)方法提供了一種替代方法，其中在整個(gè)聯(lián)系過程中保持節(jié)點(diǎn)到節(jié)點(diǎn)的聯(lián)系。該方法基于任意拉格朗日-歐拉算法（ALE）。兩體接觸問題中的一個(gè)或兩個(gè)物體都具有ALE網(wǎng)格，該網(wǎng)格與材料粒子無關(guān)，并具有規(guī)定的運(yùn)動(dòng)集以維持節(jié)點(diǎn)到節(jié)點(diǎn)的接觸。 ALE網(wǎng)格運(yùn)動(dòng)的策略包括兩個(gè)步驟：（1）移動(dòng)活動(dòng)集中的節(jié)點(diǎn)以保持節(jié)點(diǎn)到節(jié)點(diǎn)的接觸（2）使用Laplacian或基于角度的平滑算法來平滑ALE網(wǎng)格以提高網(wǎng)格質(zhì)量。 ；本研究中感興趣的問題是接觸/碰撞問題，其中隱式中點(diǎn)規(guī)則用作主要的時(shí)間步長(zhǎng)算法來逐步找到解。為了節(jié)省系統(tǒng)能量，將持久性條件合并為接觸約束。增強(qiáng)拉格朗日方法主要用于施加接觸約束。如果存在摩擦，則使用非經(jīng)典庫(kù)侖摩擦定律。給出了幾個(gè)準(zhǔn)靜態(tài)和影響示例，以證明新方法的性能和有效性。

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  • 作者

    Xu, Daqing.;

  • 作者單位

    University of Illinois at Urbana-Champaign.;

  • 授予單位 University of Illinois at Urbana-Champaign.;
  • 學(xué)科 Applied Mechanics.;Engineering Civil.
  • 學(xué)位 Ph.D.
  • 年度 2008
  • 頁(yè)碼 127 p.
  • 總頁(yè)數(shù) 127
  • 原文格式 PDF
  • 正文語(yǔ)種 eng
  • 中圖分類 應(yīng)用力學(xué);建筑科學(xué);
  • 關(guān)鍵詞

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