復刊 非線形有限要素法の基礎と応用(電子書籍版)

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発行日： 2020-11-30
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ISBN： 9784621305676
電子書籍版： 2020-11-30 （電子書籍版）
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1995年12月に刊行された同名書籍の待望の復刊。有限要素法が固体・構造解析の実用に供されるようになって久しいが、高度の非線形問題も、最近の解析手法の発展とコンピュータの高速化により、研究レベルから実用レベルへと近付きつつある。本書は、その内容をほぼ非線形問題に絞り、有限要素解析の基礎から応用までをつとめて詳しく、かつ具体的に紹介したものである。数理・物理的な側面と実用的な側面を併せ持つ魅力ある学問分野である非線形有限要素法の面白さ、奥深さを味わっていただきたい。

目次

  • 表紙
  • 序文
  • 目次
  • 1. 連続体力学の基礎
  • 1.1 テンソル
  • 1.2 変形
  • 1.3 歪, 歪速度
  • 1.4 応力, 応力速度
  • 1.5 構成式
  • 1.6 境界値問題と仮想仕事の原理
  • 2. 幾何学的非線形有限要素解析の枠組み
  • 2.1 2章以後の諸記号について
  • 2.2 仮想仕事式の増分分解と離散化
  • 2.3 大変形トラスの接線剛性と内力の誘導例
  • 3. アイソパラメトリック要素
  • 3.1 アイソパラメトリック要素の基礎
  • 3.2 接線剛性マトリックスおよび等価節点力ベクトル
  • 3.3 外力ベクトル
  • 3.4 質量マトリックス
  • 3.5 数値積分
  • 3.6 要素の選択
  • 3.7 埋込み座標系を用いた幾何学的非線形有限要素法定式化
  • 4. 混合型有限要素法
  • 4.1 混合変分原理
  • 4.2 非圧縮超弾性ソリッド要素の定式化
  • 4.3 構造要素 ( 梁, 板 / シェル要素 ) における混合法定式化
  • 4.4 離散化 inf - sup 条件
  • 5. 非線形方程式の解析手法
  • 5.1 静的解析手法
  • 5.2 動的解析手法
  • 6. 弾塑性解析
  • 6.1 弾塑性解析の基礎
  • 6.2 consistent 接線剛性マトリックス
  • 6.3 有限変形弾塑性解析
  • 7. 座屈解析
  • 7.1 座屈解析のための準備 ( トラス構造物の解析 )
  • 7.2 有限要素座屈解析の基礎式 ( その定義, 分類および判定 )
  • 7.3 有限要素座屈解析
  • 8. 接触解析
  • 8.1 摩擦のない大変形接触問題
  • 8.2 摩擦のある接触問題への拡張
  • 9. ALE 有限要素流体解析
  • 9.1 ALE 法の概念と基礎式
  • 9.2 Navier - Stokes 方程式の ALE 表記
  • 9.3 ALE 有限要素メッシュの制御
  • 9.4 離散化
  • 9.5 Predictor Multicorrector Algorithm
  • 9.6 解析例
  • 10. 感度解析
  • 10.1 負荷経路非依存型静的問題
  • 10.2 負荷経路依存型静的問題
  • 10.3 動的問題
  • 10.4 座屈問題
  • 10.5 接触問題
  • 参考文献
  • 索引
  • 奥付

この書籍の参考文献

参考文献のリンクは、リンク先の都合等により正しく表示されない場合がありますので、あらかじめご了承下さい。

本参考文献は電子書籍掲載内容を元にしております。

1. 連続体力学の基礎

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3. アイソパラメトリック要素

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4. 混合型有限要素法

P.191 掲載の参考文献
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5. 非線形方程式の解析手法

P.247 掲載の参考文献
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6. 弾塑性解析

P.273 掲載の参考文献
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7. 座屈解析

P.299 掲載の参考文献
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8. 接触解析

P.323 掲載の参考文献
[1] Bathe, K.-J. and Chaudhary, A. B., A Solution Method for Planar and Axisymmetric Contact Problems, Int. J. for Num. Meth. in Eng., Vol. 21, 1985, pp. 65-88.
 
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[4] 陳献, 森昌彦, 久田俊明, 野口裕久, 大変形弾塑性無摩擦接触問題の感度解析, 日本機械学会論文集 (A編), Vol.61, No. 589, 1995, pp. 2100-2107.
 
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9. ALE 有限要素流体解析

P.341 掲載の参考文献
[1] Baaijens, F. P. T., An U-ALE Formulation of 3-D Unsteady Viscoelastic Flow, Int. J. for Num. Meth. in Eng., Vol. 36, 1993, pp. 1115-1143.
 
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[6] Huerta. A., Progress in Arbitrary Lagrangian-Eulerian Analysis of Fluid and Solid Problems, Trans. SMiRT-12, Vol. B, 1993, pp. 1-12.
 
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10. 感度解析

P.361 掲載の参考文献
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