Transcription of G. P. Nikishkov
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I NTRODUCTION TO THE F INITE. E LEMENT M ETHOD. G. P. Nikishkov 2004 lecture Notes. University of Aizu, Aizu-Wakamatsu 965-8580, Japan 2. Updated 2004-01-19. Contents 1 Introduction 5. What is the finite element method .. 5. How the FEM works .. 5. Formulation of finite element equations .. 6. Galerkin method .. 6. Variational formulation .. 8. 2 Finite Element Equations for Heat Transfer 11. Problem Statement .. 11. Finite element discretization of heat transfer equations .. 12. Different Type Problems .. 13. 3 FEM for Solid Mechanics Problems 15. Problem statement .. 15. Finite element equations .. 16. Assembly of the global equation system .. 18. 4 Finite Elements 21. Two-dimensional triangular element .. 21. Two-dimensional isoparametric elements .. 22. Shape functions .. 22. Strain-displacement matrix .. 23. Element properties .. 24. Integration in quadrilateral elements .. 25. Calculation of strains and stresses .. 26. Three-dimensional isoparametric elements.
2004 Lecture Notes. University of Aizu, Aizu-Wakamatsu 965-8580, Japan niki@u-aizu.ac.jp. 2 Updated 2004-01-19. Contents ... one dimensional bar with cross-sectional areaA made of material with the elasticity modulus E and subjected to a distributed load b and a concentrated load R at its right end as shown in Fig 1.3.
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