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1、Analysis of Three Dimensional Problems1Analysis of Three Dimensional ProblemsJOINTS For realistic analysis of certain 3D problems (空空间问题间问题)， like joints(接头接头), thick short beams(短短粗梁粗梁), thick pressure vessels (厚壁压力容器厚壁压力容器) and so on, we have to apply 3 - D elements. Thick Pressure Vessel2Analysis
2、 of Three Dimensional ProblemsFE Model for Short Thick Beam and Thick Cylinder3Analysis of Three Dimensional Problems4Analysis of Three Dimensional Problems5.1 Convergence Considerations(收敛性考虑收敛性考虑) 5Analysis of Three Dimensional Problems6Analysis of Three Dimensional Problems7Analysis of Three Dime
3、nsional Problems8Analysis of Three Dimensional ProblemsCompleteness Condition(完备条件完备条件)(提供单元刚体位移提供单元刚体位移)9Analysis of Three Dimensional ProblemsCompleteness Condition(完备条件完备条件)（提供单元中的常应变）（提供单元中的常应变）10Analysis of Three Dimensional ProblemsCompatibility Condition(协调条件协调条件)11Analysis of Three Dimension
4、al ProblemsCompatibility Condition(协调条件协调条件)(位移模式在单元内要连续并使相邻单元间的位移必须协调。位移模式在单元内要连续并使相邻单元间的位移必须协调。)12Analysis of Three Dimensional ProblemsCompleteness Elements(完备单元完备单元): Elements satisfying completeness condition Conformable Elements(协调单元或保续单元协调单元或保续单元): Elements satisfying compatibility condition1
5、3Analysis of Three Dimensional ProblemsFig.5.1 Deflection of a beamElement Convergence Criteria 14Analysis of Three Dimensional Problems15Analysis of Three Dimensional ProblemsDisplacement Function:16Analysis of Three Dimensional ProblemsFor beam elements, it is required that not only the vertical d
6、isplacement but also its first derivative must be continuous across the element boundaries. 17Analysis of Three Dimensional Problems18Analysis of Three Dimensional Problems- Specific Notation for the degree of Compatibility19Analysis of Three Dimensional Problems20Analysis of Three Dimensional Problems21Analysis of Three Dimensional Problems22Analysis of Three Dimensional Problems23Analysis of Three Dimensional Problems24Analysis of Three Dimensional Problems25
