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Elements Clasiffication Each element is characterized by the following: Family Degrees of freedom Number of nodes:Order of interpolation function (Shape function) Order of geometric description Formulation Integration Family The element families most commonly used in a stress analysis 23

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Degrees of freedom The fundamental variables calculated during the analysis Stress/displacement simulation : Translations and rotation at each node Heat transfer simulation : Temperatures at each node 1 Translation in direction 1 2 Translation in direction 2 3 Translation in direction 3 4 Rotation about the 1-axis 5 Rotation about the 2-axis 6 Rotation about the 3-axis 7 Warping in open-section beam elements 8 Acoustic pressure, pore pressure, or hydrostatic fluid pressure 9 Electric potential 10 Temperature List of some degrees of freedom in Abaqus 24

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Number of nodesorder of interpolation Displacements, rotations, temperatures, and the other degrees of freedom are calculated only at the nodes of the element. At any other point in the element, the displacements are obtained by interpolating from the nodal displacements. Usually the interpolation order is determined by the number of nodes used in the element Abaqus/Standard offers a wide selection of both linear and quadratic elements. Abaqus/Explicit offers only linear elements, with the exception of the quadratic beam and modified tetrahedron and triangle elements. 25

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Order of geometric description 27

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Formulation Mathematical theory used to define the element's behavior Lagrangian or material description of behavior: Material remains associated with the element throughout the analysis. Material cannot flow across element boundaries. Eulerian or spatial description: Elements are fixed in space as the material flows through them. Eulerian methods are used commonly in fluid mechanics. 28

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Bar Element or Truss Element 29

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Beam Element The cross-sectional dimensions of the solid are much smaller than in the axial (x) directions External forces are applied in the transverse (z) direction. Deflection of the beam is a function of x only. Euler–Bernoulli assumption for thin beam: The plane cross-sections that are normal to the undeformed, centroidal axis, remain plane and normal to the deformed axis after bending deformation. We hence have 32

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The middle plane of a rectangular shell element. 41

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43 Coil Spring Analysis:

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