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23. 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

24. 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 List of some degrees of freedom in Abaqus 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

25. Number of nodes—order 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.

27. Order of geometric description

28. 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 .

29. Bar Element or Truss Element

32. 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

41. The middle plane of a rectangular shell element.

43. Coil Spring Analysis: