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ChaPter 6




                             sTATic AnAlysis using


                                 VolumE ElEmEnTs








                      6.1   tUtorial 7: statiC analysis Using
                            volUme elements: ComPonent design


                      In this tutorial, the  analysis of an  open-ended cylinder with internal
                      pressure is presented. The unknown to be found is the stresses in a thick
                      open-ended steel cylinder (shown) with an internal pressure (such as a
                      pipe discharging to the atmosphere).
                          Material properties: Young’s modulus: E = 30 × 106 psi, Poisson’s
                      ratio: ν = 0.3
                          Geometry: Internal radius: r  = 5 in, external radius: r  = 11 in, length:
                                                                    o
                                                i
                      arbitrary, for segment of a long, open-ended cylinder
                          Loading: Internal pressure: p = 1,000 psi.
                          Constraints:  uz = 0 on a radial  surface  parallel  to the  x-y plane,
                      ux = 0 on a radial surface parallel to y-z plane, uy = 0 on top/bottom
                      surface (prevent rigid body motion in y-direction)




                                                                    Y

                                                                          X






                                                                       5 in


                                                                           11 in
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