The Earthquake Engineering Online Archive

Dynamic stress analysis of axisymmetric structures under arbitrary loading

Ghosh, Sukumar; Wilson, Edward L.

UCB/EERC-69/10, Earthquake Engineering Research Center, University of California, Berkeley, 1969-09-01, 197 pages (525/G48/1969)

A finite element method is presented for the dynamic analysis of complex axisymmetric structures subjected to any arbitrary static or dynamic loading or base acceleration. The three-dimensional axisymmetric continuum is represented either as an axisymmetric thin shell or as a solid of revolution or as a combination of both. The axisymmetric shell is discretized as a series of frustrums of cones and the solid of revolution as triangular or quadrilateral "toroids" connected at their nodal point circles. Hamilton's variational principle is used to derive the equations of motion for this discrete structure. This leads to a mass matrix, stiffness matrix and load vectors that are all consistent with the assumed displacement field. But to minimize computer storage and execution time a diagonal mass matrix has been assumed in writing the computer program. These equations of motion are solved numerically through the time domain either by direct integration or by mode superposition. In both cases, a step-by-step integration procedure was used. For an earthquake analysis, the response spectrum technique may be used to obtain approximate values of the maximum response quantities if detailed time history of the response is not desired. A different approach of solving the set of integral equations of motion instead of the differential equations is indicated. This method of analysis is applied to various practical cases like nuclear reactor containment pressure vessel, response of tubes to moving pressure, and so forth. The formulation is also applied to investigate structure-foundation interaction effects. Some recommendations are made for the design of nuclear reactor pressure vessel under seismic forces which takes into account the interaction effects of the foundation.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-69-10.pdf (10 MB)