Data Structure and Error Estimation for an Adaptive p-Version Finite Element Method in 2-D and 3-D Solids
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The stress error indicator introduced is found to be more reliable and to converge faster than the error indicator measured in an energy norm called the residual method. The use of the stress error indicator results in approximately 20% fewer degrees of freedom than the residual method. Agreement of the calculated stress error values and the stress error indicator values confirms the convergence of final stresses to the analyst. The error order of the stress error estimate is postulated to be one order higher than the error order of the error estimate using the residual method. The mapping of a curved boundary element in the working coordinate system from a square-shape element in the natural coordinate system results in a significant improvement in the accuracy of stress results.
Numerical examples demonstrate that refinement using non-uniform p analysis is superior to uniform p analysis in the convergence rates of output stresses or related terms. Non-uniform p analysis uses approximately 50% to 80% less computational time than uniform p analysis in solving the selected stress concentration and stress intensity problems. More importantly, the non-uniform p refinement procedure scales the number of equations down by 1/2 to 3/4. Therefore, a small scale computer can be used to solve equation systems generated using high order p-elements. In the calculation of the stress intensity factor of a semi-elliptical surface crack in a finite-thickness plate, non-uniform p analysis used fewer degrees of freedom than a conventional h-type element analysis found in the literature.
- Doctoral Dissertations