Static and dynamic analysis of axisymmetric structures using harmonic solid ring finite element modeling

Static, free and forced vibration analysis of axisymmetric structures under non-axisymmetric loadings such as wind and earthquake as well as axisymmetric loadings such as internal or external pressure were studied using harmonic solid ring finite elements. With the help of harmonic analysis physically three dimensional problems can be reduced to two dimensional problems by expressing non-axisymmetric loading in the form of Fourier series. The complete solution for the problem is obtained by superimposing a reasonable number of solutions for load components. 4-noded (Ring4) and 9-noded (Ring9) solid quadrilateral ring elements were used for the finite element analysis. A computer program for the purpose was coded in Matlab and verified solving several benchmark problems. During verification process these elements were compared with each other for accuracy, shear and volumetric locking. Ring9 seemed to be free of locking problems whereas Ring4 suffered from locking.After verification process a cooling tower was analyzed quasi-statically under wind loadings described in accordance with TS 498 and Eurocode and dynamically under Düzce earthquake using Ring9. It was realized that the circumferential distribution of wind pressure influenced the displacements and stresses significantly. Additionally, Fourier series coefficients of wind loadings indicate that the significant portion of the loading will cause shell or beam like deformations. Finally, the influence of height, thickness and curvature on the free vibration and seismic response of cooling towers were examined with a parametric study. It was recognized that the period of vibration tended to decrease approximately linearly with increasing curvature, but for high curvatures this trend reversed. Likewise, the variations in the fundamental period of vibration with shell thickness and height were approximately linear. As well, remarkable changes in stresses were noticed for cooling towers with different wall thickness and curvature in seismic analysis.