DETERMINISTIC AND NON-DETERMINISTIC RESPONSE ANALYSIS OF COMPLEX SHELLS (FINITE ELEMENT, RANDOM VIBRATIONS, WIND LOADS)
Abstract
Finite element analysis capabilities are developed for performing deterministic and non-deterministic responses of complex thin shells. A set of shell elements is adopted, modified or extended to study the seismic and wind responses of column-supported cooling towers. The elements are formulated intending to achieve optimum finite element modeling of the column-supported cooling towers according to the distributions of dominating bending and membrane stresses, and intending to model the vulnerable shell-column region using discrete column elements and quadrilateral shell elements. The set includes: a 16 d.o.f. column element; a 48 d.o.f. doubly-curved quadrilateral general shell element; a 42 d.o.f. doubly-curved general membrane transition element; a 21 d.o.f. and a 39 d.o.f. doubly-curved triangular membrane filler element; and a 28 d.o.f. doubly-curved quadrilateral membrane element. Examples are illustrated to evaluate a single type, combined types and the whole set of elements. For the deterministic responses, both the modal superposition and the time integration methods are used and for the non-deterministic responses both frequency domain analysis and the time analysis methods are used. For the frequency-domain analysis, a finite element formulation and Gaussian quadrature procedure, using both the direct complex matrix inversion and the modal superposition methods, are presented. The random distributed loads are assumed as stationary in time but can be nonhomogeneous in space. The shape functions are used to form the matrix of cross-spectral densities of the generalized nodal forces for distributed loads. The shape functions are also used to interpolate the response quantities at an arbitrary pair of points located within two different elements. Results are obtained for a simply supported cylindrical panel under purely random loads and for a cooling tower subjected to random wind loads at three different wind velocities, based on the quasi-steady aerodynamic theory and Davenport's spectrum for wind fluctuations. Random wind response analysis of a cooling tower is also performed using Monte-Carlo simulation approach. Five different wind simulation models are then tested, based on quasi-steady aerodynamics and ARIMA models derived from measured data, all with different correlation assumptions in the meridional and circumferential directions. Assumption of ergodicity is made to obtain the response statistics. For the most realistic wind loading, the frequency domain results are also obtained to compare with the time domain results. Favorable agreement is found.
Degree
Ph.D.
Subject Area
Aerospace materials
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