Finite Element Random Response Analysis of Cooling Tower

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Abstract
A finite element formulation and Gaussian quadrature procedure, using both the direct complex matrix inversion and the modal superposition methods, are presented for studying the stationary random response of shell structures, such as a cooling tower. The random distributed loads are assumed as stationary in time but can be nonhomogeneous in space. A 48 d.o.f. quadrilateral shell element with bi‐cubic Hermitian polynomial interpolation functions as displacement shape functions is adopted. 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. Cross‐spectral densities of displacement and stresses are first obtained for a simply supported cylindrical panel subjected to purely random load, using both the direct and modal superposition methods, which are in excellent agreement with an earlier analytical solution. Results for auto‐spectral densities, mean values, standard deviations, peak and gust response factors are obtained for a cooling tower subject to random wind loads at three different wind velocities, based on the quasi‐steady aerodynamic theory and Davenport's spectrum for wind fluctuations.