Buckling of short tanks due to hurricanes

A survey of finite element models for the analysis of moderately thick shells

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 a...

Finite Element Random Response Analysis of Cooling Tower

Fluctuating wind pressure distribution around full-scale cooling towers

Intending to achieve optimum finite element modeling of column supported cooling towers for seismic response studies 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, a set of elements is adopted, modified or extended. The set includes: (1) A 16 d.o.f. column element; (2) a 48 d.o.f. doubly curved quadrilateral general shell element; (3) a 42 d.o.f. doubly curved general‐membrane transition element; (4) a 21 d.o.f. and 39 d.o.f. doubly curved triangular membrane filler elements; and (5) a 28 d.o.f. doubly curved quadrilateral membrane element. Examples are given to evaluate a single type, combined types, and the whole set of elements with results in good agreement with alternative solutions. These elements may be used for accurate and efficient free vibration analysis of column supported cooling towers. The modeling may be used in seismic response analysis of ...

Shell Elements for Cooling Tower Analysis

A series of open-type elements which are compatible with axisymmetric thin shell elements have been dervied. These elements allow the effects of intermediate openings and discrete support systems for rotational shells to be realistically modelled in the dynamic regime. Also, consistent load vectors for several common cases are derived.

The availablility of these elements in a public domain computer program enhances the possibility for modelling systems which are basically axisymmetric but which include intermediate or end supports using a rotational shell code.

Finite element discretization of open-type axisymmetric elements

The purpose of this study is to collect and interpret the results of full-scale wind-pressure measurements that are available for hyperbolic cooling towers and to determine the corresponding displacements and forces in the prototype tower through finite element analysis. In some cases the time intervals for which the pressures were recorded were too long to reflect any dynamic response and static analysis is sufficient. However, in two more recent studies a shorter time interval was used and a dynamic analysis was thought to be appropriate. The main emphasis of this paper was directed towards the elucidation of a time-history analysis method that will have value for the prediction of the structural response of prototype hyperbolic cooling towers due to the measured loadings with a view towards the eventual inclusion of nonlinearities. Also, some dynamic response parameters in the form of amplification and gust factors are calculated using limited ranges of the available time records and some simplifying assumptions necessitated by available resources.

Cooling Towers Using Measured Wind Data

Direct dynamic analysis of shells of revolution using high-precision finite elements☆

A geometrical stiffness matrix suitable for the harmonic analysis of a shell of revolution is derived in a form which may accommodate high-order inter-element comparison functions. Transverse shearing strains and nonlinear bending terms are included in the formulation. Condensation procedures which may significantly reduce the size of the resulting global matrices are described. The geometric stiffness matrix derived is incorporated into the formulation of two classes of problems, linear buckling and symmetrical incremental deformation, where the appropriate condensation techniques are developed.

Prodyot K. Basu

Papers

Finite element discretization of open-type axisymmetric elements

Cooling Towers Using Measured Wind Data

Direct dynamic analysis of shells of revolution using high-precision finite elements☆

Geometric Stiffness Matrices for the Finite Element Analysis of Rotational Shells