Numerical Approach to Viscoelastic Analysis of Concrete Structures Using Equilibrium and FEM


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Title: Numerical Approach to Viscoelastic Analysis of Concrete Structures Using Equilibrium and FEM

Author(s): M. Sassone, D. Bigaran, and C. Casalegno

Publication: Special Publication

Volume: 246


Appears on pages(s): 21-36

Keywords: computational approach; creep; creep analysis; creep-induced structural effects; design tool; integral equations; structural analysis; viscoelasticity

Date: 9/1/2007

The formulation of creep problems in concrete structures, using linear viscoelasticity leads to integral equations that, generally, can not be solved in closed form. Methods of analysis developed to overcome this problem include the AAEM algebraic method, the method based on the theorems of linear viscoelasticity, or methods that assume simplified creep models. But when the structural problem is complex, involving non-homogeneities, construction steps, changes in static scheme, complex geometry, high prestressing, different materials, a computational approach based on the numerical solution of the systems of equations is required. Because of the form of the viscoelastic law, in which the present strain is a functional of the whole stress history, the stress history of the structure needs to be stored during calculation. Furthermore the numerical methods necessary to solve the integral equations are not immediately compatible with linear and non-linear finite element analysis and the substitution of integral equations with rate-type approximate laws, seemed to be necessary to allow the use of FEM solvers. In this paper a set of structural problems is described from the point of view of mathematical and computational formulation, and the general method based on coupling integral equations with the equilibrium method, and then with finite element method, is shown. The proposed formulation allows to perform the step-by-step analysis of any kind of viscoelastic structure, without regard to its complexity, and the computational load, in terms of memory requirements, appears to be no longer prohibitive.