Abstract
The problem of dynamic structural response dependent on random variations of design parameters is presented in the paper. A variational formulation of the FEM equations of motion and the probability distribution of time instant stochastic sensitivity are described. The suggested perturbation technique is completely second-order accurate, unlike in conventional approach. For instance, three different structural systems, excited by a Heaviside impact, are implemented and discussed. Numerical results for the first two probabilistic moments of displacement sensitivity gradients are obtained by the mode superposition method. Concluding remarks show that dynamic sensitivity analysis in the stochastic context better describes the real structural response and allows us to find the appropriate design point.
Highlights
Nowadays, buildings are often characterized by complicated forms and slenderness
An appropriate computational technique, such as the finite element method (FEM), which is implemented in most structural analysis computer codes [1,2,3] is needed
Dynamic sensitivity is worth analyzing especially for structures exposed to wind or sea waves
Summary
Buildings are often characterized by complicated forms and slenderness. an appropriate computational technique, such as the finite element method (FEM), which is implemented in most structural analysis computer codes [1,2,3] is needed. Sensitivity analysis can be carried out with respect to global [6,7] or local design variables [8,9,10,11,12]. E.g., the overall geometry, overall shape and topology Local design variables, such as cross-sectional area, element thickness, Young modulus, Poisson’s ratio, yield stress, mass and loading, are considered in this paper. It can be carried out by the spectral approach [13] or by the perturbational approach [14,15,16,17,18,19], where all the functions of random variables are expanded exponentially. A modified version of these perturbation schemes for dynamic sensitivity is presented, in which both probabilistic moments on output are second-order accurate, as for the static sensitivity given in [22]
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