In this paper, by using a combination of finite element analysis and a hybrid random convex model, a new numerical algorithm named hybrid perturbation Lagrange method (HPLM) is presented to address an uncertain static response problem of structures with a mixture of random and convex variables. The random variables are used to treat the uncertain parameters with sufficient statistical information, whereas the convex variables are used to describe the uncertain parameters with limited information. The expectation and variance of the random convex responses can be calculated effectively based on the matrix perturbation theory. Then, the interval bounds of these probabilistic characters of the structural responses can be obtained by means of the first-order Taylor series and the Lagrange multiplier method. Numerical results illustrate the feasibility and effectiveness of the proposed method to solve the static response problem of structures with hybrid or pure uncertain parameters.
Acta Mechanica – Springer Journals
Published: May 19, 2017
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