Speaker
Description
The main aim is to study natural vibrations of the Kirchhoff-Love elastic plates by various probabilistic extensions of the Boundary Element Method. Uncertainty quantification is provided for various material and geometrical parameters including especially a plate thickness [1,2]. They are traditionally considered as Gaussian due to the Maximum Entropy Principle, nevertheless the methodology presented allows for other probability distributions as well. The Response Function Method using polynomial and spline functions enables for numerical recovery of analytical representation of structural responses versus the given input uncertainty source. Then, the probabilistic moments of these responses are determined using three concurrent probabilistic methods, namely semi-analytical direct integration method, Monte-Carlo simulation statistical estimation as well as Taylor-series based perturbation method [1,2]. Numerical efficiency of this approach, especially of the first method, strongly depends upon an application of the computer algebra system enabling for analytical derivation of all probability integrals, which frequently have complex forms. Additionally, a relative entropy quantification is applied here [3] to check probabilistic distance in-between some input and output probability distributions. It may have some engineering importance in the reliability analysis [4], where limit functions are specific cases of such distances. This apparatus would serve also for traditional and probabilistic sensitivity analysis, where the first two gradients with respect to all plate parameters are inherent in the Taylor expansion of the perturbation-based method. Verification and discussion of probabilistic sensitivity would be discussed thanks to the fact that all moments and distances are parametrized in addition to the input statistical scattering. Finally, let us note that some extension of this approach towards the BEM formulation using the so-called double collocation point would be also demonstrated.
Literatrure
[1] Guminiak M., Kamiński M. On semi-analytical Stochastic Boundary Element Method and its application to eigenproblem of thin elastic plate immersed into a fluid. Engineering Analysis with Boundary Elements. 2022; 134: 219–230.
[2] Kamiński M. On iterative scheme in determination of the probabilistic moments of the structural response in the Stochastic perturbation-based Finite Element Method. International Journal for Numerical Methods in Engineering. 2015; 104(11):1038–1060.
[3] Bhattacharyya A. On a measure of divergence between two multinomial populations. Indian J. Stat. 7:401–406, 1946.
[4] Xiang Y, Liu Y. Application of inverse first-order reliability method for probabilistic fatigue life prediction. Probabilistic Engineering Mechanics. 2011; 26(2): 148–156.
