The Use of Trigonometric Series for the Study of Isotropic Beam Deflection

Abstract

The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined in advance, then it is considered an infinite sum of sinusoidal functions that are successively evaluated using sinusoidal trigonometric series if it is considered a periodic function, or using Fourier series if it is considered a non-periodic function. The method is examined by solving several beam problems. The results indicate that the method can be used with confidence for solving any bending beam problem.

Global Sensitivity Analysis of Structural Reliability Using Cliff Delta

“…In civil engineering, estimating the resistance R using nonlinear FEM calculations is very timeconsuming, and studies are limited by the number of computationally expensive Monte Carlo or LHS method runs required to accurately simulate real structural behavior, see e.g., [60,61,62,63]. In recent years, the role of mathematical models that offer quick analytical solutions has become increasingly significant due to their efficiency in providing rapid responses [64,65]. For each model, it is useful to utilize all realized simulations to estimate failure probability as efficiently as possible.…”