Calculation of Bending Stiffness and its First Derivatives Related to Optimization of a Steel-Reinforced Concrete Cross Section

Abstract

This article focuses on creating an algorithm for the calculation of bending stiffness of an arbitrary polygonal cross section, including the first derivatives of this stiffness with respect to all the input variables. The coordinates of vertices of the cross section are also among these input variables. The algorithm is in principle based on dividing the cross section into trapezoids, calculating zero, first and second moment of area of these trapezoids, including partial derivatives with respect to all the input variables, and then compiling all these partial results into a final output. A DLL library based on this algorithm is then used in an optimization solver based on a reduced‑gradient method. This solver is put into practice to optimize the given cross section characteristics according to prescribed criteria.

Simulation of repair and technical maintenance processes for power-generating equipment components at chemical factories

“…These ideas are implemented in an equation in the Matlab system [13]. The scientific paper [14] is devoted to the creation of algorithm for calculating the bending stiffness of arbitrary polygonal section, including the first derivatives of stiffness with respect to all input variables.…”

Stochastic Optimization of a Reinforced Concrete Elements Using Heuristic Algorithm

“…This paper aims to introduce an optimization algorithm, which works in two cycles. The internal cycle is deterministic and based on previous work (see [5,6]). The external cycle deals with probability and as mentioned it is heuristic, based on simulation and also on regression analysis.…”