Optimization of Rectangular Articulated Reinforced Concrete Smooth and Ribbed Slabs Using Resource Reduction Method

Abstract

The paper considers the optimization problem of hinged reinforced concrete rectangular smooth and ribbed slabs. The static calculation of the slabs has been performed while using the finite element method. The model is built from rectangular finite elements containing four nodes each and having twelve degrees of freedom.  The load is presented in the form of nodal vertical forces. To take into account the nonlinearity of the deformation of reinforced concrete, the finite elements are taken as inhomogeneous multilayer plates. The modulus of elasticity changed according to the hyperbolic dependence. The determination of the stress-strain state has been carried out by the iterative method. For optimization, a method has been used to reduce resources for strength, stiffness, and crack opening with gradient descent along the boundary of the allowable area. The cost of the material spent on the manufacture of the slab and the volume of concrete are taken as objective functions.  Restrictions on strength, stiffness and width of cracks are set. By scanning, the boundaries of the admissible search area for the optimal solution are set; the boundary of this region has a curvilinear outline. According to the results of the calculation, the trajectories of the search for optimal solution are obtained. Examples are given and optimal solutions are found for various starting points. It has been established that for the accepted conditions of the problem, the extreme points are located near  the boundaries of the admissible region. The speed of gradient descent and the location of the starting points do not significantly affect the results. Due to the fact that the objective function can have several minima, a method is proposed to search for a global minimum by preliminary scanning and analysis of extrema values. It is confirmed that the applied method ensures  the stability of the optimal solution.