Determining the Rheological Parameters of Polymers Using Artificial Neural Networks

Artificial neural networks have great prospects in solving the problems of predicting the properties of polymers. The purpose of this work was to study the possibility of using artificial neural networks to determine the rheological parameters of polymers from stress relaxation curves. The nonlinear Maxwell–Gurevich equation was used as the deformation law. The problem was solved in the MATLAB environment. The substantiation for the choice of the neural network input and output parameters was made. An algorithm for obtaining the data for neural network training was also proposed. Neural networks were trained on theoretical stress relaxation curves constructed with the Euler method. The value of the mean square error (MSE) was used as a criterion for the performance of the training. The constructed model of the artificial neural network was tested on the experimental relaxation curves of recycled polyvinyl chloride. The quality of the experimental curve approximation was quite good and was comparable with the standard methods for processing stress relaxation curves. Unlike the standard methods, when using artificial neural networks, no preliminary data smoothing was required. It is possible to use the proposed technique for processing not only relaxation curves, but also creep curves as well as processing creep tests not only in central tension, but also in bending, torsion and shear

Simplified Method for Determining Thermal Stresses during the Construction of Massive Monolithic Foundation Slabs

For massive monolithic foundation slabs, the problem of early cracking due to the intense heat release of concrete during the hardening process is relevant. The purpose of this article is to develop a simplified method for determining thermal stresses during the construction of massive monolithic foundation slabs. The proposed technique is based on the hypothesis of parabolic temperature distribution over the thickness of the structure at each moment of time. In addition to the parabolic distribution, the half-wave cosine distribution is also used. A hypothesis is also introduced about the same conditions of heat exchange with the environment on the lower and upper surfaces of the foundation. As a result, formulas are obtained that establish a direct relationship between thermal stresses and the temperature difference between the center and the surface. The solution to the test problem for the foundation slab is presented and compared with an alternative technique that does not use the hypothesis about the character of the temperature distribution over the thickness. Also, the inverse problem of determining the allowable temperature drop between the center and the surface of the structure is solved, at which the stresses on the upper surface at each moment of time will not exceed the tensile strength of concrete

Calculation of a three-layer plate by the finite element method taking into account the creep of the filler

In the article the derivation of the resolving equations for the calculation of a three-layer plate taking into account the creep of the middle layer by the finite element method is given. Rectangular finite elements are used. The problem reduces to a system of linear algebraic equations. An example of calculating a three-layer plate hinged on the contour and loaded with a uniformly distributed load is considered. A comparison of the results with the solution based on the finite difference method is presented

DETERMINATION OF CONCRETE RHEOLOGICAL PARAMETERS USING NONLINEAR OPTIMIZATION METHODS

The article proposes a method for processing concrete creep curves based on the nonlinear equation of V.M. Bondarenko. The experimental data of A.V. Yashin is used. The problem of finding rheological parameters and the nonlinearity function is posed as a nonlinear optimization problem. The objective function represents the sum of the squared deviations of the experimental values of the creep strain from the theoretical values for all creep curves for one concrete at different stress levels. The minimum of the objective function is found using the interior point method, the surrogate optimization method, the pattern search method, the genetic algorithm, and the particle swarm method. It has been established that the first of these methods has the greatest efficiency. The proposed approach provides high quality approximation of experimental curves at all stress levels. It is shown that for concrete the nonlinearity of creep deformations is more pronounced than the nonlinearity of instantaneous deformations, and the same function cannot be used to describe these two types of nonlinearity

Calculation of the rotation shells on axisymmetric load taking the creep into account

The paper presents a derivation of governing equations and the method of calculation of shells of revolution taking the creep into account. Moment theory is considered. The problem is reduced to a system of two second order differential equations. We also present an example of the calculation of reinforced concrete shell on the effect of its own weight. Viscoelastic model of hereditary concrete aging is used

Trihedral Lattice Towers Optimization with a Limitation on the Resonant Vortex Excitation Occurrence

Trihedral lattice towers are widely used as transmission line supports, wind turbine supports, cell towers, and floodlight towers. The aim of this work is to develop a technique for optimizing trihedral lattice supports to reduce their weight, taking into account the limitation on resonant vortex excitation. At the same time, restrictions are also introduced on the maximum stress, as well as the ultimate slenderness of the elements. Thus, with a minimum weight, the tower must meet all the requirements of the design codes. A lattice tower used as a floodlight mast is considered. The tower consists of two sections, the upper of which is of constant width, and the width of the lower section varies according to a linear law. The elements of the tower are made from pipes with an annular cross section. The sections’ widths and heights, the dimensions of elements’ cross-sections, and the number of panels are the variable parameters. The solution of the nonlinear optimization problem is implemented in MATLAB software. Internal forces in the tower and natural frequencies are calculated by the finite element method. The tower is subjected to the action of ice and wind loads, dead weight and the weight of the equipment. The wind load is considered as the sum of the average and pulsation components. To solve the problem of nonlinear optimization, the surrogate optimization method and the genetic algorithm are used. One of the serially used designs was chosen as the initial approximation. The design obtained as a result of optimization compared to the initial approximation has a mass more than two times less and at the same time satisfies all design requirements

Numerical-analytical calculation of a cylindrical reservoir taking into account creep

The article proposes a numerical-analytical solution to the problem of axisymmetric loading of the closed cylindrical shell, taking into account the creep of the material. The calculation is performed using the functions of A.N. Krylov in combination with the method of Euler and Runge-Kutta of the fourth order. Comparison with the solution using the finite difference method is presented

Calculation of beams with corrugated wall on the stability of a flat bending shape

The article presents the method of calculating beams with a corrugated wall on the stability of a flat bending shape. The problem reduces to a differential equation of fourth order with respect to the twist angle. The solution is performed numerically by the finite difference method. A comparison of the results with the software package LIRA is presented

Calculation of shallow polymer shell taking the creep into account

In this paper, we obtain the equations allowing the calculation of shallow shells taking the creep into account under an arbitrary law of relationship between creep deformations and stresses. We also consider the methodology of calculation of polymeric membranes, the material of which is subject to a nonlinear equation of Maxwell-Gurevich

The location of supports under the monolithic reinforced concrete slabs optimization

We consider the problem of finding the optimal location of point supports under a monolithic reinforced concrete floor slab, which provides the minimum of the objective function. The maximum deflection, potential strain energy, and reinforcement consumption are selected as the objective function. The load and plate configuration can be arbitrary. A restriction on the number of supports is introduced. The solution is performed using stochastic and deterministic optimization methods in combination with the finite element method to determine the objective functions An assessment of the proposed methods for a different number of supports n is made. Particular solutions are presented for n = 3,4,5.The optimal relations between the marginal and middle spans are established for buildings with a rectangular grid of columns with large n. It is shown that only the pitch of the columns of the marginal rows can act as a variable parameter, and the steps of the middle rows at the optimal arrangement are equal to each other. The developed methods were tested for the real object. It is established that of the three criteria used, the criterion of the minimum potential strain energy is preferable. It was also revealed that in most of the considered problems, the selected criteria give very close results. The plate thickness and material characteristics do not affect the optimal arrangement of columns