# Vol 19, No 2 (2023)

**Year:**2023**Articles:**11**URL:**https://journals.rudn.ru/structural-mechanics/issue/view/1677**DOI:**https://doi.org/10.22363/1815-5235-2023-19-2

## Full Issue

## Analytical and numerical methods of analysis of structures

### Use of interpolation methods for modeling the stress-strain state of operated oil storage tanks

#### Abstract

The aim of the research is the comparison of two approaches for computer modeling of the stress-strain state of thin-walled shells of engineering structures, considering the imperfections of the geometric shapes arising due to their operation. The object of the study is the operated steel vertical cylindrical reservoir with imperfections of the geometric shape intended for storage of petroleum products. The first, so-called classical, approach provides geometric modeling of the surface of the tank's shell with the subsequent import of the geometric model into one of the systems of finite element analysis to calculate the stress-strain state of the structure and determine its technical condition, and the possibility of further operation. The geometric modeling of the shell surface with imperfections was performed using a two-dimensional interpolation method based on the 1st order smoothness outlines implemented in the point calculus. The calculation of the stress-strain state of the shell was carried out in the SCAD Office computer complex, taking into account geometric and structural non-linearity on the basis of the octahedral tangential stress theory. The second approach assumes modeling of an array of functions of vertical deflection of the tank wall by means of interpolation, solution of an array of differential equations of the elastic cylindrical shell under axisymmetric loading, improved by introduction of vertical deflection functions of the wall, followed by two-dimensional interpolation and analysis of the deformed state of the shell based on displacements arising in the tank wall from the hydrostatic load. As a result of the effective use of two-dimensional interpolation in the process of implementing the second approach, it was possible to achieve a significant increase in the speed of the numerical solution while maintaining sufficient accuracy for engineering calculations.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):119-129

### Numerical modeling of nonlinear deformation processes for shells of medium thickness

#### Abstract

When modeling a nonlinear isotropic eight-node finite element, the main kinematic and physical relationships are determined. In particular, isoparametric approximations of the geometry and an unknown displacement increment vector, covariant and contravariant components of basis vectors, metric tensors, strain tensors (Cauchy - Green and Almansi) and true Cauchy stresses in the initial and current configuration are introduced. Next, a variational equation is introduced in the stress rates in the actual configuration without taking into account body forces and the Seth material is considered, where the Almansi strain tensor is used as the finite strain tensor. Linearization of this variational equation, discretization of the obtained relations (stiffness matrix, matrix of geometric stiffness) is carried out. The resulting expressions are written as a system of linear algebraic equations. Several test cases are considered. The problem of bending a strip into a ring is presented. This problem is solved analytically, based on kinematic and physical relationships. Examples of nonlinear deformation of cylindrical and spherical shells are also shown. The method proposed in this paper for constructing a three-dimensional finite element of the nonlinear theory of elasticity, using the Seth material, makes it possible to obtain a special finite element, with which it is quite realistic to calculate the stress state of shells of medium thickness using a single-layer approximation in thickness. The obtained results of test cases demonstrate the operability of the proposed technique.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):130-148

### Consideration of damping in a continuous medium using the rod approximation by A.R. Rzhanitsyn

#### Abstract

The work is focused on creating a method for accounting of internal friction, which provides frequency independence, considers the dependence of internal friction on the level of the stress state, and is suitable for physically nonlinear tasks at large and small displacements. The authors consider an approximated method of accounting the damping in plates using the rod approximation according to A.R. Rzhanitsyn. An analysis of the discrete Rzhanitsyn medium with a square cell is given in terms of isotropy of its damping properties. The exact fulfillment of the isotropic damping properties is shown for the eight specific directions in the orientation of the deformations. The solution for a test example is given, where a rod oscillating in tension is calculated according to two computational schemes. One of these schemes is a real rod, the other is a rectangular plate experiencing uniaxial tension, and for its dynamic modeling, in turn, the discrete model by A.R. Rzhanitsyn is applied. The use of the same damping parameters for the real rod and rods in the Rzhanitsyn approximation leads to close damping. An approximate approach has been developed to account for internal friction during vibrations of a two-dimensional continuous medium, as well as a variant of clarifying the damping forces in the plate. A numerical example of damping modeling is given in the case of considering geometrically and physically nonlinear oscillations.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):149-161

### Models of nonlinear deformation of concrete in a triaxial stress state and their implementation in the PRINS computational complex

#### Abstract

Modern construction standards and regulations prescribe to carry out calculations of concrete and reinforced concrete structures in a nonlinear formulation with account of the real properties of concrete and reinforcement. However, the most of finite-element program complexes cannot perform such calculations in a nonlinear formulation with account of plastic deformations of concrete and reinforcement. To solve this problem, a methodology has been developed and a solid finite element adapted to the PRINS computing complex has been created, which made it possible to perform calculations of reinforced concrete structures considering their actual work. The aim of the study - development and implementation of a method for calculating reinforced concrete structures under conditions of a three-dimensional stress state, considering both brittle fracture and elastic-plastic deformation of concrete. A finite-element methodology, algorithm, and program for calculation of massive reinforced concrete structures with account of plastic deformations of concrete have been presented. The methodology is based on the modified Willam and Warnke strength criterion supplemented with the flow criterion. Two models of volumetric deformation of concrete have been regarded: the elastic model at brittle failure and the ideal elastoplastic model. An eight-node finite element with linear approximating functions of displacements implementing the mentioned deformation models is created. Verification calculations of a massive concrete structure in three-axial compression testify to the accuracy and convergence of the developed finite elements. The PRINS can be effectively used by engineers of designing and scientific organizations to solve a wide class of engineering problems related to calculations of building structures.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):162-177

## Analysis and design of building structures

### Strengthening of reinforced concrete structures by composite materials taking into consideration the carbonization of concrete

#### Abstract

One of the main causes for deterioration of reinforced concrete structures in modern construction is corrosion of reinforcement. Corrosion leads to decrease of adhesion between reinforcement and concrete, formation of cracks and destruction of the protective layer of concrete. All this reduces the load-bearing capacity of reinforced concrete structures. The structures of sludge reservoirs exposed to carbon dioxide were used as an object of the study. The characteristic defects and damages revealed by visual inspection were described. The verification calculation of the considered construction depending on the pH of the medium was performed on the basis of the results of technical inspection and study. The degree of carbon dioxide impact on the considered structures was determined by the phenolphthalein test method, which is based on the color change of acid-base indicator solution on the surface of concrete and reinforced concrete depending on the pH value of its medium. The phenolphthalein test revealed that pH of the medium is less than 8 for the depth more than the thickness of the concrete protective layer. A verification calculation of the considered structure was performed on the basis of the technical inspection results and the conducted research. According to the calculation results, a variant of beam reconstruction and strengthening using external reinforcement based on carbon fibers FibARM 230/150 was proposed. The reconstruction was carried out with account of the carbonized concrete layer.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):178-185

### Theory of short-term and long-term resistance of structures based on the principle of plastic fracture

#### Abstract

The authors analyze the theory used in many countries, containing two independent directions: 1) the theory of stability of rod systems, including flat frames; 2) the theory of calculation of structural elements from various materials. The main feature of these theories is the application of the principle of plastic fracture. The assumption about a plastic hinge, due to the inconsistency with the experimental data, is supplemented by the incorrect application of theories of infinite elastic deformations, as well as of infinite creep deformations, which are incompatible with this hinge. Using the rules of mathematics, the principles of mechanics and the results of reliable experiments, it has been revealed that the analyzed theory contains several theories for different applications that reject each other, including the erroneous ones.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):186-198

### Rational structural solutions for triangular trusses

#### Abstract

Wooden rafter structures have undoubted advantages, which determine their wide application. The object of the study is triangular rafter structures. The purpose of the research is to find the dependence of force values in the elements of the studied structure on the magnitude of its lifting boom. The calculation of a triangular truss using the Maxwell - Cremona diagram is presented. The efficiency of the proposed method was estimated on the basis of a study of the structure of a wooden truss of the “scissors” type. The following pattern has been established: the change in the coordinates of the points (abscissas) of the force diagram is inversely proportional to the change in f . It is determined the area of rational values of the lift (roof slope) at which the values of internal forces tend to a minimum. It was revealed that the values of force increments in the truss elements at each step increase from 27% to 2 times when the roof slope de-creases. Based on the graphical analysis of the obtained data the range of effective values of the roof slope at which the forces in the elements of the truss take minimum values was found. Using a graphic method of determining the forces, it is possible to check variants of the roof slope in the search for a rational solution of the “scissor” type truss structure. It follows that the proposed method contributes to the choice of the most economical structural solutions.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):199-209

## Geometrical investigations of middle surfaces of shells

### Surfaces with a main framework of three given curves which include one circle

#### Abstract

Superellipses are becoming more and more in demand in various branches of science and national economy due to their versatility. They found the most application in shipbuilding. Suggestions for the use of superellips in architecture and construction have appeared recently. The author proposes explicit and parametric equations of surfaces with a main framework of three predetermined superellips lying in three coordinate planes. These equations describe a large set of analytical shapes suitable for the formation middle surfaces of thin building shells. One of the superellipses is taken in a form of a circle. The shells can be designed on circular and rhombic plans, and also on plans in the shape of superellips of general type with convex and concave sides. All recommended surfaces are illustrated in 24 examples using computer graphics. A network of curvilinear non-orthogonal coordinates is generated on the surfaces using dimensionless independent parameters. The considered surfaces can become a part of the reserve of surfaces for further application in real structures and facilities.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):210-219

### Modern software features for shape optimization of shells

#### Abstract

Shape optimization, as one of the types of structural optimization problems, is an important process in the design of shells, since it contributes to the creation of a structure with fine performance characteristics, expansion of design variations and knowledge base to obtain high-quality results. To solve the problems associated with determining the shape and creating more advanced structures, software packages include a special optimization module, which can be based on one or more mathematical methods, the purpose of which is to provide the best solution in the shortest possible time. The research is focused on the process of shape optimization in three well-known universal software packages: Ansys Mechanical, COMSOL Multiphysics and Simulia Abaqus, as well as in Rhinoceros modeling software with a special visual Grasshopper plugin. The purpose of the study is to analyze the technology of shape optimization in four software packages and to compare them with each other in terms of the problem-solving process, user interface, the fullness of libraries, accessibility for educational purposes and system requirements for a computer. The authors specify and describe the characteristic features of each software package. It was found that all the software packages under consideration are equipped with great opportunities for shape optimization of structures and have a variety of functionality for solving this type of tasks. The development of optimization technology in calculation and modeling software packages will allow obtaining the most effective solutions in the process of designing shells of complex shapes.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):220-232

## Construction materials and products

### Effect of gelatin powder, almond shell, and recycled aggregates on chemical and mechanical properties of conventional concrete

#### Abstract

The objective of the research is to study the effect of different additives on the conventional concrete. In this term, three types of materials have been added to the concrete: gelatin powder as the binder, recycled aggregates, and almond shell as the fine and coarse aggregates. Several experiments have been made tо determine physical and mechanical properties, such as test for compressive and tensile strengths, for impact loading strength, durability test (water absorption) and deep penetration tests. Moreover, the microstructure results for the new type of concrete have been studied by means of scanning electron microscopy (SEM) and energy-dispersive x-ray spectroscopy (EDXS). The results show that when 70 kg of gelatin powder is added to 1 m3 of concrete, the concrete’s compressive strength and tensile strength are improved more than 22%; during impact loading the first and ultimate cracks are 11 and 129 by numbers, and the first and ultimate cracks’ strength is more than 223 and 2346 J respectively. The durability of sample from concrete with additional gelatin has been improved. SEM results illustrate that the weakness of almond shell concrete is related to cracks and voids between the cement matrix and almond shell. The voids of gelatin concrete are higher than that of conventional concrete. The conventional concrete has smooth crystals, and gelatin concrete has sharp and cubic crystals. EDXS results show that chemical content of these two types of concrete is different: conventional concrete contains silicon, while EDXS results show that chemical content of these two types of concrete is different: conventional concrete contains silicon, while gelatin concrete contains calcium and also C-S-H gel is generated in it.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):233-250

### Mechanical properties of fine-grained carbonate concretes with a complex additive, including fine limestone filler and superplasticizer

#### Abstract

The stress-strain properties of fine-grained carbonate concretes, despite the fact that they have proven themselves well in various types of construction, have not been studied to the same extent as the deformation and strength properties of traditional heavy concrete. The object of the study is to find ways to improve the physical and mechanical properties of fine-grained carbonate concretes by using a mineral complex additive consisting of a finely dispersed limestone filler and a superplasticizer in the composition of concrete. The relationship between the ultimate values of strength characteristics (cubic strength) and crack-initiating stresses and deformations for conventional and carbonate fine-grained concrete compositions were analyzed. Through the damping mechanism of the cracking process in concrete, due to the joint work of a superplasticizer and a carbonate microdisperse filler a composition of carbonate fine-grained concrete was obtained, capable of resisting static and dynamic loads, with a dense structure and increased reliability and durability.

**Structural Mechanics of Engineering Constructions and Buildings**. 2023;19(2):251-257