Applied Numerical Analysis in Civil Engineering

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 6107

Special Issue Editors


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Guest Editor
Soil Mechanics and Geotechnics Department, MSUCE, Moscow, Russia
Interests: finite element methods in geotechnical engineering

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Guest Editor
Department of Computer Science and Applied Mathematics, National Research Moscow State Civil Engineering University, Moscow, Russia
Interests: theory of structures; numerical and numerical-analytical methods; mathematical modelling

Special Issue Information

Dear Colleagues,

This Special Issue focuses on the following: the application of numerical and numerical analytic methods; advanced mathematical and computerized modelling technologies used to solve applied problems of analysis and the optimal design of structures through the employment of cutting-edge research-based approaches; and the application and development of innovative computing systems designed for research and engineering tasks that facilitate the high-tech development of construction.

This is a call for research and review articles on numerical and numerical analytic analysis, as well as mathematical and computerized modelling in engineering science and construction. In addition, we welcome research which addresses the relevant problems in the development and application of advanced approaches to the modelling of construction facilities in the course of surveying, design, construction, operation and reconstruction of buildings and structures, including issues of development, advancement and verification, as well as the application of numerical and numerical analytic methods, application of cutting-edge software packages, using theoretical computation and experiments researching the stress–strain state, strength, stability, reliability and safety of facilities in civil and industrial engineering, power engineering, machine building and transportation.

Sincerely yours,
Dr. Armen Ter-Martirosyan
Dr. Vladimir Sidorov
Guest Editors

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Keywords

  • mathematical and computer modelling
  • numerical analysis
  • analysis and optimal design
  • computational mathematics
  • numerical methods
  • finite element methods
  • structural analysis
  • civil engineering

Published Papers (6 papers)

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Research

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13 pages, 8192 KiB  
Article
Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out
by Lyudmila Frishter
Axioms 2023, 12(11), 1030; https://doi.org/10.3390/axioms12111030 - 02 Nov 2023
Viewed by 702
Abstract
A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with [...] Read more.
A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain. Full article
(This article belongs to the Special Issue Applied Numerical Analysis in Civil Engineering)
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14 pages, 2816 KiB  
Article
Passive Damping of Longitudinal Vibrations of a Beam in the Vicinity of Natural Frequencies Using the Piezoelectric Effect
by Nelly Rogacheva, Vladimir Sidorov and Yulia Zheglova
Axioms 2023, 12(10), 981; https://doi.org/10.3390/axioms12100981 - 18 Oct 2023
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Abstract
To significantly reduce the amplitude of longitudinal vibrations of the beam in the vicinity of its natural frequencies, a fundamentally new method of damping vibrations is used. For this purpose, the beam surfaces are covered with layers of polarized piezoceramics with a strong [...] Read more.
To significantly reduce the amplitude of longitudinal vibrations of the beam in the vicinity of its natural frequencies, a fundamentally new method of damping vibrations is used. For this purpose, the beam surfaces are covered with layers of polarized piezoceramics with a strong piezoelectric effect. We will use two types of electrical conditions on the electrodes of the piezoelectric layers: short-circuited electrodes and disconnected electrodes. On short-circuited electrodes, the electric potential is zero. As a result of the piezoelectric effect, an electric charge appears on the disconnected electrodes when the beam is deformed. The electroelastic state of a beam with different electrical conditions is described by different boundary value problems. A new approach to damping vibrations in the vicinity of natural frequencies is based on the following rule for controlling the dynamic characteristics of a structure: when the beam vibration frequency approaches its natural vibration frequency, we change the electrical conditions on the electrodes of the piezoelectric layers, thereby changing the spectrum of its natural frequencies. Let, for example, the vibration frequency of a beam with short-circuited electrodes approach its natural frequency. In this case, the amplitudes of the sought quantities grow without limit. The natural frequency spectrum of a beam with disconnected electrodes will differ from the spectrum of a beam with short-circuited electrodes. As a result, the amplitudes of the sought quantities will decrease. It is shown that the efficiency of vibration damping can be significantly increased by choosing the direction of the preliminary polarization of the piezoelectric material and the location of its electrodes. Numerical examples are given that demonstrate the effectiveness of the proposed method. The advantage of the method lies in its simplicity and the low cost of the piezoelectric material, which serves as a non-inertial damper. Full article
(This article belongs to the Special Issue Applied Numerical Analysis in Civil Engineering)
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15 pages, 813 KiB  
Article
Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary
by Lyudmila Frishter
Axioms 2023, 12(9), 893; https://doi.org/10.3390/axioms12090893 - 19 Sep 2023
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Abstract
Large values and gradients of stress and strain, triggering concentrated stress and strain, arise in angular areas of a structure. The strain action, leading to the finite loss of contact between structural elements, also triggers concentrated stress. The loss of contact reaches an [...] Read more.
Large values and gradients of stress and strain, triggering concentrated stress and strain, arise in angular areas of a structure. The strain action, leading to the finite loss of contact between structural elements, also triggers concentrated stress. The loss of contact reaches an irregular point and a line on the boundary. The theoretical analysis of the stress–strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous strain is reduced to the study of singular solutions to the homogeneous problem of elasticity theory with power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the area located near the vertex of an angular cutout in the boundary features substantial strain and rotations, and it corresponds to higher values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighborhood of an irregular boundary point. As far as these areas are concerned, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of strain, to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equilibrium equation in the polar system of coordinates for a V-shaped area under the action of temperature-induced strain, taking into account geometric non-linearity and physical linearity. Full article
(This article belongs to the Special Issue Applied Numerical Analysis in Civil Engineering)
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18 pages, 16907 KiB  
Article
Settlement of a Foundation on an Unsaturated Sandy Base Taking Vibrocreep into Account
by Armen Z. Ter-Martirosyan, Alexander N. Shebunyaev and Evgeny S. Sobolev
Axioms 2023, 12(6), 594; https://doi.org/10.3390/axioms12060594 - 15 Jun 2023
Cited by 1 | Viewed by 1250
Abstract
Dynamic loading causes (1) a substantial change in the strength and deformation parameters of sandy soil and (2) excessive viscoplastic deformation. The goal of this study is to create a new analytical solution to the problem of the settlement of (1) the foundation [...] Read more.
Dynamic loading causes (1) a substantial change in the strength and deformation parameters of sandy soil and (2) excessive viscoplastic deformation. The goal of this study is to create a new analytical solution to the problem of the settlement of (1) the foundation that is the source of dynamic loading, and (2) a nearby foundation, taking into account the rheological properties of sandy soil subjected to vibration, given that these rheological properties depend on shear stresses. The proposed solution allows the progress of deformation over time to be described. The present paper states and provides an analytical solution for the problem of evaluating the settlement of a single foundation that transmits static and dynamic harmonic pressure to the base. The authors also analyze the settlement of another foundation located at some distance from the transmitting foundation. The second foundation transmits static pressure to the base. The dependence of the viscosity coefficient on the shear stress intensity and vibration intensity, as well as the vibrocreep decay over time, are based on the exponential and homographic dependencies previously identified by two of the authors (A.Z. Ter-Martirosyan and E.S. Sobolev). The solution to the problem is obtained by numerical integration in the Mathcad program of an analytical expression for nonlinear viscoplastic deformations. As a result of the research, the authors have found that the dynamic viscoplastic component makes the greatest contribution to foundation settlement. The settlement of the transmitting foundation increases along with increasing static and dynamic pressure transmitted to the base. The settlement of the nearby foundation increases when the pressure increases under the foundation, but it reduces when static pressure from the transmitting foundation, the depth of the foundation, and the distance between the foundations increase. General analytical dependencies obtained by the authors comply with the results of laboratory and field experiments performed by other researchers. These dependencies can be used to predict the settlement of foundations in whose unsaturated sandy bases mechanical vibrations propagate. Full article
(This article belongs to the Special Issue Applied Numerical Analysis in Civil Engineering)
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10 pages, 8483 KiB  
Article
A Mathematical Analysis of the Stress Statement of the Soil Basis under Complex Loading near the Retaining Wall
by Armen Z. Ter-Martirosyan and Yulia V. Vanina
Axioms 2023, 12(6), 536; https://doi.org/10.3390/axioms12060536 - 30 May 2023
Viewed by 861
Abstract
The present paper describes and provides an analytical solution to the problem of the stress state of a limited-thickness soil basis resting on an incompressible soil base, under the action of two distributed loads of different intensities near the retaining wall of an [...] Read more.
The present paper describes and provides an analytical solution to the problem of the stress state of a limited-thickness soil basis resting on an incompressible soil base, under the action of two distributed loads of different intensities near the retaining wall of an excavation pit. It is proposed that the method for identifying components of the stress statement within the framework of the engineering problem in question is improved, and the solution is based on the trigonometric Ribiere–Fileon series. The results obtained by the authors allow for an evaluation of the supplementary effect on a retaining wall produced by loads from heavy machinery and materials stored near this retaining wall. These findings are useful for the design of underground constructions of buildings and structures. Theoretical results are provided together with those of numerical experiments to validate the research reliability. Full article
(This article belongs to the Special Issue Applied Numerical Analysis in Civil Engineering)
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Review

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21 pages, 4321 KiB  
Review
Review of Nonlocal-in-Time Damping Models in the Dynamics of Structures
by Vladimir Sidorov, Marina Shitikova, Elena Badina and Elena Detina
Axioms 2023, 12(7), 676; https://doi.org/10.3390/axioms12070676 - 10 Jul 2023
Cited by 2 | Viewed by 866
Abstract
In the present paper, the nonlocal-in-time damping models, called “damping-with-memory” models, are reviewed. Since such models do not involve the distribution along the longitudinal coordinate, they are easily adjustable for the FEM (Finite Element Model) algorithm, which is a big advantage due to [...] Read more.
In the present paper, the nonlocal-in-time damping models, called “damping-with-memory” models, are reviewed. Since such models do not involve the distribution along the longitudinal coordinate, they are easily adjustable for the FEM (Finite Element Model) algorithm, which is a big advantage due to the fact that FEM is the most-used method in engineering calculations. Within damping-with-memory models, the internal damping of a structure at the current time, is assumed to be dependent not only on the instant strain-rate magnitude or displacement-velocity magnitude but also on the strain-rate or velocity values along the previous time history. The greater the gap between the two time points, the lower the influence that one of them has on the other. To implement a composite beam vibration simulation involving damping with memory, the equation of motion of a structure written in the matrix form could be solved using the central difference method. The models constructed could be calibrated based on 3D numerical simulation data with the least squares method. It has been shown that the results obtained using the implementation of a calibrated damping-with-memory model within the 1D finite-element beam algorithm are in good correlation with those given by the 3D-FEM numerical simulation data. Full article
(This article belongs to the Special Issue Applied Numerical Analysis in Civil Engineering)
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