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Axioms
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Applied Numerical Analysis in Civil Engineering
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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 5276

Special Issue Editors

Dr. Armen Ter-Martirosyan

E-Mail Website
Guest Editor
Soil Mechanics and Geotechnics Department, MSUCE, Moscow, Russia
Interests: finite element methods in geotechnical engineering
Dr. Vladimir Sidorov

E-Mail Website
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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

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

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

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 - 2 Nov 2023
Cited by 1 | Viewed by 1207
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
Viewed by 1429
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
Viewed by 1448
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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