Special Issue "Applied Mathematics and Solid Mechanics"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 December 2020.

Special Issue Editors

Prof. Dr. Eduard-Marius Craciun
Website
Guest Editor
Fac. of Mech. Ind. and Maritime Eng. Bd. Mamaia 124, University of Constanta, 900527, Constanta, Romania
Interests: applied mathematics and mechanics; solid mechanics; fracture
Prof. Dr. Marin Marin
Website
Co-Guest Editor
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania
Interests: applied mathematics
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Special Issue Information

Dear Colleagues,

The present Special Issue covers most areas of Applied Mathematics in the theory of classical and non-classical solid mechanics and the purpose is to gather articles reflecting the latest developments in these fields, including theoretical, numerical/computational, and experimental aspects.

The topics of interest for publication include but are not limited to the boundary value problems, the study of mixed problems for generalized continua and recent developments in the field of mathematical modeling for fracture mechanics problems.

All interested researchers are kindly invited to contribute to this Special Issue with their original research articles, short communications, and review articles.

Prof. Dr. Eduard-Marius Craciun
Prof. Dr. Marin Marin
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 papers will be 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. Mathematics 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 1200 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

  • Solids mechanics
  • Fracture mechanics
  • Mathematical approaches
  • Mathematical models
  • Asymptotic analysis
  • Composites
  • Piezoelectricity
  • Mixed problems in generalized continua
  • Biomechanics

Published Papers (4 papers)

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Research

Open AccessArticle
Kane’s Method-Based Simulation and Modeling Robots with Elastic Elements, Using Finite Element Method
Mathematics 2020, 8(5), 805; https://doi.org/10.3390/math8050805 - 15 May 2020
Abstract
The Lagrange’s equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and [...] Read more.
The Lagrange’s equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and then a series of differentiations that involve a great computational effort. The last decade has shown an increased interest of researchers in the study of multibody systems (MBS) using alternative analytical methods, aiming to simplify the description of the model and the solution of the systems of obtained equations. The method of Kane’s equations is one possibility to do this and, in the paper, we applied this method in the study of a MBS applying finite element analysis (FEA). The number of operations involved is lower than in the case of Lagrange’s equations and Kane’s equations are little used previously in conjunction with the finite element method (FEM). Results are obtained regardless of the type of finite element used. The shape functions will determine the final form of the matrix coefficients in the equations. The results are applied in the case of a planar mechanism with two degrees of freedom. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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Open AccessArticle
A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation
Mathematics 2020, 8(5), 653; https://doi.org/10.3390/math8050653 - 25 Apr 2020
Abstract
In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, [...] Read more.
In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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Open AccessArticle
Optimum Design of Infinite Perforated Orthotropic and Isotropic Plates
Mathematics 2020, 8(4), 569; https://doi.org/10.3390/math8040569 - 11 Apr 2020
Abstract
In this study, an attempt was made to introduce the optimal values of effective parameters on the stress distribution around a circular/elliptical/quasi-square cutout in the perforated orthotropic plate under in-plane loadings. To achieve this goal, Lekhnitskii’s complex variable approach and Particle Swarm Optimization [...] Read more.
In this study, an attempt was made to introduce the optimal values of effective parameters on the stress distribution around a circular/elliptical/quasi-square cutout in the perforated orthotropic plate under in-plane loadings. To achieve this goal, Lekhnitskii’s complex variable approach and Particle Swarm Optimization (PSO) method were used. This analytical method is based on using the complex variable method in the analysis of two-dimensional problems. The Tsai–Hill criterion and Stress Concentration Factor (SCF) are taken as objective functions and the fiber angle, bluntness, aspect ratio of cutout, the rotation angle of cutout, load angle, and material properties are considered as design variables. The results show that the PSO algorithm is able to predict the optimal value of each effective parameter. In addition, these parameters have significant effects on stress distribution around the cutouts and the load-bearing capacity of structures can be increased by appropriate selection of the effective design variables. The main innovation of this study is the use of PSO algorithm to determine the optimal design variables to increase the strength of the perforated plates. Finite element method (FEM) was employed to examine the results of the present analytical solution. The results obtained by the present solution are in accordance with numerical results. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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Open AccessArticle
Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure
Mathematics 2020, 8(4), 497; https://doi.org/10.3390/math8040497 - 02 Apr 2020
Cited by 1
Abstract
The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, [...] Read more.
The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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