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Mathematics
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Mathematical Modelling and Computer Simulation in Solid Mechanics and Hydrodynamics
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Mathematical Modelling and Computer Simulation in Solid Mechanics and Hydrodynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 4023

Special Issue Editors

Prof. Dr. Jan Valdman

E-Mail Website
Guest Editor
1. Faculty of Science, University of South Bohemia, České Budějovice, Czech Republic
2. Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic
Interests: finite element method; computational nonlinear mechanics of solids; a posteriori error estimates; vectorized implementations in MATLAB
Dr. Maksim Frolov

E-Mail Website
Guest Editor
Institute of Physics and Mechanics, Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia
Interests: finite element method; computational mechanics; a posteriori error estimates; adaptive algorithms
Prof. Dr. Michal Kuráž

E-Mail Website
Guest Editor
Faculty of Environmental Sciences, Czech University of Life Sciences, 16500 Prague, Czech Republic
Interests: finite element method; quasilinear coupled convection-diffusion-reaction problems; hydrodynamics in porous media (including phase changes); domain decompositions; adaptive strategies
Dr. Jan Fesl

E-Mail Website
Guest Editor
1. Faculty of Science, University of South Bohemia, 37005 České Budějovice, Czech Republic
2. Faculty of Information Technology, Czech Technical University in Prague, 16000 Prague, Czech Republic
Interests: simulations; artificial intelligence; computer networks; cyber-security; high-performance computing, distributed systems

Special Issue Information

Dear Colleagues,

Mathematical modelling transforms real-life problems to the language of mathematics that utilizes its methods and provides solutions that can be tested back in real life. Models in solid mechanics and hydrodynamics are typically formulated by partial differential equations that can be coupled so that complex and realistic description of real-world processes is obtained. The finite element method is an efficient method to approximately obtain numerical solutions of partial differential equations. It consists of discretization of a computation domain into smaller parts and of setting up large systems of equations and their computer solutions. Due to the massive expansion of computers, vectorized and parallel algorithms are developed taking into account modern computer architectures and new trends in information technologies. The usage of specifically designed computer systems interconnected via high-speed computer networks can rapidly decrease the computation time, which is the main factor for real-time processing. The development and implementation of algorithms for such architectures represents a specific area of high-level programming with substantially higher complexity in comparison to the classical approach.

This Special Issue focuses on the use of current advances in mathematical modeling and large-scale computer simulations in solid mechanics and hydrodynamics including (but not limited to) models for porous media. The topics of the issue are wide and cover various aspects of modeling and a broad spectrum of problems related to computer simulations and development of numerical algorithms, taking into account modern hardware architectures and trends.

Prof. Dr. Jan Valdman
Prof. Dr. Maxim Frolov
Prof. Dr. Michal Kuráž
Dr. Jan Fesl
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 modelling
  • Computer simulations
  • Finite element methods
  • Mechanics of solids
  • Hydrodynamics

Published Papers (2 papers)

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Research

17 pages, 1564 KiB  
Article
Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys
by Miroslav Frost and Jan Valdman
Mathematics 2022, 10(23), 4412; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234412 - 23 Nov 2022
Cited by 1 | Viewed by 1552
Abstract
The incremental energy minimization principle provides a compact variational formulation for evolutionary boundary problems based on constitutive models of rate-independent dissipative solids. In this work, we develop and implement a versatile computational tool for the resolution of these problems via the finite element [...] Read more.
The incremental energy minimization principle provides a compact variational formulation for evolutionary boundary problems based on constitutive models of rate-independent dissipative solids. In this work, we develop and implement a versatile computational tool for the resolution of these problems via the finite element method (FEM). The implementation is coded in the MATLAB programming language and benefits from vector operations, allowing all local energy contributions to be evaluated over all degrees of freedom at once. The monolithic solution scheme combined with gradient-based optimization methods is applied to the inherently nonlinear, non-smooth convex minimization problem. An advanced constitutive model for shape memory alloys, which features a strongly coupled rate-independent dissipation function and several constraints on internal variables, is implemented as a benchmark example. Numerical simulations demonstrate the capabilities of the computational tool, which is suited for the rapid development and testing of advanced constitutive laws of rate-independent dissipative solids. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computer Simulation in Solid Mechanics and Hydrodynamics)
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15 pages, 4390 KiB  
Article
Numerical Approach for Detecting the Resonance Effects of Drilling during Assembly of Aircraft Structures
by Alexey Vasiliev, Sergey Lupuleac and Julia Shinder
Mathematics 2021, 9(22), 2926; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222926 - 17 Nov 2021
Cited by 2 | Viewed by 1353
Abstract
This paper is devoted to the development of a numerical approach that allows quick detection of the conditions favorable for the beginning of noticeable vibrations during drilling. The main novelty of the proposed approach lies in taking into account the deviations of the [...] Read more.
This paper is devoted to the development of a numerical approach that allows quick detection of the conditions favorable for the beginning of noticeable vibrations during drilling. The main novelty of the proposed approach lies in taking into account the deviations of the assembled compliant parts during non-stationary contact analysis by means of variation simulation. The approaches to stationary analysis of assembly quality are expanded and generalized for modeling such non-stationary effects as vibration and resonance. The numerical procedure is based on modeling the stress–strain state of the assembled structures by solving the corresponding transient contact problem. The use of Guyan reduction, the node-to-node contact model and the application of the generalized α method allow the reformulation of the contact problem in terms of a series of quadratic programming problems. The algorithm is thoroughly tested and validated with commercial software. The efficiency of the developed numerical procedure is illustrated by analysis of the test joints of two aircraft panels. The unsteady process of drilling the panels with periodic drilling force was simulated. The influence of deviations in the shape of the parts on the non-stationary interlayer gap was modeled by setting different initial gaps between parts. It is shown that the oscillation amplitudes of the interlayer gap depend on the initial gaps and do not correlate with the mean value of the stationary residual gap. Thus, non-stationary analysis provides new information about the quality of the assembly process, and it should be applied if the assembly process includes periodic impact on the assembled parts. Full article
(This article belongs to the Special Issue Mathematical Modelling and Computer Simulation in Solid Mechanics and Hydrodynamics)
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