Computational Mechanics and Applied Mathematics

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

Deadline for manuscript submissions: 30 September 2024 | Viewed by 3084

Special Issue Editor


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Guest Editor
Associate Professor, Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, FGPA, Smetanova 17, 2000 Maribor, Slovenia
Interests: computational mechanics; finite element methods

Special Issue Information

Dear Colleagues,

Structural engineering and mathematics have always existed mutually. Structural engineering deals with mechanics, providing complex adequate computational models, while mathematics provides computational solution algorithms. Structural analysis is therefore one of the most important and demanding engineering processes, as it combines several parts (proper structural computational model selection, the implementation of mathematical methods, the critical evaluation of the results with the possible modification or upgrade of the computational model and recalculation, and the execution of details following the obtained results), which, although carried out separately, lead to reliable and safe solutions as a whole. The almost natural synergy between mathematics and mechanics thus presents a potent tool in computational structural mechanics, allowing engineers to design structures reliably without the help of experiments.

The evident and rapid progress in computational mechanics in recent decades (both in mathematical models and computational algorithms) has already raised the level of knowledge through various numerical methods (such as finite volume, finite element, boundary element, and meshless methods) and simulations for various problems in the fields of computational mechanics and engineering. This progress, supported by the simultaneous development of computer technology, has allowed new models and approaches to become more comprehensive and complex (including more information and detail), fast (i.e., computationally more efficient), robust, and accurate.

Nevertheless, there is still room for improvement, and moreover, recent unfortunate natural disasters have reinforced the need for advanced and thorough constitutive modeling and structural analyses.

We therefore invite articles for submission to this Special Issue, focused on “Computational Mechanics and Applied Mathematics”. The scope of this Special Issue covers areas related to the application of new mathematical models, methods, or techniques in computational engineering mechanics, including the analytical, semi-numerical, and numerical-based computational modeling and analysis of structural engineering problems. 

Dr. Matjaz Skrinar
Guest Editor

Manuscript Submission Information

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Keywords

  • computational mechanics
  • structural analysis
  • numerical procedures and mathematical methods

Published Papers (4 papers)

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Research

41 pages, 6345 KiB  
Article
A Robust Flexible Optimization Model for 3D-Layout of Interior Equipment in a Multi-Floor Satellite
by Masoud Hekmatfar, M. R. M. Aliha, Mir Saman Pishvaee and Tomasz Sadowski
Mathematics 2023, 11(24), 4932; https://doi.org/10.3390/math11244932 - 12 Dec 2023
Viewed by 666
Abstract
Defanging equipment layout in multi-floor satellites consists of two primary tasks: (i) allocating the equipment to the satellite’s layers and (ii) placing the equipment in each layer individually. In reviewing the previous literature in this field, firstly, the issue of assigning equipment to [...] Read more.
Defanging equipment layout in multi-floor satellites consists of two primary tasks: (i) allocating the equipment to the satellite’s layers and (ii) placing the equipment in each layer individually. In reviewing the previous literature in this field, firstly, the issue of assigning equipment to layers is observed in a few articles, and regarding the layout, the non-overlapping constraint has always been a challenge, particularly for components that do not have a circular cross-section. In addition to presenting a heuristic method for allocating equipment to different layers of the satellite, this article presents a robust flexible programming model (RFPM) for the placement of equipment at different layers, taking into account the inherent flexibility of the equipment in terms of placement and the subject of uncertainty. This model is based on the existing uncertainty between the distances between pieces of cuboid equipment, which has not been addressed in any of the previous research, and by comparing its outputs with cases from past studies, we demonstrate a significantly higher efficiency related to placing the equipment and meeting the limit of non-overlapping constraints between the equipment. Finally, it would be possible to reduce the design time in the conceptual and preparatory stages, as well as the satellite’s overall size, while still satisfying other constraints such as stability and thermal limitations, moments of inertia and center of gravity. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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21 pages, 5232 KiB  
Article
An Enhanced Hybrid-Level Interface-Reduction Method Combined with an Interface Discrimination Algorithm
by Seunghee Cheon and Jaehun Lee
Mathematics 2023, 11(23), 4867; https://doi.org/10.3390/math11234867 - 04 Dec 2023
Viewed by 670
Abstract
This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been [...] Read more.
This study proposes an interface localizing scheme to enhance the performance of the previous hybrid-level interface-reduction method. The conventional component mode synthesis (CMS) only focuses on interior reduction, while the interface is fully retained for convenient synthesis. Thus, various interface-reduction methods have been suggested to obtain a satisfactory size for the reduced systems. Although previous hybrid-level interface-reduction approaches have addressed major issues associated with conventional interface-reduction methods—in terms of accuracy and efficiency through considering partial substructure synthesis—this method can be applied to limited modeling conditions where interfaces and substructures are independently defined. To overcome this limitation, an interface localizing algorithm is developed to ensure an enhanced performance in the conventional hybrid-level interface-reduction method. The interfaces are discriminated through considering the Boolean operation of substructures, and the interface reduction basis is computed at the localized interface level, which is constructed by a partially coupled system. As a result, a large amount of computational resources are saved, achieving the possibility of efficient design modifications at the semi-substructural level. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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13 pages, 5264 KiB  
Article
Study of Transversely Isotropic Visco-Beam with Memory-Dependent Derivative
by Kulvinder Singh, Iqbal Kaur and Eduard-Marius Craciun
Mathematics 2023, 11(21), 4416; https://doi.org/10.3390/math11214416 - 25 Oct 2023
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Abstract
Based on the modified Moore–Gibson–Thompson (MGT) model, transversely isotropic visco-thermoelastic material is investigated for frequency shift and thermoelastic damping. The Green–Naghdi (GN) III theory of thermoelasticity with two temperatures is used to express the equations that govern heat conduction in deformable bodies based [...] Read more.
Based on the modified Moore–Gibson–Thompson (MGT) model, transversely isotropic visco-thermoelastic material is investigated for frequency shift and thermoelastic damping. The Green–Naghdi (GN) III theory of thermoelasticity with two temperatures is used to express the equations that govern heat conduction in deformable bodies based on the difference between conductive and dynamic temperature acceleration. A mathematical model for a simply supported scale beam is formed in a closed form using Euler Bernoulli (EB) beam theory. We have figured out the lateral deflection, conductive temperature, frequency shift, and thermoelastic damping. To calculate the numerical values of various physical quantities, a MATLAB program has been developed. Graphical representations of the memory-dependent derivative’s influence have been made. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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23 pages, 3541 KiB  
Article
Variational Solution and Numerical Simulation of Bimodular Functionally Graded Thin Circular Plates under Large Deformation
by Xiao-Ting He, Xiao-Guang Wang, Bo Pang, Jie-Chuan Ai and Jun-Yi Sun
Mathematics 2023, 11(14), 3083; https://doi.org/10.3390/math11143083 - 12 Jul 2023
Viewed by 703
Abstract
In this study, the variational method and numerical simulation technique were used to solve the problem of bimodular functionally graded thin plates under large deformation. During the application of the variational method, the functional was established on the elastic strain energy of the [...] Read more.
In this study, the variational method and numerical simulation technique were used to solve the problem of bimodular functionally graded thin plates under large deformation. During the application of the variational method, the functional was established on the elastic strain energy of the plate while the variation in the functional was realized by changing undetermined coefficients in the functional. As a result, the classical Ritz method was adopted to obtain the important relationship between load and maximum deflection that is of great concern in engineering design. At the same time, the numerical simulation technique was also utilized by applying the software ABAQUS6.14.4, in which the bimodular effect and functionally graded properties of the materials were simulated by subareas in tension and compression, as well as the layering along the direction of plate thickness, respectively. This study indicates that the numerical simulation results agree with those from the variational solution, by comparing the maximum deflection of the plate, which verifies the validity of the variational solution obtained. The results presented in this study are helpful for the refined analysis and optimization design of flexible structures, which are composed of bimodular functionally graded materials, while the structure is under large deformation. Full article
(This article belongs to the Special Issue Computational Mechanics and Applied Mathematics)
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