Computational Mechanics and Finite Element Method: Theory and Applications

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

Deadline for manuscript submissions: 20 December 2025 | Viewed by 2260

Special Issue Editor


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Guest Editor
Civil Engineering Program, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro 68506, Brazil
Interests: structural analysis; offshore structures; finite element method; computational mechanics

Special Issue Information

Dear Colleagues,

Computational mechanics is a discipline that combines principles from engineering mechanics and computer science to study and analyze the behavior of complex structures and materials. Finite element methods (FEM) serve as a fundamental tool in computational mechanics, providing a systematic approach to discretize and solve the governing equations of a physical system. The application of computational mechanics has revolutionized the design and analysis of structures, enabling engineers to predict and optimize the behavior of systems under different loading conditions. In addition, finite element analysis enables the accurate modeling of complex geometries, material properties, and boundary conditions, facilitating the study of structural integrity, mechanical response, and failure mechanisms. Hence, this Special Issue encourages submissions that apply the FEM in the various fields of computational mechanics, involving theoretical aspects and practical applications. Suggested topics include, but are not limited to, numerical analysis, structural mechanics, structures dynamics, mechanics of materials, fluid mechanics, thermal sciences, computer-aided engineering, optimization, discretization, and mesh generation.

Dr. José Renato Mendes De Sousa
Guest Editor

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Keywords

  • numerical analysis
  • structural mechanics
  • structures dynamics
  • mechanics of materials
  • fluid mechanics
  • thermal sciences
  • computer-aided engineering
  • optimization
  • discretization
  • mesh generation

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Published Papers (2 papers)

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Research

12 pages, 2106 KiB  
Article
On the Development of a Modified Timoshenko Beam Element for the Bending Analysis of Functionally Graded Beams
by Mofareh Hassan Ghazwani and Pham V. V. Vinh
Mathematics 2025, 13(1), 73; https://doi.org/10.3390/math13010073 - 28 Dec 2024
Viewed by 571
Abstract
This study examines the static bending behavior of functionally graded beams using a newly developed modified Timoshenko beam element. The mixed finite element formulation and Timoshenko beam theory serve as the foundation for the formulation of the proposed beam element. There are two [...] Read more.
This study examines the static bending behavior of functionally graded beams using a newly developed modified Timoshenko beam element. The mixed finite element formulation and Timoshenko beam theory serve as the foundation for the formulation of the proposed beam element. There are two nodes and two degrees of freedom in each node of the new beam element. The suggested element is free of shear locking, without the need for reduced or selective integrations, because of the mixed finite element formulation. Comparative results demonstrate high accuracy in computations, even with both regular and irregular meshes, as well as coarse and fine discretization. Because of its rapid convergence rate, the proposed element is an excellent tool for analyzing beam structures with complex geometries and load conditions. Several examples are provided to demonstrate the accuracy and high convergence of the proposed beam element. Additionally, the effects of various parameters, such as the power-law index and thickness-to-length ratio, on the bending behavior of functionally graded beams are investigated. The findings highlight the robustness and versatility of the developed beam element, which makes it a useful contribution to research into the computational mechanics of beam structures. Full article
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29 pages, 6220 KiB  
Article
A Coupled, Global/Local Finite Element Methodology to Evaluate the Fatigue Life of Flexible Risers Attached to Floating Platforms for Deepwater Offshore Oil Production
by Monique de Carvalho Alves, Fabrício Nogueira Corrêa, José Renato Mendes de Sousa and Breno Pinheiro Jacob
Mathematics 2024, 12(8), 1231; https://doi.org/10.3390/math12081231 - 19 Apr 2024
Cited by 2 | Viewed by 1127
Abstract
This study introduces a Finite Element (FE) hybrid methodology for analyzing deepwater offshore oil and gas floating production systems. In these systems, flexible risers convey the production and are connected to a balcony on one side of the platform. The proposed methodology couples, [...] Read more.
This study introduces a Finite Element (FE) hybrid methodology for analyzing deepwater offshore oil and gas floating production systems. In these systems, flexible risers convey the production and are connected to a balcony on one side of the platform. The proposed methodology couples, in a cost-effective manner, the hydrodynamic model of the platform with the FE model that represents the risers and the mooring lines, considering all nonlinear dynamic interactions. The results obtained and the associated computational performance are then compared with those from traditional uncoupled analyses, which may present inaccurate results for deepwater scenarios, and from fully coupled analyses that may demand high computational costs. Moreover, particular attention is dedicated to integrating global and local stress analyses to calculate the fatigue resistance of the flexible riser. The results demonstrate that the coupled global analyses adequately capture the asymmetric behavior due to all risers being connected to one of the sides of the platform, thus resulting in a more accurate distribution of fatigue damage when compared to the uncoupled methodology. Also, fatigue life is significantly affected by adequately considering the coupling effects. Full article
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