Progress in Computational and Applied Mechanics

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1999

Special Issue Editors


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Guest Editor
Institute of Continuum Mechanics, Leibniz University Hannover, 30823 Hannover, Germany
Interests: virtual element method; nonlinear analysis

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Guest Editor
Department of Mathematics, College of Science, National University of Defense Technology, Changsha 410073, China
Interests: finite element method; virtual element method; eigenvalue problem; inverse problem

Special Issue Information

Dear Colleagues,

Computational and applied mechanics play an important role in engineering problems, allowing us to address a variety of challenges in various fields of science and engineering. This Special Issue endeavors to consolidate the forefront of computational and applied mechanics, spotlighting innovative research and envisioning future advancements. We encourage researchers to provide relevant papers, including theoretical development and rational applications of mathematical models, variational formulations, and numerical methods related to finite element, finite volume, virtual element, isogeometric and meshless discretization methods.

Topics of interest include, but are not limited to, the following:

  • Computational methods: including finite element method, meshless method, virtual element method, and particle methods;
  • Mechanics of materials: plasticity, damage, phase field fracture;
  • Dynamics, vibrations, and waves in solids;
  • Multiscale and multiphysics simulations;
  • High-performance computing techniques;
  • Uncertainty quantification and sensitivity analysis;
  • Computational fluid dynamics: compressible flow, incompressible flow, numerical heat transfer.

Dr. Bingbing Xu
Dr. Jian Meng
Guest Editors

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Keywords

  • computational mechanics
  • numerical methods
  • finite elements
  • meshless methods
  • solid mechanics
  • dynamics
  • fluid mechanics
  • computer simulation

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Published Papers (1 paper)

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Research

19 pages, 1774 KiB  
Article
Solution of Internal Forces in Statically Indeterminate Structures Under Localized Distributed Moments
by Pengyun Wei, Junhong Hu, Haizhong Man and Shunjun Hong
Mathematics 2024, 12(23), 3649; https://doi.org/10.3390/math12233649 - 21 Nov 2024
Viewed by 890
Abstract
Classical methods for manually solving internal forces in statically indeterminate structures mainly include force and displacement methods. While the force method involves substantial work when solving the internal forces of structures with higher degrees of indeterminacy, the displacement method offers a fixed and [...] Read more.
Classical methods for manually solving internal forces in statically indeterminate structures mainly include force and displacement methods. While the force method involves substantial work when solving the internal forces of structures with higher degrees of indeterminacy, the displacement method offers a fixed and easily understood approach. However, the displacement method requires prior knowledge of load constant formulas. Common methods for deriving load constant formulas include the force method, virtual beam method, and energy method. Nevertheless, deriving load constant formulas for localized distributed moments using these methods proves to be highly challenging. This study aims to derive load constant formulas for localized distributed moments. Firstly, the load constant formula for a single concentrated moment is derived using the formula for a single concentrated force. Then, the load constant formulas for localized uniform moments and localized linearly distributed moments are derived via the integral method, leveraging the load constant formula for a single concentrated moment. This approach addresses the problem of solving internal forces in statically indeterminate structures under distributed moments via the displacement method. Finally, the proposed approach is verified using three typical examples. The promotion of the research results in this article in teaching can deepen students’ understanding of load constants and the displacement method, enrich teaching content, and have certain engineering applications and teaching practical significance. Full article
(This article belongs to the Special Issue Progress in Computational and Applied Mechanics)
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