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Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (20 August 2023) | Viewed by 25133

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Prof. Dr. Marcin Graba

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Department of Metrology and Non-Conventional Manufacturing Methods, Faculty of Mechatronics and Mechanical Engineering, Kielce University of Technology, Al. Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland
Interests: fracture; fracture mechanics; finite element modeling; finite element analysis; mechanical properties; mechanical testing; failure analysis; mechanics of materials; stress analysis; solid mechanics; computational mechanics; FE analysis; structural analysis; tensile test modeling; construction materials; welding; 3D printing; industrial design
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Prof. Dr. Stanisław Adamczak

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Faculty of Mechatronics and Machine Design, Department of Mechanical Technology and Metrology, Kielce University of Technology, Al. 1000-lecia P.P. 7, 25-314 Kielce, Poland
Interests: technical metrology; quality systems; machine technology

Special Issue Information

Dear Colleagues,

As you are an expert in the field of solid mechanics, invite you to publish your work in a Special Issue of Applied Sciences, which will be devoted to the field of finite element methods for structural, linear and nonlinear mechanical problems. The Special Issue will be oriented towards the numerical methods of mechanics, particularly FEM analysis, linear mechanics, nonlinear mechanics, structural mechanics, solid mechanics, numerical methods, computer methods, FEM in design, plasticity, continuum mechanics, and fracture mechanics. The scope includes the application of finite element method in solving various problems in the field of mechanics—from linear to non-linear problems, including the determination of the ultimate load capacity. In addition to solving theoretical problems, we welcome the submission of articles focused on FEM applications in design and fracture mechanics.

We would be delighted if you sent us an article for this Special Issue, or if you informed your colleagues working in the field about this Special Issue.

Prof. Dr. Marcin Graba
Prof. Dr. Stanisław Adamczak
Guest Editors

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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. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

FEM analysis
linear mechanics
nonlinear mechanics
structural mechanics
solid mechanics
numerical methods
computer methods
FEM in design
plasticity
continuum mechanics
fracture mechanics

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Published Papers (10 papers)

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Research

14 pages, 5319 KiB

Open AccessArticle

Numerical Study on Welding Structure of Connecting Fin Used in Thermal Power Plant

by Entao Guo, Weiqiang Huang, Xian Shi, Yuce Zhu, Yimin Cui, Xianming Wang, Chuanyang Lu, Yumin Lou and Yanming He

Appl. Sci. 2023, 13(22), 12454; https://doi.org/10.3390/app132212454 - 17 Nov 2023

Viewed by 1267

Abstract

The background of deep peak-shaving poses demanding requirements for the performance of metal components in thermal power plants. The cracking of the connecting fins on the side wall of the flue seriously endangers the safe operation of the system. Herein, welding simulations were carried out using the finite element method to understand the cracking process of the connecting fins. By changing the welding process and fin size, their effect on stress and deformation was explored. The results showed that increasing the welding rate would decrease the flexural deformation of the flue-side wall. Additionally, the yield range of the connecting fin depended more on width than thickness, and increased with increasing width. As for the relationship between fin size and flexural deformation, the maximum deformation decreased with the increase in thickness, while it first decreased and then increased with increasing width. Overall, the post-welding stress and deformation of the boiler flue side wall exhibited more sensitivity to the fin width compared with the fin thickness and welding rate. This article clarifies the stress distribution status of the connecting fins in the flue side wall under different welding conditions, providing a basis for analyzing its cracking phenomenon, and further providing theoretical guidance for optimizing the structural parameter design of the side wall. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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16 pages, 4660 KiB

Open AccessArticle

Numerical Investigation of the Evolving Inelastic Deformation Path of a Solder Ball Joint under Various Loading Conditions

by Jae-Hyuk Lim, Da-Hun Lee and Eun-Ho Lee

Appl. Sci. 2023, 13(22), 12137; https://doi.org/10.3390/app132212137 - 8 Nov 2023

Cited by 2 | Viewed by 1478

Abstract

Solder joints of ball grid arrays (BGA) have been widely used to connect electronic components to printed circuit boards (PCBs) and are often subjected to mechanical stress. Several studies have been conducted on the mechanical reliability of solder joints. While these studies have been useful in the industry, detailed studies on how the inelastic deformation path of the solder ball joints evolves under specific loading conditions have not been sufficiently reported. This study aims to understand how the inelastic deformation path evolves when a solder joint is subjected to a constant external force by utilizing the theory of mechanics. It has also been found that the mechanical failure is strongly influenced by the evolution history of the deformation modes in materials. For this study, an elastoplastic constitutive model and a ductile fracture criterion were implemented into the vectorized user-defined material (VUMAT) subroutine of the ABAQUS program for finite element (FE) analysis. With the model, the evolution of the inelastic deformation path of a single solder ball under different loading conditions was numerically analyzed. Three loadings (shear, compression, and bending) were chosen as the basic loading conditions. In addition, combinations of the basic loadings resulted in three dual loadings and one complex loading. The simulation results showed that the shear and bending caused the fracture for both single and dual loadings, but when combined with compression, the fracture was suppressed. The results indicate that fracture is not solely determined by the magnitude of equivalent plastic strain but also by the evolution of inelastic deformation mode. This research offers an improved understanding of the significance of the inelastic deformation path and fracture. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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18 pages, 6685 KiB

Open AccessArticle

Modeling of Pipe Whip Phenomenon Induced by Fast Transients Based on Fluid–Structure Interaction Method Using a Coupled 1D/3D Modeling Approach

by Isaac Solomon and Gintautas Dundulis

Appl. Sci. 2023, 13(19), 10653; https://doi.org/10.3390/app131910653 - 25 Sep 2023

Cited by 6 | Viewed by 1885

Abstract

The sudden increase in the operating pressure of nuclear power plants (NPPs) is due to the water hammer phenomenon, which tends to produce a whipping effect that causes serious damage to the pipes and their surroundings. The mechanical response of these pipelines under the influence of such fast fluid transients can be estimated using the fluid–structure interaction (FSI) method. The computational time and expense are predominantly dependent on the number of finite elements developed in the model. Hence, an effective modeling technique with limited and efficient nodes and elements is desired to obtain the closest possible results. A coupled 1D/3D finite element modeling approach using the FSI method is proposed to determine the influence of fast transients on the mechanical pipe whipping behavior of gas pipelines in NPPs. The geometric coupled modeling approach utilizes the presence of both the 3D solid elements and the 1D beam elements sharing a local conjunction. The computational model is modelled for a pipe-to-wall impact test scenario taken from the previously conducted French Commissariat a l’Energie Atomique (CEA) pipe whip experiments. The results of displacement, stresses, and impact velocity at the 3D section featuring the elbow are compared for the change in the 3D solid length varied at the juncture of the elbow. The computed results from the Ansys FSI coupling method using the Fluent and Transient Structural modules provides fair validation with the previously conducted experimental results and correlates with the CEA pipe whip tests on pipe-to-wall impact models. Thus, the 1D/3D coupled modeling approach, which minimizes the area of the solid region by constricting it to the impact area with appropriate contact modeling at the junctures, can be considered in the future for decreasing the computational time and the creation of finite elements. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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13 pages, 4339 KiB

Open AccessArticle

Effects of Dry Granulation Operating Parameters on Forming Quality

by Xiaowen Xie, Haozheng Gao, Zhongze Xie and Mingge Wu

Appl. Sci. 2023, 13(19), 10619; https://doi.org/10.3390/app131910619 - 23 Sep 2023

Viewed by 1813

Abstract

To address the issues of the existing dry granulation process, which mostly relies on manual adjustments based on empirical experience and lacks the analysis of theoretical data, a simplified model of tablet pressing based on a modified Drucker–Prager Cap (DPC) material constitutive model was proposed to simulate and analyze the forming process of tablets, and study the impacts of the feeding speed, roller speed, friction coefficient and roller clearance on the density distribution of the pressed tablets via ABAQUS. The results show that the roller speed significantly impacts the density of tablets, and a lower roller speed and a higher friction coefficient are beneficial to the formation of tablets. As the roller clearance decreases, the average density at the clearance increases, and the unevenness of the lateral density distribution of the tablets increases, showing a distribution trend of larger density at the center and smaller density on both sides. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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29 pages, 24039 KiB

Open AccessArticle

Source and Accumulation Analysis of Deviation during Multi-Level Assembly of an Aircraft Rear Fuselage Frame

by Yaohui Zheng, Xiaoyue Huang, Minghai Wang and Pengcheng Hu

Appl. Sci. 2023, 13(17), 9914; https://doi.org/10.3390/app13179914 - 1 Sep 2023

Cited by 2 | Viewed by 1271

Abstract

During the production process of aircraft assembly, weakly rigid parts are gradually assembled into rigid support structures in the aircraft skeleton through several assembly stations. The assembly deviations of this structure determine the quality of the aerodynamic shape of the aircraft. In this paper, we consider multiple sources of deviation (manufacturing deviation, fixture positioning deviation, assembly contact deviation) and investigate the interaction between these sources. Based on the state space approach, a state space equation is developed to reveal the transformation, accumulation and transfer of deviations in the multi-level assembly process (MAP) of weakly rigid parts, and a model is established to accurately simulate and predict the transfer of deviations in the MAP of weakly rigid parts. In this model, the part manufacturing and fixture positioning deviations in typical dimensional planes are regarded as rigid deviations, while the deviations in atypical dimensional planes are regarded as flexible deviations. A spatial triangle penetration detection algorithm based on part measurement point deviations is proposed, combined with the theory of linear elasticity, to describe the relationship between part deviations and assembly contact forces. An example analysis of the assembly process of an aircraft rear fuselage frame structure illustrates the validity of a multi-level assembly deviation transfer model for weakly rigid parts. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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18 pages, 6476 KiB

Open AccessArticle

Mechanical Behaviour of the Rotating Target SORGENTINA-RF

by Marco Lamberti, Ranieri Marinari, Andrea Mancini, Gianni Gadani, Antonino Pietropaolo and The SRF Collaboration

Appl. Sci. 2023, 13(15), 8967; https://doi.org/10.3390/app13158967 - 4 Aug 2023

Viewed by 1386

Abstract

The SORGENTINA-RF project aims at developing a 14 MeV neutron source based on a deuterium/tritium ion accelerator and a rotating target where fusion reactions take place. Among the different research fields, the most interesting and promising is medical radioisotope production. In this framework, intense research work on the design of the rotating target has been carried out. More in detail, to define the optimal design configuration, a sensitivity analysis on the mechanical performance of the rotating target considering the influence of some relevant parameters, such as material type, thickness, and presence of internal stiffeners, was carried out. Among the materials analyzed, aluminium alloy represents the best compromise to efficiently address all the critical requirements in the design phase. One of the most demanding project requirements that the conceptual design must fulfill is the ability of the target to dissipate a thermal power of 250 kW without precluding its mechanical properties and resistance. To investigate the performance of the rotating target, some thermo-mechanical analyses were undertaken with finite element method under some thermal transients and mechanical loads able to simulate the working conditions of the system. The numerical results emphasise the target’s ability to withstand operating conditions. The main outcomes of the present study have been implemented as engineering solutions in the project design. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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23 pages, 13982 KiB

Open AccessArticle

A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme

by Hyung-Gyu Choi, Young Il Byun, Chul Ki Song, Martin B.G. Jun, Chaemin Lee and San Kim

Appl. Sci. 2023, 13(12), 7114; https://doi.org/10.3390/app13127114 - 14 Jun 2023

Cited by 2 | Viewed by 2245

Abstract

This paper presents a novel and efficient solution procedure to improve 3D solid finite element analysis with an enrichment scheme. To this end, we employ finite elements enriched by polynomial cover functions, which can expand their solution space without requiring mesh refinement or additional nodes. To facilitate this solution procedure, an error estimation method and cover function selection scheme for 3D solid finite element analysis are developed. This enables the identification of nodes with suboptimal solution accuracy, allowing for the adaptive application of cover functions in a systematic and efficient manner. Furthermore, a significant advantage of this procedure is its consistency, achieved by excluding arbitrary coefficients from the formulations employed. The effectiveness of the proposed procedure is demonstrated through several numerical examples. In the majority of the examples, it is observed that the stress prediction error is reduced by more than half after applying the proposed procedure. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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19 pages, 3896 KiB

Open AccessArticle

A Dynamic Response Analysis of Vehicle Suspension System

by Rogério Lopes, Behzad V. Farahani, Francisco Queirós de Melo and Pedro M. G. P. Moreira

Appl. Sci. 2023, 13(4), 2127; https://doi.org/10.3390/app13042127 - 7 Feb 2023

Cited by 4 | Viewed by 6938

Abstract

Automotive engineering is a very important branch of design and development in mechanical engineering devoted to vehicle manufacturing. It demands solid knowledge focusing on the kinematics and dynamics of mechanical systems, either using structural analysis or modelling techniques. In this manuscript, a model based on the application of the fundamentals of the static and dynamic behaviour of the suspension system of a bus vehicle is developed. Therefore, a set of mathematical equations is expanded following the structural dynamic formulations to obtain an analytical solution on natural frequencies and the displacement under an external load. The problem is also solved using the Finite Element Method (FEM) to confirm the analytical results. Equivalent material parameters and boundary conditions were used for the FEM simulation. This work aims to propose a methodology based on modal analysis with a simplified model to predict the dynamic response of an automotive structure. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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18 pages, 5206 KiB

Open AccessArticle

Tool Failure Analysis and Multi-Objective Optimization of a Cutting-Type Energy-Absorbing Structure for Subway Vehicles

by Qianchen Gao, Shoune Xiao, Xiaorui Wang, Mingmeng Wang and Tao Zhu

Appl. Sci. 2023, 13(3), 1619; https://doi.org/10.3390/app13031619 - 27 Jan 2023

Cited by 6 | Viewed by 2118

Abstract

This paper aims to provide essential guidance for the crashworthiness design of cutting energy-absorbing structures for subway vehicles. By investigating tool failure with experiment and numerical approaches, a new energy-absorbing tube structure was proposed and optimized to improve the crashworthiness and reliability of the cutting energy-absorption structure. The impact test results revealed that multiple failure modes occurred in the tool. Mechanical wear occurs mainly in the middle of the cutting edge, while the tool’s tip failure is primarily due to thermal wear. Impact forces were no longer stable due to tool failure. The simulation results of the established tool-tube thermal–structural coupling finite element model were consistent with the tests. The temperature distribution indirectly validated the failure modes in different tool areas. By eliminating the tearing-type fracture mode, the proposed new structure effectively reduced the high temperature of the tool’s tip, better maintained the uniform temperature of the cutting edge, and smoothed changing of the cutting force. Finally, the Kriging surrogate model and NSGA-II algorithm were utilized to obtain the tool’s minimum steady-state temperature (STT) and maximum mean average cutting force (MCF). The optimal solution determined by the minimum distance method is STT = 514 K, MCF = 131 kN. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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19 pages, 7243 KiB

Open AccessArticle

Assessing the Crashworthiness Analysis on Frontal and Corner Impacts of Vehicle on Street Poles Using FEA

by Mohsen Alardhi, Rahul Sequeira, Melad Fahed, Jasem Alrajhi and Khalid Alkhulaifi

Appl. Sci. 2022, 12(23), 12287; https://doi.org/10.3390/app122312287 - 1 Dec 2022

Cited by 2 | Viewed by 3004

Abstract

The impact analysis of vehicle collision on street poles was investigated, as well as an assessment of which type of impact—frontal or corner—contributes to the most damages on both the car and the streetlamp. This work was accomplished using Abaqus/Explicit software to numerically simulate the crashes at three different velocities, 12, 17, and 22 m·s⁻¹, and extract relations such as the energy models, the specific energy absorption (SEA) of the materials tested, and the impact forces. Two materials were used for the street pole: aluminum Al-6061 and ASTM A36 grade steel. Findings such as the influence of the SEA on the vehicle’s velocity, the relationship between the deformation of the street pole and the vehicle’s velocity, as well as the improvement of previously studied models by including damage parameters are presented. Full article

(This article belongs to the Special Issue Finite Element Methods for Structural, Linear and Nonlinear Mechanical Problems)

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