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Research progress and performance evaluations for self-starting single-solve explicit time integrators
LI Jinze, LIU Yaokun, YU Kaiping, CUI Naigang
 doi: 10.6052/1000-0992-24-030
Abstract(189) HTML(46) PDF(45)
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Direct time integration methods play a critical role in the numerical computation of large-scale nonlinear dynamic systems, particularly in the field of engineering simulation and design. The self-starting single-solve explicit time integration methods have become essential tools in this domain due to their efficiency and reliability in handling complex nonlinear systems. However, as these algorithms continue to evolve and diversify, their performance varies significantly, underscoring the urgent need for a systematic review and in-depth analysis of their capabilities. This paper first introduces the key performance metrics for evaluating time integration methods, including accuracy, stability, amplitude and phase error, providing a theoretical foundation for readers. It then offers a detailed review of the development of self-starting single-solve explicit time integration methods, systematically tracing the evolution of various algorithms. Finally, the performance of several self-starting single-solve explicit methods is compared in terms of spectral properties, accuracy, stability, and error characteristics, with numerical verification performed using typical examples and engineering structures. The paper highlights two explicit methods that currently exhibit superior performance: The fully explicit GSSE method and the velocity-implicit GSSI method. Both methods are characterized by their self-starting capability, single-solution, explicitness, maximized conditional stability, controllable numerical dissipation (over the full range), and identical second-order accuracy. The primary distinction between the two lies in the computational effort required for damping problems and the size of the conditional stability domain in the presence of damping. The paper also explores future research directions for explicit time integration methods, emphasizing the potential for further optimization and development.
Research advances in wind-train-bridge coupling vibration
HAN Yan, HU Peng, WANG Lidong, LIU Hanyun, CAI Chunsheng
 doi: 10.6052/1000-0992-24-032
Abstract(165) HTML(52) PDF(50)
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Researching the coupling vibration of wind-train-bridge systems is one of the crucial means to ensure the safe operation of trains on bridges under strong wind conditions. In the last two decades, domestic and foreign scholars have conducted extensive research in this field, accumulating fruitful research results. The study of the coupling vibration of the wind-train-bridge system mainly includes three aspects: the aerodynamic characteristics of the train-bridge system, the calculation of the coupling vibration of the wind-train-bridge system, and the evaluation, prevention, and control of driving safety. Firstly, the primary purpose of studying the aerodynamic characteristics of the train-bridge system is to analyze the aerodynamic interference mechanism of the train-bridge system and accurately obtain the wind loads acting on the train and bridge. Depending on whether the train on the bridge is stationary or moving, it can be divided into two cases, i.e., stationary train and moving train. Secondly, on the basis of obtaining wind loads on the train-bridge system, it is necessary to solve the dynamic response of the wind-train-bridge system to obtain the response time-history curve of the entire process of the train passing through the bridge. This research mainly involves modeling methods for the train-bridge system, solving theories of wind-train-bridge coupling vibration equations, and using efficient calculation methods. Thirdly, based on the obtained dynamic response, the ultimate goal is to evaluate the driving safety of trains on the bridge and propose prevention and control measures. This research mainly includes the evaluation indicators and methods of driving safety and the main preventive and control measures for ensuring the driving safety of trains under strong wind conditions. Finally, in conjunction with the main issues existing in the field of the coupling vibration of wind-train-bridge systems, prospects for future research directions are provided to promote the development of this research field.
Numerical simulation method and application of aircraft multi-body separation
LI Huan, CUI Pengcheng, JIA Hongyin, TANG Jing, ZHANG Jian, GONG Xiaoquan, WU Xiaojun, ZHANG Chao, ZHANG Peihong, ZHOU Naichun, ZHANG Yaobing
 doi: 10.6052/1000-0992-24-040
Abstract(311) HTML(63) PDF(208)
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The problems of aircraft multi-body separation, such as airborne weapon delivery separation, spacecraft series/parallel stage separation, fairing separation and submunition scattering, are common in the aerospace field at present. Safe and controllable multi-body separation is an important prerequisite for aircraft to perform aerospace tasks. In recent years, with the expansion of flight boundaries and the diversification of flight missions, aircraft are facing more complex multi-body separation scenarios, so it is necessary to carry out refined multi-body separation scheme design, which puts forward higher requirements for the fidelity and fineness of multi-body separation numerical simulation. In recent years, CFD has made great progress in high-fidelity simulation of complex scenes, aiming at the extremely complex and challenging multi-body separation problem. In this paper, the latest research progress of high-fidelity numerical simulation methods and applications of aircraft multi-body separation is reviewed and prospected. Firstly, the refined simulation methods of aircraft multi-body separation are summarized, including coupled grid dynamic optimization technology, coupled separation vortex simulation method and high-precision time-marching coupling algorithm. Secondly, the coupling simulation method of aircraft multi-body separation under complex constraints/flow field/control and its application are introduced. Then, the understanding of complex mechanism of dynamic interference of aircraft multi-body separation in typical complex scenes is introduced. Finally, the existing problems and future development direction of high fidelity numerical simulation of aircraft multi-body separation are pointed out.
Cellular mechanical intelligence
CHENG Bo, LU Mengnan, JIA Yuanbo, XU Feng
 doi: 10.6052/1000-0992-24-028
Abstract(337) HTML(88) PDF(129)
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Biological intelligence, which includes features such as perception, memory, learning, problem-solving and decision-making, is widely observed in humans, animals and other higher organisms with nervous systems. Recent studies have shown that single cells also exhibit behaviours that resemble human-like intelligence in their interactions with the microenvironment, such as “multimodal perception”, “problem solving”, “learning and memory”, and “evolutionary adaptation”. Cellular intelligence, as a newly proposed and disruptive theoretical concept, raises fundamental questions, including the principles underlying the emergence of cellular intelligence, the mechanisms by which collective cell behaviour emerges as collective intelligence, and the evolutionary drivers for single cells to evolve into multicellular life forms. As the fields of biomechanics and mechanobiology have advanced, numerous studies have demonstrated the significant influence of the mechanical microenvironment on cellular physiological behaviour. Under mechanical stimulation, even single cells exhibit intelligent behaviours similar to those observed in higher organisms. Based on this, the concept of “cellular mechanical intelligence” is proposed in this paper. We summarise the characteristics of intelligent behaviours in terms of mechanical perception, mechanical decision making, mechanical memory and mechanical learning, with the aim of providing new insights and perspectives on the mechanisms underlying cellular mechanical intelligence and its potential applications, such as in cellular intelligent medicine.
Quantum computing: The new focus in computational mechanics
XU Yongchun, KUANG Zengtao, HUANG Qun, YANG Jie, HU Heng
 doi: 10.6052/1000-0992-24-039
Abstract(621) HTML(146) PDF(160)
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Quantum computing has the potential to exponentially surpass classical computing in terms of computational power, but its practical applications need further expansion. At the same time, computational mechanics offers a wide range of applications, but faces challenges of significant computational power requirements arising from multi-scale, multi-physics, and extreme conditions, among others. Therefore, the complementary development of quantum computing and computational mechanics holds great promise. This paper reviews the current state of quantum computing applications in computational mechanics and discusses future trends in this field.
AI for PDEs in solid mechanics: A review
WANG Yizheng, ZHUANG Xiaoying, TIMON Rabczuk, LIU Yinghua
 doi: 10.6052/1000-0992-24-016
Abstract(4079) HTML(683) PDF(1783)
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In recent years, deep learning has become ubiquitous and is empowering various fields. In particular, the combination of artificial intelligence and traditional science (AI for science, AI4Science) has attracted widespread attention. In the field of AI4Science, the use of artificial intelligence algorithms to solve partial differential equations (AI4PDEs) has become the focus of computational mechanics research. The core of AI4PDEs is to fuse data with equations and can solve almost any PDEs. Due to the advantages of AI4PDEs in data fusion, computational efficiency using AI4PDEs is usually increased by tens of thousands of times compared to traditional algorithms. Therefore, this article comprehensively reviews the research on AI4PDEs, summarizes the existing AI4PDEs algorithms and theories, discusses its application in solid mechanics, including forward and inverse problems, and outlines future research directions, especially the foundation model of computational mechanics. Existing algorithms of AI4PDEs include physics-informed neural networks (PINNs), deep energy methods (DEM), operator learning, and (physics-informed neural operator, PINO). AI4PDEs has numerous applications in scientific computing, and this paper focuses on application of AI4PDEs in the forward and inverse problems of solid mechanics. The forward problems include linear elasticity, elasto-plasticity, hyperelasticity, and fracture mechanics; while the inverse problems encompass the identification of material parameters, constitutive laws, defect recognition, and topology optimization. AI4PDEs represents a novel method of scientific simulation, which offers approximate solutions for specific problems by leveraging large datasets and then fine-tunes according to the specific physical equations, avoiding the need to start calculations from scratch as traditional algorithms do. Thus, AI4PDEs is a prototype for the foundation model of computational mechanics in the future, capable of significantly accelerating traditional numerical methods. We believe that utilizing artificial intelligence to empower scientific computing is not only a vital direction for the future of computation but also a dawn of humanity in scientific research, laying the foundation for mankind to reach new heights in scientific development.
Review
Dynamics and control of on-orbit assembly of ultra-large space structures
HU Haiyan, TIAN Qiang, WEN Hao, LUO Kai, MA Xiaofei
2025, 55(1): 1-29.   doi: 10.6052/1000-0992-24-044
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On-orbit assembly of ultra-large space structures serves as the technological foundation for future space missions including high-capacity space-based communications, high-precision space-based observations and space-based solar power stations. It holds significant scientific and engineering values. Addressing the demands for assembling ultra-large structures like 100-m parabolic antennas on orbit, this review article surveys the research progress and challenges in the dynamics and control of ultra-large space structures assembled on orbit. The article focuses on five key aspects, including the overall assembly design and its dynamic problems, the dynamic modeling and computation of flexible multibody systems, the motion planning and control of robots, the dynamic verification and adjustment of assembly outcomes, and the ground simulation experiments. It highlights the necessity of solving critical issues such as the multi-scaled spatiotemporal coupling dynamics of flexible components undergoing large overall motions, the efficient motion planning and accurate control method of robots, and the thermal-mechanically coupled error verification and adjustment strategies. As such, the necessity requires a comprehensive research framework integrating theoretical analysis, numerical simulation, and ground experimental validation to realize the ultra-large space structures in a scale from 100 to 1000 m. Finally, the article outlines research priorities for the next decade, including the efficient dynamics modeling, the motion planning and control of robots in complex environments, the dynamic prediction and adjustment of multi-module closed-loop assembly, and the earth-space consistent experiment validation systems, providing systematic suggestions for promoting the on-orbit assembly technology of ultra-large space structures.
Advances in data-driven models for fatigue life prediction of metallic materials
GAN Lei, WU Hao, ZHONG Zheng
2025, 55(1): 30-79.   doi: 10.6052/1000-0992-24-025
Abstract(608) HTML(237) PDF(295)
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Fatigue life models are fundamental when assessing the integrity and reliability of engineering components made of metallic materials. Hence, a plethora of domain knowledge-driven models have been developed over the past centuries, pursuing the consistency with fatigue failure mechanisms and the rationality of mathematical expressions. They generally demonstrate physical significance and can describe the complex processes of fatigue damage evolution explicitly and comprehensively. However, with the increasing demand for the operational safety of critical components and high-performance structural materials emerging constantly, they are facing limitations in the aspects of predictive capability, application scope, and engineering practicality. As an alternative, data-driven models, under the impetus of Artificial Intelligence tide, have attained growing attention and found increasing applications in life-prediction issues under various loading patterns. Data-driven models feature their powerful ability to derive optimal explicit/implicit relationships between fatigue life with numerous influential factors, without suffering from human errors. Moreover, they can quickly discover the physical laws governing fatigue failure which are difficult to be clarified by domain knowledge-driven models. Nowadays, data-driven models are recognized as opening a new pathway for fatigue damage analysis and life prediction, being a hot spot in fatigue research. This paper reviews the progress of research in developing data-driven models for predicting the fatigue life of metallic materials. Different types of data-driven models, including pure data-driven models and knowledge informed data-driven models, are summarized, along with their distinct construction methodologies and application advantages. The future prospects and challenges in this field are also discussed.
A review of research advances in analytical methods for symmetry and conservation laws in mechanical analysis
QIU Zhiping, QIU Yu, ZHANG Peixuan
2025, 55(1): 80-112.   doi: 10.6052/1000-0992-24-033
Abstract(291) HTML(48) PDF(135)
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This paper reviews the research progress on symmetry and conservation laws in mechanical analysis. It begins by introducing Lie group symmetries in continuous systems, including the symmetries of differential equations, partial differential equations, functionals, and approximate Lie symmetries of perturbed differential equations, with practical applications demonstrated through examples. The paper then explores symmetries and conservation laws in discrete systems, focusing on the dynamics equations, Noether symmetries, Lie symmetries, and Mei symmetries, with explanations supported by specific application examples. Finally, it reviews symmetries and conservation laws in stochastic systems, discussing the symmetries of Ito and Stratonovich stochastic differential equations, particularly in the statistical sense. The aim of this paper is to provide theoretical references for subsequent research and to advance the development of related fields.
Recent advances in research on large-deformation dynamics of slender pipes conveying fluid
CHEN Wei, CAO Runqing, HU Jiachun, DAI Huliang, WANG Lin
2025, 55(1): 113-174.   doi: 10.6052/1000-0992-24-027
Abstract(906) HTML(215) PDF(257)
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Slender pipes conveying fluid are an important structure in various engineering equipment systems such as engine hydraulic device, aviation tanker, nuclear heat exchanger and offshore drilling platform. When the flow velocity is sufficiently high, the slender pipe may be subjected to flow-induced instability including buckling and flutter, which may lead to safety accidents in serious cases. Flow-induced instability and nonlinear vibration of pipes conveying fluid are typical fluid-structure interaction behaviors, and have become a generic paradigm and fertile dynamics problem in nonlinear dynamics and fluid-structure interaction mechanics. After establishing governing equation, clarifying the stability mechanism and analyzing the nonlinear vibration mechanism of pipes conveying fluid, much attention has been payed to the large-deformation dynamics of this dynamical system in recent years. In this review, the research progress of nonlinear vibrations, especially the large-deformation bending dynamics of slender pipes are systematically introduced. Firstly, the nonlinear characteristics and classification of the fluid-conveying pipe system are summarized, and the applicability of some common assumptions is briefly analyzed. Secondly, the Taylor expansion approximation model, geometrically exact model, absolute node coordinate formulation model, data-driven model and other related modeling and solving methods are reviewed. Then, the nonlinear dynamics mechanism and evolution law of cantilevered and supported pipes are reviewed, and some recent research progress of cantilevered pipes from small-deformation hypothesis to large-deformation response is emphasized. On this basis, several typical methods of improving the stability of the pipe, suppressing the nonlinear vibrations of the pipe and utilizing the large-deformation response of the pipe are also introduced. Finally, the research status of large-deformation dynamics of slender pipe conveying fluid is summarized, and several basic scientific problems worthy of attention are pointed out.
Research progress on the stability mechanism and control of ventilated supercavitation
WANG Zhiying, WANG Jingzhu, HUANG Jian, WANG Zhan, WANG Yiwei
2025, 55(1): 175-217.   doi: 10.6052/1000-0992-24-024
Abstract(420) HTML(111) PDF(164)
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Ventilated supercavity drag reduction is a key technology to break through the traditional underwater speed limit and achieve high-speed operation of underwater vehicles, which has important engineering application value. The navigation stability of underwater vehicles is a bottleneck problem that restricts the development of supercavitating vehicles, which is closely related to the stability of ventilated supercavity. Therefore, accurate prediction and control of supercavity shape are one of the key factors in the overall design of supercavitating vehicles. This paper first introduces the research progress on the flow morphology characteristics of ventilated supercavities under different flow conditions, and further sorts out the key scientific issues that affect the flow morphology, including the characteristics and stability mechanism of the cavity interface, the closure mechanism of the supercavity, and the interaction between the jet and the supercavity. Finally, based on the understanding and recognition of the morphology of ventilated supercavities, a method for achieving flow control of ventilated supercavities is introduced.
News
Overview of proposal applications, peer review and funding of discipline of mechanics, NSFC in 2024
CHEN Meng, WEN Xin, LI Jianqing, MAO Jiajia, MEI Qichang, ZHANG Panfeng
2025, 55(1): 218-227.   doi: 10.6052/1000-0992-25-004
Abstract(2113) HTML(208) PDF(1461)
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This paper summarizes and analyzes statistically the applications, peer reviews and funding of the discipline of mechanics of National Natural Science Foundation of China in 2024, and also reports the progress reforms and problems during the project review. The objective is to draw wide attentions from scientists in the communities of mechanics, and work together to advance the funding progress in the discipline of mechanics of NSFC.
2025, 55(1): 228-230.  
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