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The smoothed finite element method (S-FEM): A framework for the design of numerical models for desired solutions

Gui-Rong Liu

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 456-477 doi: 10.1007/s11709-019-0519-5

摘要：

The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects; 2) upper-bound solutions; 3) accurate solutions and higher convergence rates; 4) insensitivity to mesh distortion; 5) Jacobian-free; 6) volumetric-locking-free; and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on AI-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

关键词： computational method finite element method smoothed finite element method strain smoothing technique smoothing domain weakened weak form solid mechanics softening effect upper bound solution

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Adaptive selective ES-FEM limit analysis of cracked plane-strain structures

H. NGUYEN-XUAN,T. RABCZUK

《结构与土木工程前沿（英文）》 2015年第9卷第4期页码 478-490 doi: 10.1007/s11709-015-0317-7

摘要： This paper presents a simple and efficient approach for predicting the plastic limit loads in cracked plane-strain structures. We use two levels of mesh repartitioning for the finite element limit analysis. The master level handles an adaptive primal-mesh process through a dissipation-based indicator. The slave level performs the subdivision of each triangle into three sub-triangles and constitutes a dual mesh from a pair of two adjacent sub-triangles shared by common edges of the primal mesh. Applying a strain smoothing projection to the strain rates on the dual mesh, the incompressibility constraint and the flow rule constraint are imposed over the edge-based smoothing domains and everywhere in the problem domain. The limit analysis problem is recast into the compact form of a second-order cone programming (SOCP) for the purpose of exploiting interior-point solvers. The present method retains a low number of optimization variables. It offers a convenient way for designing and solving the large-scale optimization problems effectively. Several benchmark examples are given to show the simplicity and effectiveness of the present method.

关键词： cracked structure limit analysis von Mises criterion edge-based strain smoothing second-order cone programming adaptive

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A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations

Dongdong WANG, Jiarui WANG, Junchao WU, Junjun DENG, Ming SUN

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 337-352 doi: 10.1007/s11709-018-0467-5

摘要： A three-dimensional two-level gradient smoothing meshfree method is presented for rainfall induced landslide simulations. The two-level gradient smoothing for meshfree shape function is elaborated in the three-dimensional Lagrangian setting with detailed implementation procedure. It is shown that due to the successive gradient smoothing operation without the requirement of derivative computation in the present formulation, the two-level smoothed gradient of meshfree shape function is capable of achieving a given influence domain more efficiently than the standard gradient of meshfree shape function. Subsequently, the two-level smoothed gradient of meshfree shape function is employed to discretize the weak form of coupled rainfall seepage and soil motion equations in a nodal integration format, as provides an efficient three-dimensional regularized meshfree formulation for large deformation rainfall induced landslide simulations. The exponential damage and pressure dependent plasticity relationships are utilized to describe the failure evolution in landslides. The plastic response of soil is characterized by the true effective stress measure, which is updated according to the rotationally neutralized objective integration algorithm. The effectiveness of the present three-dimensional two-level gradient smoothing meshfree method is demonstrated through numerical examples.

关键词： meshfree method landslide rainfall three-dimensional two-level gradient smoothing nodal integration

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应用指数平滑技术预测边坡位移

沈良峰

《中国工程科学》 2007年第9卷第6期页码 94-97

摘要：

应用趋势型指数平滑模型根据其观测值的数据特点（具线性趋势），选取趋势型二次指数平滑的线性预测公式和相应at，bt的计算公式及合适的平滑系数值进行计算，预测了某市滑坡区５号监测点的位移量。预测结果表明，该方法应用于斜坡变形位移的预测，可使预测值与实际位移值之间的误差很小。

关键词：指数平滑预测边坡位移自适应过滤

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Concepts and implementation of strain-based criteria in design codes for steel structures

Reidar BJORHOVDE

《结构与土木工程前沿（英文）》 2012年第6卷第3期页码 210-216 doi: 10.1007/s11709-012-0165-7

摘要： A uniaxial tension test is commonly used to determine the mechanical properties of steel, but it has no meaning for the response of the material in a structure. The test was developed as a consensus solution by producers, fabricators, designers and code writers, to have a standard by which similar materials could be compared to a common base. It does not represent the actual behavior of the steel in a structure, and was never intended to do so. To study the true behavior of the structure and how the material responds it would be better to determine the strains and deformations that will take place during actual service condition. Such characteristics reflect the real behavior, whether in the elastic or inelastic range. If stresses or forces are needed, these are easily determined by the value of the strain and the relevant material modulus, along with the type of cross section, whether elastic or inelastic. The paper addresses the properties of a range of structural steels, how these are incorporated into design standards and how the standards define deformation characteristics and demands for bolted and welded connections.

关键词： steel stress-strain characteristics tension test strain design actual behavior improved design codes

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数字散斑相关法在陶瓷材料准静态破坏行为研究中的应用

于少娟,李永池,刘颢文

《中国工程科学》 2008年第10卷第7期页码 132-136

摘要：

研究了引入高精度数字散斑相关法光学测量技术对A９５陶瓷材料在准静态压缩试验中的变形过程，得到了该材料在压缩变形过程不同时刻的试件表面的全场位移分布，推导出应力应变曲线与材料的本构关系。与传统方法相比较，数字散斑相关法所具有的非接触、高精度、全场测量等特点，避免了人为干扰，可以对试件表面全场的变形进行研究。

关键词：陶瓷材料；数字散斑相关法；应变测量

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大力测量技术的新进展——附着式超轻型大力传感器

沈久珩

《中国工程科学》 2001年第3卷第10期页码 22-27

摘要：

大力传感器是现代重型装备的高科技电子信息器件。文章围绕重型大力传感器的微型化问题论述了重型装备大力测量的意义、特征及发展，讨论了大力分流测量的物理模型，介绍了作者发明的超轻型附着式大力传感器及其工程应用。

关键词：重型装备大力传感器支承式附着式电阻应变计分流测量

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Full-field dynamic strain reconstruction of an aero-engine blade from limited displacement responses

《机械工程前沿（英文）》 2023年第18卷第1期 doi: 10.1007/s11465-022-0731-1

摘要： Blade strain distribution and its change with time are crucial for reliability analysis and residual life evaluation in blade vibration tests. Traditional strain measurements are achieved by strain gauges (SGs) in a contact manner at discrete positions on the blades. This study proposes a method of full-field and real-time strain reconstruction of an aero-engine blade based on limited displacement responses. Limited optical measured displacement responses are utilized to reconstruct the full-field strain. The full-field strain distribution is in-time visualized. A displacement-to-strain transformation matrix is derived on the basis of the blade mode shapes in the modal coordinate. The proposed method is validated on an aero-engine blade in numerical and experimental cases. Three discrete vibrational displacement responses measured by laser triangulation sensors are used to reconstruct the full-field strain over the whole operating time. The reconstructed strain responses are compared with the results measured by SGs and numerical simulation. The high consistency between the reconstructed and measured results demonstrates the accurate strain reconstructed by the method. This paper provides a low-cost, real-time, and visualized measurement of blade full-field dynamic strain using displacement response, where the traditional SGs would fail.

关键词： aero-engine blade displacement response dynamic strain reconstruction mode shape strain gauge

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Smoothing ramp events in wind farm based on dynamic programming in energy internet

Jiang LI, Guodong LIU, Shuo ZHANG

《能源前沿（英文）》 2018年第12卷第4期页码 550-559 doi: 10.1007/s11708-018-0593-8

摘要：

The concept of energy internet has been gradually accepted, which can optimize the consumption of fossil energy and renewable energy resources. When wind power is integrated into the main grid, ramp events caused by stochastic wind power fluctuation may threaten the security of power systems. This paper proposes a dynamic programming method in smoothing ramp events. First, the energy internet model of wind power, pumped storage power station, and gas power station is established. Then, the optimization problem in the energy internet is transformed into a multi-stage dynamic programming problem, and the dynamic programming method proposed is applied to solve the optimization problem. Finally, the evaluation functions are introduced to evaluate pollutant emissions. The results show that the dynamic programming method proposed is effective for smoothing wind power and reducing ramp events in energy internet.

关键词： energy internet wind power ramp events dynamic programming

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Strain and process engineering toward continuous industrial fermentation

《化学科学与工程前沿（英文）》 2023年第17卷第10期页码 1336-1353 doi: 10.1007/s11705-022-2284-6

摘要： Most current biotechnology industries are based on batch or fed-batch fermentation processes, which often show low productivity and high production costs compared to chemical processes. To increase the economic competitiveness of biological processes, continuous fermentation technologies are being developed that offer significant advantages in comparison with batch/fed-batch fermentation processes, including: (1) removal of potential substrates and product inhibition, (2) prolonging the microbial exponential growth phase and enhancing productivity, and (3) avoiding repeated fermentation preparation and lowering operation and installation costs. However, several key challenges should be addressed for the industrial application of continuous fermentation processes, including (1) contamination of the fermentation system, (2) degeneration of strains, and (3) relatively low product titer. In this study, we reviewed and discussed metabolic engineering and synthetic biology strategies to address these issues.

关键词： continuous fermentation productivity contamination strain degeneration metabolic engineering

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Behavior of steel fiber–reinforced high-strength concrete at medium strain rate

Chujie JIAO, Wei SUN, Shi HUAN, Guoping JIANG

《结构与土木工程前沿（英文）》 2009年第3卷第2期页码 131-136 doi: 10.1007/s11709-009-0027-0

摘要： Impact compression experiments for the steel fiber–reinforced high-strength concrete (SFRHSC) at medium strain rate were conducted using the split Hopkinson press bar (SHPB) testing method. The volume fractions of steel fibers of SFRHSC were between 0 and 3%. The experimental results showed that, when the strain rate increased from threshold value to 90 s , the maximum stress of SFRHSC increased about 30%, the elastic modulus of SFRHSC increased about 50%, and the increase in the peak strain of SFRHSC was 2-3 times of that in the matrix specimen. The strength and toughness of the matrix were improved remarkably because of the superposition effect of the aggregate high-strength matrix and steel fiber high-strength matrix. As a result, under impact loading, cracks developed in the SFRHSC specimen, but the overall shape of the specimen remained virtually unchanged. However, under similar impact loading, the matrix specimens were almost broken into small pieces.

关键词： steel fiber–reinforced high-strength concrete (SFRHSC) high strain rates split Hopkinson press bar (SHPB) strain rate hardening effects

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Vibration analysis of nano-structure multilayered graphene sheets using modified strain gradient theory

Amir ALLAHBAKHSHI,Masih ALLAHBAKHSHI

《机械工程前沿（英文）》 2015年第10卷第2期页码 187-197 doi: 10.1007/s11465-015-0339-9

摘要：

In this paper, for the first time, the modified strain gradient theory is used as a new size-dependent Kirchhoff micro-plate model to study the effect of interlayer van der Waals (vdW) force for the vibration analysis of multilayered graphene sheets (MLGSs). The model contains three material length scale parameters, which may effectively capture the size effect. The model can also degenerate into the modified couple stress plate model or the classical plate model, if two or all of the material length scale parameters are taken to be zero. After obtaining the governing equations based on modified strain gradient theory via principle of minimum potential energy, as only infinitesimal vibration is considered, the net pressure due to the vdW interaction is assumed to be linearly proportional to the deflection between two layers. To solve the governing equation subjected to the boundary conditions, the Fourier series is assumed for w=w(x, y). To show the accuracy of the formulations, present results in specific cases are compared with available results in literature and a good agreement can be seen. The results indicate that the present model can predict prominent natural frequency with the reduction of structural size, especially when the plate thickness is on the same order of the material length scale parameter.

关键词： graphene van der Waals (vdW) force modi- fied strain gradient elasticity theory size effect parameter

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FEM-based strain analysis study for multilayer sheet forming process

Rongjing ZHANG,Lihui LANG,Rizwan ZAFAR

《机械工程前沿（英文）》 2015年第10卷第4期页码 373-379 doi: 10.1007/s11465-015-0371-9

摘要：

Fiber metal laminates have many advantages over traditional laminates (e.g., any type of fiber and resin material can be placed anywhere between the metallic layers without risk of failure of the composite fabric sheets). Furthermore, the process requirements to strictly control the temperature and punch force in fiber metal laminates are also less stringent than those in traditional laminates. To further explore the novel method, this study conducts a finite element method-based (FEM-based) strain analysis on multilayer blanks by using the 3A method. Different forming modes such as wrinkling and fracture are discussed by using experimental and numerical studies. Hydroforming is used for multilayer forming. The Barlat 2000 yield criteria and DYNAFORM/LS-DYNA are used for the simulations. Optimal process parameters are determined on the basis of fixed die-binder gap and variable cavity pressure. The results of this study will enhance the knowledge on the mechanics of multilayer structures formed by using the 3A method and expand its commercial applications.

关键词： finite element method (FEM) strain analysis multilayer sheet forming

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Stress-strain relationship of concrete in freeze-thaw environment

ZOU Chaoying, ZHAO Juan, LIANG Feng

《结构与土木工程前沿（英文）》 2008年第2卷第2期页码 184-188 doi: 10.1007/s11709-008-0029-3

摘要： Adopting the ASTM C666 quick freeze-thaw method, freeze-thaw tests with the number of freeze-thaw cycles being 0, 100, 150, 200, 250, and 300, were carried out on eighteen concrete prism specimens, the frost-resistant level of which, reaches D300 grade. The internal micro-structures of these specimens were observed by means of scanning electron microscopy (SEM) in order to detect damages caused by the freeze-thaw action. Afterwards these frozen-thawed specimens were tested on monotonic axial load; stress-strain testing curves after the freeze-thaw action were obtained. The testing results show that with the increasing time of freeze-thaw cycles, both the internal micro-structures and the basic mechanical parameters, including the ultimate bearing capacity, the Poisson ratio and the modulus of elasticity, degenerate in various degrees. Finally, stress-strain theoretical curvilinear equations and correlated parameters relating to the loss of relative dynamic modulus of elasticity were proposed. These results provide great reference for further research on the behavior and the calculation model of concrete structures in a freeze-thaw environment.

关键词： stress-strain theoretical freeze-thaw capacity reference eighteen concrete

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Fictitious soil pile model for dynamic analysis of pipe piles under high-strain conditions

《结构与土木工程前沿（英文）》页码 915-934 doi: 10.1007/s11709-023-0907-8

摘要： A fictitious soil pile (FSP) model is developed to simulate the behavior of pipe piles with soil plugs undergoing high-strain dynamic impact loading. The developed model simulates the base soil with a fictitious hollow pile fully filled with a soil plug extending at a cone angle from the pile toe to the bedrock. The friction on the outside and inside of the pile walls is distinguished using different shaft models, and the propagation of stress waves in the base soil and soil plug is considered. The motions of the pile−soil system are solved by discretizing them into spring-mass model based on the finite difference method. Comparisons of the predictions of the proposed model and conventional numerical models, as well as measurements for pipe piles in field tests subjected to impact loading, validate the accuracy of the proposed model. A parametric analysis is conducted to illustrate the influence of the model parameters on the pile dynamic response. Finally, the effective length of the FSP is proposed to approximate the affected soil zone below the pipe pile toe, and some guidance is provided for the selection of the model parameters.

关键词： fictitious soil pile soil plug pipe piles high-strain dynamic analysis one-dimensional wave theory pile dynamics