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Nonlinear analysis of cable structures using the dynamic relaxation method

Mohammad REZAIEE-PAJAND, Mohammad MOHAMMADI-KHATAMI

《结构与土木工程前沿（英文）》 2021年第15卷第1期页码 253-274 doi: 10.1007/s11709-020-0639-y

摘要： The analysis of cable structures is one of the most challenging problems for civil and mechanical engineers. Because they have highly nonlinear behavior, it is difficult to find solutions to these problems. Thus far, different assumptions and methods have been proposed to solve such structures. The dynamic relaxation method (DRM) is an explicit procedure for analyzing these types of structures. To utilize this scheme, investigators have suggested various stiffness matrices for a cable element. In this study, the efficiency and suitability of six well-known proposed matrices are assessed using the DRM. To achieve this goal, 16 numerical examples and two criteria, namely, the number of iterations and the analysis time, are employed. Based on a comprehensive comparison, the methods are ranked according to the two criteria. The numerical findings clearly reveal the best techniques. Moreover, a variety of benchmark problems are suggested by the authors for future studies of cable structures.

关键词： nonlinear analysis cable structure stiffness matrix dynamic relaxation method

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Finding buckling points for nonlinear structures by dynamic relaxation scheme

Mohammad REZAIEE-PAJAND, Hossein ESTIRI

《结构与土木工程前沿（英文）》 2020年第14卷第1期页码 23-61 doi: 10.1007/s11709-019-0549-z

摘要： Dynamic Relaxation Method (DRM) is an explicit approach for solving the simultaneous systems of equations. In this tactic, the fictitious mass and damping are added to the static governing equations, and an artificial dynamic system is constructed. By using DRM for nonlinear analysis, the structural static equilibrium path is obtained. This outcome is extremely valuable, since it leads to the behavior of structures. Among the finding related to the structural static path are the critical and buckling points for nonlinear structures. In this paper, a new way for calculating the load factor is proposed by setting the external work zero. Mixing the dynamic relaxation scheme with external work technique has not been formulated so far. In all incremental-iterative methods, the load factor increment sign should be determinated by extra calculations. This sign leads to increase or decrease of the load increment. It is worth emphasizing that sign of the load factor increment changes at the load limit points. Therefore, the sign determinations are required in the common work control methods. These disadvantages are eliminated in the proposed algorithm. In fact, the suggested load factor depends only on the Dynamic Relaxation (DR) fictitious parameters. Besides, all DR calculations are performed via vector operation. Moreover, the load factor is calculated only by one formula, and it has the same relation in the all solution processes. In contrast to the arc length techniques, which requires the sign determined, the proposed scheme does not need any sign finding. It is shown that author’s technique is quicker than the other dynamic relaxation strategies. To prove the capability and efficiency of the presented scheme, several numerical tests are performed. The results indicate that the suggested approach can trace the complex structural static paths, even in the snap-back and snap-through parts.

关键词： load factor external work dynamic relaxation static equilibrium path large displacement

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A fast and accurate dynamic relaxation scheme

Mohammad REZAIEE-PAJAND, Mohammad MOHAMMADI-KHATAMI

《结构与土木工程前沿（英文）》 2019年第13卷第1期页码 176-189 doi: 10.1007/s11709-018-0486-2

摘要： Dynamic relaxation method (DRM) is one of the suitable numerical procedures for nonlinear structural analysis. Adding the fictitious inertia and damping forces to the static equation, and turning it to the dynamic system, are the basis of this technique. Proper selection of the DRM artificial factors leads to the better convergence rate and efficient solutions. This study aims to increase the numerical stability, and to decrease the analysis time. To fulfil this objective, the reduction rate of analysis error for consecutive iterations is minimized. Based on this formulation, a new time step is found for the viscous dynamic relaxation. After combining this novel relationship with the other DRM factors, various geometrical nonlinear structures, such as, trusses, frames and shells are analyzed. The obtained results verify the efficiency of authors’ scheme.

关键词： viscous dynamic relaxation time step displacement error geometric nonlinear analysis

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Deformation control criterion of shield tunnel under lateral relaxation of soft soil

《结构与土木工程前沿（英文）》 2023年第17卷第5期页码 780-795 doi: 10.1007/s11709-023-0944-3

摘要： Metro shield tunnels under the lateral relaxation of soil (LRS) are susceptible to significant lateral deformations, which jeopardizes the structural safety and waterproofing. However, deformation control standards for such situations have not been clearly defined. Therefore, based on a specific case, a model test is conducted to realize the LRS of a shield tunnel in a sandy stratum to reveal its effect on segment liners. Subsequently, a deformation control criterion is established. The LRS is simulated by linearly reducing the loads applied to the lateral sides of the segment structure. During lateral unloading, the lateral earth pressure coefficient on the segment decreases almost exponentially, and the structural deformation is characterized by horizontal expansion at the arch haunches and vertical shrinkage at the arch vault and arch bottom. Based on the mechanical pattern of the segment structure and the acoustic emission, the deformation response of a segment can be classified into three stages: elastic and quasi-elastic, damage, and rapid deformation development. For a shield tunnel with a diameter of approximately 6 m and under the lateral relaxation of sandy soil, when the ellipticity of the segment is less than 2.71%, reinforcement measures are not required. However, the segment deformation must be controlled when the ellipticity is 2.71% to 3.12%; in this regard, an ellipticity of 3% can be used as a benchmark in similar engineering projects.

关键词： shield tunnel lateral relaxation of soil deformation control criterion of segment structure model test

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Dynamic simulation based optimized design method of concrete production system for RCC dam

ZHAO Chunju, ZHOU Yihong

《结构与土木工程前沿（英文）》 2007年第1卷第4期页码 405-410 doi: 10.1007/s11709-007-0055-6

摘要： The construction system of roller compacted concrete (RCC) dam is running according to a series of connected procedures which are highly impacted and interacted consisting with the resource level. Therefore, a dynamic simulation mode

关键词： interacted dynamic simulation construction resource RCC

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The stress relaxation of cement clinkers under high temperature

Xiufang WANG,Yiwang BAO,Xiaogen LIU,Yan QIU

《机械工程前沿（英文）》 2015年第10卷第4期页码 413-417 doi: 10.1007/s11465-015-0357-7

摘要：

The energy consumption of crushing is directly affected by the mechanical properties of cement materials. This research provides a theoretical proof for the mechanism of the stress relaxation of cement clinkers under high temperature. Compression stress relaxation under various high temperatures is discussed using a specially developed load cell, which can measure stress and displacement under high temperatures inside an autoclave. The cell shows that stress relaxation dramatically increases and that the remaining stress rapidly decreases with an increase in temperature. Mechanical experiments are conducted under various temperatures during the cooling process to study the changes in the grinding resistance of the cement clinker with temperature. The effects of high temperature on the load-displacement curve, compressive strength, and elastic modulus of cement clinkers are systematically studied. Results show that the hardening phenomenon of the clinker becomes apparent with a decrease in temperature and that post-peak behaviors manifest characteristics of the transformation from plasticity to brittleness. The elastic modulus and compressive strength of cement clinkers increase with a decrease in temperature. The elastic modulus increases greatly when the temperature is lower than 1000 °C. The compressive strength of clinkers increases by 73.4% when the temperature drops from 1100 to 800 °C.

关键词： stress relaxation high temperature cement clinker compression elastic modulus

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Separating method and dynamic processes of Nano-Al13

GAO Baoyu, YUE Qinyan, WANG Xiaona, CHU Yongbao, KONG Chunyan

《环境科学与工程前沿（英文）》 2007年第1卷第3期页码 368-373 doi: 10.1007/s11783-007-0063-8

摘要： In order to investigate the characteristics of pure Nano-Al, Nano-Al was separated and purified from a series of poly-aluminum chloride (PAC) solutions which had the same Al percentage but different total Al concentrations, by using column chromatography, ethanol-acetone resolving and SO/Ba displacement. The Al species yield was characterized by Al-ferron timed complexation spectrophotometry and Al-NMR (nuclear magnetic resonance). The coagulation efficiency of Nano-Al, PAC and AlCl in synthetic water was also investigated by Jar tests. The dynamic process and aggregation state of kaolin suspensions coagulating with Nano-Al, PAC and AlCl were similarly investigated using a photometric dispersion analyzer 2000 (PDA2000). The experimental results indicated that the ethanol-acetone resolving method was simple and could separate the PAC solution at different concentrations, while column chromatography could separate PAC solutions at low concentrations. The SO/Ba displacement method could separate PAC solutions at high concentrations. However, extra inorganic cation and anion could be added in the solution during separation. The coagulation efficiency and dynamic experimental results showed that Nano-Al with high positive-charged species was effective in removing turbidity and color. The dynamic process results showed that Nano-Al also had the best recovery capability after shearing compared with PAC and AlCl because the Nano-Al conformation is more effective in charge neutralization.

关键词： displacement PAC coagulation efficiency poly-aluminum inorganic

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An efficient method for the dynamic interaction of open structure-foundation systems

LIU Jingbo, GU Yin, LI Bin, WANG Yan

《结构与土木工程前沿（英文）》 2007年第1卷第3期页码 340-345 doi: 10.1007/s11709-007-0045-8

摘要： The structure-foundation system is transformed from an original open system into an approximately hermetic system through a viscous-spring artificial boundary. In addition, the seismic wave scattering problem is changed to a wave source problem by employing an equivalent seismic wave input method. Subsequently, the modal superposition method is adopted to solve the approximated hermetic system. This procedure is highly efficient in analyzing dynamic structure-foundation interaction problems in the time domain. Two numerical examples are presented to illustrate the characteristics of the proposed method: one is a wave source problem in 2-dimensions (2-D) elastic semi-infinite space, and the other is a dynamic structure-foundation interaction problem under seismic excitations. Compared with the traditional direct step-by-step integration method, the proposed method, with a sufficient number of modes included, can significantly reduce the computational time with almost the same precision. The results also indicate that the proposed method is more advantageous for solving large structure-foundation systems of many degrees of freedom.

关键词： structure-foundation interaction superposition interaction problem freedom efficient

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Identification of dynamic stiffness matrix of bearing joint region

Feng HU, Bo WU, Youmin HU, Tielin SHI

《机械工程前沿（英文）》 2009年第4卷第3期页码 289-299 doi: 10.1007/s11465-009-0064-3

摘要： The paper proposes an identification method of the dynamic stiffness matrix of a bearing joint region on the basis of theoretical analysis and experiments. The author deduces an identification model of the dynamic stiffness matrix from the synthetic substructure method. The dynamic stiffness matrix of the bearing joint region can be identified by measuring the matrix of frequency response function (FRFs) of the substructure (axle) and whole structure (assembly of the axle, bearing, and bearing housing) in different positions. Considering difficulty in measuring angular displacement, applying moment, and directly measuring relevant FRFs of rotational degree of freedom, the author employs an accurately calibrated finite element model of the unconstrained structure for indirect estimation. With experiments and simulation analysis, FRFs related with translational degree of freedom, which is estimated through the finite element model, agrees with experimental results, and there is very high reliability in the identified dynamic stiffness matrix of the bearing joint region.

关键词： frequency response function (FRFs) dynamic stiffness finite element synthetic substructure method joint region

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Improved numerical method for time domain dynamic structure-foundation interaction analysis based onscaled boundary finite element method

DU Jianguo, LIN Gao

《结构与土木工程前沿（英文）》 2008年第2卷第4期页码 336-342 doi: 10.1007/s11709-008-0054-2

摘要： Based on the reduced set of base function in scaled boundary finite element method (SBFEM), an improved time domain numerical approach for the dynamic structure-foundation interaction analysis was proposed. With reasonable choice of the number of base functions, the degrees of freedom on the structure-foundation interface were reduced and the associated computation for the calculation of convolution integral was greatly reduced. The results of this proposed approach applied to the calculation of a gravity dam and an arch dam. The acceleration frequency response functions were calculated and the influences affected by different reduced set of base functions as well as full set were compared. It was found that a higher degree of reduced set of base functions resulted in a significant increase of computational efficiency but a little bit of loss in accuracy. When the reduced set was decreased by 60%, the efficiency may be increased to up to five times, while the loss of accuracy of peak value of response will be less than 4%. It may be concluded that the proposed approach is suitable for large-scale structure-foundation interaction analysis.

关键词： structure-foundation interface computational efficiency different suitable numerical approach

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Explicit finite element method for calculation and analysis to the elasto-plastic dynamic response of

LI Liang, DU Xiuli, LI Liyun, ZHAO Chenggang

《结构与土木工程前沿（英文）》 2007年第1卷第4期页码 436-442 doi: 10.1007/s11709-007-0059-2

摘要： In order to describe the elasto-plastic dynamic response of fluid-saturated porous media, the incremental elasto-plastic wave propagation equations of fluid-saturated porous media are developed by the fundamental theory of continuum mechanics and appointing to the characteristic of fluid-saturated porous media. Then, the space discretization of these equations is performed to get their Galerkin formula. At last, the time discretization of this formula is carried out with the integral method which consists of central difference method and Newmark constant average acceleration method to get the explicit time integral formula for solving the wave propagation equations of porous media. On the basis of the integral formula mentioned above, the time-domain explicit finite element method is developed for calculation and analysis of the elasto-plastic dynamic response of fluid-saturated porous media. In this method, the decoupling technique is adopted and it does not need to solve simultaneous linear equations in each time step, so the computational effort and memory requirement can be reduced considerably by using this method.

关键词： discretization computational calculation integral requirement

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A block zero-padding method based on DCFT for L1 parameter estimations in weak signal and high dynamic

Chao WU,Lu-ping XU,Hua ZHANG,Wen-bo ZHAO

《信息与电子工程前沿（英文）》 2015年第16卷第9期页码 796-804 doi: 10.1631/FITEE.1500058

摘要： Weak L1 signal acquisition in a high dynamic environment primarily faces a challenge: the integration peak is negatively influenced by the possible bit sign reversal every 20 ms and the frequency error. The block accumulating semi-coherent integration of correlations (BASIC) is a state-of-the-art method, but calculating the inter-block conjugate products restricts BASIC in a low signal-to-noise ratio (SNR) acquisition. We propose a block zero-padding method based on a discrete chirp-Fourier transform (DCFT) for parameter estimations in weak signal and high dynamic environments. Compared with the conventional receiver architecture that uses closed-loop acquisition and tracking, it is more suitable for open-loop acquisition. The proposed method combines DCFT and block zero-padding. In this way, the post-correlation signal is coherently post-integrated with the bit sequence stripped off, and the high dynamic parameters are precisely estimated using the threshold set based on a false alarm probability. In addition, the detection performance of the proposed method is analyzed. Simulation results show that compared with the BASIC method, the proposed method can precisely detect the high dynamic parameters in lower SNR when the length of the received signal is fixed.

关键词： Threshold detection Discrete chirp-Fourier transform Block zero-padding High dynamic Weak L1 signal acquisition

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A dynamic model of mobile concrete pump boom based on discrete time transfer matrix method

Wu REN, Yunxin WU, Zhaowei ZHANG

《机械工程前沿（英文）》 2013年第8卷第4期页码 360-366 doi: 10.1007/s11465-013-0280-8

摘要：

Mobile concrete pump boom is typical multi-body large-scale motion manipulator. Due to posture constantly change in working process, kinematic rule and dynamic characteristic are difficult to solve. A dynamics model of a mobile concrete pump boom is established based on discrete time transfer matrix method (DTTMM). The boom system is divided into sub-structure A and sub-structure B. Sub-structure A is composed by the 1st boom and hydraulic actuator as well as the support. And sub-structure B is consists of the other three booms and corresponding hydraulic actuators. In the model, the booms and links are regarded as rigid elements and the hydraulic cylinders are equivalent to spring-damper. The booms are driven by the controllable hydraulic actuators. The overall dynamic equation and transfer matrix of the model can be assembled by sub-structures A and B. To get a precise result, step size and integration parameters are studied then. Next the tip displacement is calculated and compared with the result of ADAMS software. The displacement and rotation angle curves of the proposed method fit well with the ADAMS model. Besides it is convenient in modeling and saves time. So it is suitable for mobile concrete pump boom real-time monitoring and dynamic analysis. All of these provide reference to boom optimize and engineering application of such mechanisms.

关键词： multi-body mobile concrete pump boom discrete time transfer matrix method (DTTMM) kinematic dynamic tip displacement

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动态规划的正向递推方法

张钊,裴燕玲,张仁宝

《中国工程科学》 2005年第7卷第2期页码 62-65

摘要：

动态规划求最优解是一个反向递推的求解过程，以实例为依据，用正向递推的方法求解动态规划的最优值，并推出动态规划的基本方程和密尔顿-雅可比方程，是对动态规划求最优解方法的探讨。利用动态规划的正向递推方法，在应用中可以大大减少计算量，扩大了它的应用范围。

关键词：动态规划多级决策泛函最优值

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Evaluation of site response characteristic using nonlinear method (Case study: Babol, Iran)

Asskar Janalizadeh CHOOBBASTI, Sadegh REZAEI, Farzad FARROKHZAD, Pedram Haidarzaeh AZAR

《结构与土木工程前沿（英文）》 2014年第8卷第1期页码 69-82 doi: 10.1007/s11709-014-0231-4

摘要： In this the present study, an attempt has been made to evaluate the seismic hazard considering local site effects by carrying out detailed geotechnical site characterization in Babol, Iran. Use of geotechnical data and synthesis of drilling data extracted from the Babol’s subsurface database have enabled authors to determine the geotechnical properties of each site. These data are consisted of twenty five boreholes up to depth of 40 m. Based on the obtained data from geotechnical investigation the study area is divided to five zones. Dynamic analysis was performed in time domain, using fully nonlinear model by PLAXIS. A series of analysis in the study area showed the site period, ranging from 0.4 to 0.8 s. Finally the obtained response spectra from fully nonlinear method were compared with site response spectra of Iran’s 2800 (earthquake) code.

关键词： fully nonlinear method site effect dynamic analysis response spectra