Incremental Displacement Research Articles

Research on UWB fusion location algorithm

In order to solve the problem that ultra-wideband (ultra-wideband, UWB) positioning is greatly affected by the environment in the indoor environment of mobile robot, an indoor positioning algorithm based on UWB, odometer and inertial measurement unit is proposed. Taking advantage of the high positioning accuracy of UWB in indoor environment and the high accuracy of odometer positioning in a small range, the adaptive parameter equation of error is constructed by using linear regression function. The weight coefficient is obtained by combining the position data solved by UWB and the previous moment fusion algorithm to solve the position difference and the mileage displacement formula, and the weight value of angle increment is given according to the state of the system. Through the calculation, the displacement increment matrix of each measurement of the system is obtained, and the final linear optimal value is obtained by substituting the extended Kalman filter algorithm. Compared with the single UWB positioning method, the results show that the system can maintain good accuracy and robustness, and the mean error of the whole system is less than 8cm, which provides a solution for the single UWB positioning of mobile robot affected by NLOS error.

The Instability of High-Steep Road Cutting Slope: A 3D Continuum-Discrete Coupling Method

In this paper, the 3D continuum-discrete coupling analysis method combined with the strength reduction theory is used to study the macrodeformation, stress law, and microfracture mechanism of a high and steep cutting slope of Zhongkai Expressway in Guangdong Province. The 3D continuum-discrete coupling slope model is established based on the finite difference software FLAC and the discrete element program PFC. Then, based on the correlations between stress tensor and force chain, displacement and shear strain increment, plastic deformation, and microfracture, the mechanism of slope instability is analyzed from macro- and microscales. The research shows the following: (1) the continuum-discrete coupling model is reasonable and effective in the three-dimensional slope stability analysis. (2) The coupling domain was penetrated by the shear band, and the upper part displacement of the coupling domain was large, whose direction was basically consistent with the shear band direction; thus, the slope slip surface was formed. (3) The microfracture can represent the macroscopic failure phenomenon, and the slope landslide can be interpreted as the result of shear fracture in slip direction, accompanied by the extension and penetration of tension crack.

Design of a Panoramic Scanning Device Based on a Piezoelectric Ceramic Stack Actuator and Friction Transmission

In view of the complex structure and inaccurate positioning capabilities of the existing panoramic scanning system, a panoramic scanning device based on a piezoelectric ceramic stack actuator and friction transmission was designed. In our model, the output displacement of the piezoelectric ceramics is amplified by a bridge-type flexure hinge and applied to a shaft by friction to achieve panoramic scanning imaging. The mathematical model of the device was established, and the working characteristics were analyzed. The analysis demonstrated that the linear displacement increment of the shaft is a superposition. A modality simulation was performed, and the simulation results show that the designed device works normally at a frequency of 511.5 Hz. The test results indicated that the displacement of the actuator can reach 6 μm at an input voltage of 100 V. Moreover, the laser scanning results showed that the designed device can perform panoramic scanning imaging, which meets the requirements for use on the high-speed imaging system.

Monitoring-data mechanism-driven dynamic evaluation method for slope safety

Many high and steep slopes are formed in the construction of hydropower, highway, and railway projects. The long-term safety risk management and control problems are prominent. Slope deformation monitoring is one of the means to directly characterize the safety status of a slope, so it is of great significance to use slope deformation monitoring information to accomplish the dynamic evaluation of slope safety for safe engineering operations. In this study, the aging component of the slope displacement was separated using the empirical mode decomposition method. Combined with the response surface equation and the genetic optimization algorithm, a parameter back analysis method based on the aging displacement increment of the slope was proposed, and the determined calculation parameters can better reflect the creep characteristics of rock slope. Based on the results of the back analysis parameters, the most dangerous slip surface of the slope was determined using the strength reduction method, and the time series of the safety factor of the slope was obtained. Combining the dynamic coupling relationship between the slope displacement monitoring quantity and the slope stability, a surrogate model between the safety factor of the slope and the displacement aging component was constructed for the first time. A novel monitoring-data mechanism-driven dynamic evaluation method for slope safety was proposed considering the creep characteristics of the slope. The method was applied to an engineering slope example. The relative errors of the fitting and the prediction results of the dynamic evaluation model were less than 1%. The dynamic quantitative evaluation of the slope safety based on the displacement monitoring data was achieved. This provided an effective guarantee for slope safety control.

An innovative and efficient solution for axisymmetric contact problem between structure and half-space

In this paper, with displacement increment as variables, the scaled boundary finite element equations of the axisymmetric plate and half-space are respectively derived based on the principle of virtual work. The dual vector is introduced to solve the boundary stiffness matrix. Linear complementary contact conditions are formulated as B-differentiable equations. With discrete, static assumptions of small displacement, B-differentiable equations system was formed by combining the contact conditions and the stiffness matrix of the plate-foundation. The equations can be iteratively solved by B-differentiable Newton method. In numerical experiments, the contact stress, slip and contact status of each contact node pair are compared with the results of the augmented Lagrangian contact algorithm based on FEM. When adopting different load types, thickness-to-radius ratio, plate-foundation stiffness ratio and friction coefficient, the axisymmetric contact problems between plate and half-space are discretized by 120 one-dimensional first-order elements. The applicability, accuracy and effectiveness of B-SBFEM for axisymmetric contact problems are verified by numerical examples.

Repair of a minor bridge in the state of failure with an atypical design using prestressed bridge meshes and bitumen slurry

This article discusses methodological approaches to the repair and maintenance of minor bridges with the atypical design that are in the state of failure, that doesn’t have design documentation, as well as regulatory and methodological documents for the maintenance work organization and technology. Such bridges, although in small numbers, are present on territorial and municipal road networks, for example, in the Orenburg region. The bridge floor turned out to be hydrophobic. Precipitation cannot penetrate under the asphalt concrete layer due to the loosened bitumen presence, meanwhile, the water that was under the asphalt concrete layer during the summer month came out through the asphalt concrete layer pores through pore pressure. A month after the emergency repair work, under the influence of high summer temperature and mechanical load from passing vehicles, the consolidation processes associated with the evaporation of water were completed, and the loosened bitumen turned into a film state. In the limit of a cold wet asphalt mix based on dispersed viscous bitumen, the conventional hot asphalt concretes properties are achieved. Setting smooth, durable, and waterproof coating allows for minimizing the passing traffic dynamic effects, significantly slowing down the destructive processes in the bridge’s bearing elements. For the first time, a minor bridge in the state of failure with an atypical design was repaired by grouting the soil ground around the bridge supports with a liquefied bitumen slurry to a 0.5 m depth, which made it possible to ensure its equal strength. At the same time, the dispersion degree for this project was 1–10 microns due to the bituminous slurry preparation specifics. New is the setting of a hydrophobic double-layered bridge floor without a waterproofing layer from a cold wet asphalt concrete mixture based on dispersed viscous bitumen and the use of a bridge mesh. The possibility of using bitumen-cement-concrete nonshrinking mixtures in the repair of the bridge masonry is shown. The bridge floor geometry was selected for the shockless mode of the existing traffic flow, with the account of the velocity squared of traffic, the bridge floor height, the sum of curvature radii, and the vehicle wheel. The possibility of using bitumen-cement-concrete non-shrinking mixtures in the repair of the masonry of a bridge structure is shown. A new result is also the reinforcing system construction for a bridge floor made of cold wet asphalt concrete based on prestressing of a metal bridge mesh that is flexible with tension in displacement increments.

Study on precursor information of rock instability based on displacement increments measured at multiple points

Study on precursor information of rock instability based on displacement increments measured at multiple points

Mapping of Temperature-Induced Response Increments for Monitoring Long-Span Steel Truss Arch Bridges Based on Machine Learning

Temperature-induced responses have been found to be sensitive to changes in bridge properties. Accordingly, researchers have sought to develop temperature-response mappings that could be used in assessing bridge conditions; to date, obtaining sufficiently precise mappings analytically has proven intractable. Alternatively, numerous researchers have directly developed mappings between temperature and the associated responses using measured data. However, temperature-induced responses are a function of the temperatures throughout the entire bridge, and such spatial temperature distributions using a limited number of sensors are challenging to capture, particularly for steel truss bridges, due to the large number and variety of structural members. Mappings that have been obtained are generally a function of the long-term fluctuations, corresponding to daily variations; the short-term fluctuations (i.e., higher-frequency components) in temperature data are neglected. This paper first proposes that the relationship between increments in temperature and the associated increments in responses can be used as a surrogate to assess the bridge performance. Simulation results show that the statistical distribution of the error between measured and predicted response increments can be used for identifying abnormal structural behavior. Then, various mappings for both displacement and strain increments are explored and verified using field monitoring data. The mapping with all temperature sensors performs the best; principal component analysis (PCA) can effectively reduce the dimension of input without compromising accuracy. In addition, the recorded time of temperature data is validated to be a useful indicator of the spatial temperature distribution in bridges, which can be used to improve the performance of the mappings when the bridge has only a few temperature sensors. These findings provide an improved approach for mapping the relationship between increments in temperature to increments in temperature-induced responses that shows promise for identifying abnormal bridge behavior.

Influence of Groundwater Depth on Pile–Soil Mechanical Properties and Fractal Characteristics under Cyclic Loading

The analysis of the behavior of soil and foundations when the piles in offshore areas are subjected to long-term lateral loading (wind) is one of the major problems associated with the smooth operation of superstructure. The strength of the pile-soil system is influenced by variations in the water content of the soil. At present, there are no studies carried out analyzing the mechanical and deformational behavior of both the material of the laterally loaded piles and soil with groundwater level as a variable. In this paper, a series of 1-g model tests were conducted to explore the lateral behavior of both soil and monopile under unidirectional cyclic loading, based on the foundation of an offshore wind turbine near the island. The influence of underground water level and cyclic load magnitude on the performance of the pile–soil system was analyzed. To visualize the movements of soil particles during the experimental process, particle image velocimetry (PIV) was used to record the soil displacement field under various cyclic loading conditions. The relationship curves between pile top displacement and cyclic steps, as well as the relationship curves between cyclic stiffness and cyclic steps, were displayed. Combined with fractal theory, the fractal dimension of each curve was calculated to evaluate the sensitivity of the pile–soil interaction system. The results showed that cyclic loading conditions and groundwater depth are the main factors affecting the pile–soil interaction. The cyclic stiffness of the soil increased in all test groups as loading progressed; however, an increase in the cyclic load magnitude decreased the initial and cyclic stiffness. The initial and cyclic stiffness of dry soil was higher than that of saturated soil, but less than that of unsaturated soil. The ability of the unsaturated soil to limit the lateral displacement of the pile decreased as the depth of the groundwater level dropped. The greater the fluctuation of the pile top displacement, the larger the fractal dimension of each relationship curve, with a variation interval of roughly 1.24–1.38. The average increment of the cumulative pile top displacement between each cycle step following the cyclic loading was positively correlated with fractal dimension. Based on the PIV results, the changes in the pile–soil system were predominantly focused in the early stages of the experiment, and the short-term effects of lateral cyclic loading are greater than the long-term effects. In addition, this research was limited to a single soil layer. The pile–soil interaction under layered soil is investigated, and the results will be used in more complex ground conditions in the future.

Partitioned path-following strategy for nonlinear structural analyses using the boundary element method

The appearance of snapping phenomena is frequent in structural analyses involving nonlinearities such as the propagation of localized damage zones, or cracks, as encountered in quasi-brittle materials. In the presence of snapping effects, the standard Newton-based algorithms cannot predict the equilibrium curves correctly by usual displacement or force control. This problem can be circumvented by using path-following techniques. This study proposes a numerical approach for nonlinear structural analysis based on the Boundary Element Method (BEM) coupled with a partitioned path-following strategy. In this strategy, the acting loads are divided into two groups: (a) those perfectly known and (b) those in which only the direction is known, while the magnitude (or load factor/multiplier) is determined to respect the equilibrium of the boundary fields (indirectly controlled) and an additional problem equation, the path-following constraint equation. The resulting nonlinear system is solved using an incremental iterative scheme. For each iteration, the corrections to the boundary fields are obtained in a partitioned manner. First, the portion coming from the unbalanced boundary fields is calculated. Then the correction resulting from a unit load in the direction of the load to be indirectly controlled is obtained. Finally, the load factor is calculated independently using the path-following constraint equation, which can be linear, nonlinear, differentiable, or not. In the numerical tests, the Control of the Nodal Displacement Increment (CNDI) is chosen as path-following constraint equation for the sake of illustration. The results show that the proposed approach can efficiently capture the equilibrium curve even in the presence of severe snap-backs. The approach is designed to be implemented in existing BEM codes straightforwardly, provided that the influence matrices can be accessed. Moreover, no additional pre-conditioning technique is required.

Closed-form critical response of undamped bilinear hysteretic MDOF system under pseudo-double impulse for estimating resonant response under one-cycle sine wave

Approximate closed-form maximum interstory drifts under the critical pseudo-double impulse (PDI) are derived for undamped multi-story shear building models with bilinear hysteresis by using the proposed updated mode-controlled energy-based approach (UMEA). PDI was proposed in the previous paper to simulate the critical responses of elastic-plastic MDOF models under near-fault fling-step motions. Although a double impulse (DI) is treated as a ground motion, PDI is treated as a set of impulsive lateral forces. PDI excites only the fundamental-mode responses of elastic proportionally-damped MDOF models because the fundamental participation vector is applied to the influence coefficient vector of PDI. UMEA is a kind of displacement control analyses, and the displacement increment, which is proportional to the fundamental mode evaluated by the tangent story stiffnesses, is given to the model. It is demonstrated that UMEA effectively captures the main characteristics of the maximum interstory drifts under the critical PDI and the critical one-cycle sine wave because most of the kinetic energy, which the fundamental mode has just before yielding, is given to the plastic fundamental mode just after yielding except for the case that the post-yielding stiffness is almost zero. The use of UMEA leads to much more efficient estimation of the maximum interstory drifts than the time-history response analysis because UMEA requires only 2N-time evaluations of the elastic and plastic fundamental modes at most for N-story shear mass models with bilinear hysteresis. It is shown through numerical examples that the maximum interstory drifts under the critical PDI and the corresponding one-cycle sine wave correspond well to those evaluated by the proposed method. It is also shown that the correspondence of the responses of elastic-plastic MDOF models under recorded near-fault motions and the estimated responses by the proposed method is fairly good.

Multi‐performance objectives optimum design method and vibration control application of generalized toggle–brace–damper system

AbstractThe toggle–brace–damper system (TBDS) is an effective displacement amplification damper occupying a large building space. The small deformation solution, which is widely used, cannot describe the feature that the displacement amplification capacity varies with the lateral displacement of the TBDS. This is not conducive to investigate the performance of the TBDS comprehensively. Therefore, the geometric design and optimization of the TBDS are lack of a theoretical basis. A generalized toggle–brace–damper system (GTBDS), a generalized form of TBDS, is proposed. It has a flexible layout and optimizes the space available. We also introduce an amplification factor of displacement increment (AFDI) that can accurately describe the performance of the GTBDS. The amplification capacity and the geometric sensitivity are two aspects of the performance. The influence of geometric parameters on the performance of the GTBDS is clarified based on the AFDI. Some regulations are also proposed to compare the performance of GTBDSs with different geometric constructions. Two geometric parameter optimization methods of the GTBDS are proposed to balance its amplification capacity, operation safety and geometric sensitivity. The relationship between the displacement amplification capacity and the energy dissipation capacity of the GTBDS is examined. The existing modal energy dissipation method (MEDM) is extended to calculate the additional damping ratio (ADR) provided by the GTBDS. Combining the calculation method of ADR and the geometric optimization methods of GTBDS, a multiperformance objectives design method of the GTBDS is proposed. The case analysis verifies the effectiveness and the feasibility of the design method.

High temperature effect of foamed concrete under equal displacement increment triaxial cyclic compression

Foamed concrete (FC) has been extensively used for its lightweight, good thermal insulation, and sound insulation properties. It has gained broad investigations in the past decades, but the data of triaxial cyclic compression tests are lacking. In this study, triaxial cyclic tests were conducted under different confining pressures (0 MPa, 0.3 MPa, 0.5 MPa, 0.8 MPa) with four temperature treatments (25 °C, 100 °C, 200 °C, 300 °C) to obtain the failure modes and stress-strain curves, analyze the compressive strength, residual strength, elastic modulus and brittleness index, explain the fracture mechanism and damage evolution of FC from the perspective of energy dissipation. Furthermore, the strength prediction model of FC was proposed and its yield criterion was verified. The results show that the damage pattern of FC was significantly influenced by confining pressure and the mechanical parameters were more sensitive to temperature. The energy density and damage increased linearly with the number of cycles, and the dissipated energy accounted for a large proportion under low confining pressure or high temperature. The Crushable-foam yield criterion had good applicability to FC, and thermal damage decreased the hydrostatic yield strength of FC.

Volcanic Ash Region Path Planning Based on Improved A-Star Algorithm

In civil aviation flight path planning, in order to effectively reduce the safety threat caused by the volcanic ash area to the civil aviation flight, factors such as the speed and acceleration of the aircraft in the volcanic ash area must be considered. In this paper, we propose an improved A-star algorithm by adopting the concept of potential collision set and using the velocity vector idea of optimal reciprocal collision avoidance (ORCA). The improved A-star algorithm selects the optimal speed range of the aircraft from the limited elements, obtains the speed and acceleration set of the aircraft in the volcanic ash area, calculates the flight path through the displacement increment, continuously refreshes the global starting point to the target point, and finally obtains the final path planning results by calculating the total cost value. The improved A-star algorithm is used to plan two flight paths from Madrid to Cairo and Algiers to Rome in volcanic ash areas. The verification results show that the improved A-star algorithm optimizes the flight path planning in the volcanic ash area and has the advantages of less search nodes, a small search range, and short computing time.

Non-Linear Analysis of Structures Utilizing Load-Discretization of Stiffness Matrix Method with Coordinate Update

This paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces incremental external nodal displacements, which are added to the corresponding coordinates to get a new geometrical shape of the structure. This process is iteratively repeated until the sum of the loading of all iterations matches the total initial applied loading. The size of the increments affects the technique’s accuracy, subsequently affecting the number of iterations. The configuration of non-linear geometrical structures is vital in the work; a slight change of the coordinates makes a considerable variation of nodal displacements. In this paper, three pin-jointed assemblies and a cantilever beam have been examined using the proposed technique; significantly reasonable outcomes emerged, compared to the non-linear approaches, such as Dynamic Relaxation Method (DRM) and Non-linear approach by Kwan. In a numerical sense, the dissimilarity between the results of the conventional Stiffness Matrix (SM) method and the non-linear method is about 228%, while the maximum discrepancy between the proposed approach and the non-linear methods is just above 15%.

Buckling of Bulk Structures With Finite Prebuckling Deformation

Abstract The prebuckling deformation of structures is neglected in most of the conventional buckling theory (CBT) and numerical method (CNM), because it is usually very small in conventional concepts. In the preceding paper (Su et al., 2019), we found a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation became large and essential for determining the critical buckling load, and developed a systematic buckling theory for 3D beams considering the effects of finite prebuckling deformation (FPD). For bulk structures that appear vastly in the advanced structures, a few buckling theories consider the effects of the prebuckling deformation in constitutive equations by energy method, which are significantly important but not straightforward and universal enough. In this paper, a systematic and straightforward theory for the FPD buckling of bulk structures is developed with the use of two constitutive models. The variables for the prebuckling deformation serve as the coefficients of the incremental displacements, deformation components, and stress in the buckling analysis. Four methods, including the CBT, CNM, DLU (disturbing-loading-unloading method) method and FPD buckling theory, are applied to the classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, respectively. Compared with the accurate buckling load from the DLU method, the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid).

Re-profiling response of heavily squeezed tunnels via ground reaction curves

This paper presents a simple method for determining the re-profiling response of a heavily squeezed tunnel using ground reaction curves. The ground reaction curve of certain tunnel is unique since the mechanical behavior of the original surrounding rock of each re-profiled tunnel remains the same. The dimensionless stress distribution also remains the same for a same support pressure. According to the corresponding relation of material points in the origin and current coordinates, the excavation radius of the re-profiled tunnel is determined. The location of re-profiled tunnel on the ground reaction curve and evolution curves of softening and residual radii can be determined, and the tunnel response induced by the decreasing support pressure can be further predicted using the above three curves. The critical excavation radius for a desired clearance and its corresponding plastic and residual radii can be theoretically determined. As the increase of re-profiling times and/or critical plastic shear strain, the increments of tunnel wall displacement, plastic and residual radii gradually decrease for a constant re-profiling radius.

Algorithm for calculating flat-loaded shells of environmental structures

Structures made of thin-walled shells are widely distributed elements in the environmental protection systems. In this connection, it is necessary to develop their effective and refined calculation. The point of the shell of the environmental protection structures is considered with a plane load in the initial position, deformed after j loading steps (displacement vector) and adjacent after (j + 1) loading step. The displacement increments and their derivatives are taken as nodal unknowns. The displacement vectors of the inner point of a finite element are represented in the initial basis, and their components are approximated through nodal unknowns using Hermite polynomials of the 3rd degree. To determine the deformed state of the shell, the algorithm of the method of discrete continuation with respect to the parameter in the vicinity of a singular point is used, in which the increment of loading at the step is the desired parameter. Based on the obtained dependencies, a step-by-step calculation procedure is organized, which allows you to get correct results if there is a special point.

Bearing Capacity Analysis of Transmission Tower Structure Considering Corrosion Damage

As an important part of power grid equipment, transmission towers are in direct contact with the external environment for a long time. As a coastal city in China, Fujian has been affected by marine environment and industrial pollution for a long time, which directly affects the safety of transmission towers in long-term service. In order to explore the changes of the ultimate bearing capacity of the tower structure after corrosion, this paper uses finite element software to analyse the mechanical properties of the tower structure during long-term service, and finds that the 45° wind direction is the control condition, and the overall stiffness of the tower decreases with the growth of corrosion time, and the increment of tower top displacement reaches 7% at 12 years of corrosion. The corrosion-sensitive members of the tower were clearly identified, and their stress ratios increased from 0.78, 0.79, and 0.83 to 0.97, 0.98, and 0.99, respectively, at 12 years of corrosion.

The effect of finite element division and incremental displacement size on the inelastic analysis results of the composite beam

The authors have developed a finite element analysis (FEA) program based on an explicit method, including a modified incremental technique. Moreover, it has been modified to consider the elasto-plastic (EP) behavior of refractories in the compression stress-strain curve. Firstly, this paper verifies its validity through EP analysis of the steel beam with similar mechanical properties to the bottom steel plate of the composite beam. Secondly, we show the results of FE analysis by considering the materially non-linearity of the composite beam. Finally, we indicate that the effect of finite element division and incremental displacement size on the inelastic analysis results of the composite beam consisted of refractory and steel plate subject to bending load.