This paper adopts the NGI-ADP soil model to carry out finite element analysis,based on which the effects of soft clay anisotropy on the diaphragm wall deflections in the braced excavation were evaluated.More than one ...This paper adopts the NGI-ADP soil model to carry out finite element analysis,based on which the effects of soft clay anisotropy on the diaphragm wall deflections in the braced excavation were evaluated.More than one thousand finite element cases were numerically analyzed,followed by extensive parametric studies.Surrogate models were developed via ensemble learning methods(ELMs),including the e Xtreme Gradient Boosting(XGBoost),and Random Forest Regression(RFR)to predict the maximum lateral wall deformation(δhmax).Then the results of ELMs were compared with conventional soft computing methods such as Decision Tree Regression(DTR),Multilayer Perceptron Regression(MLPR),and Multivariate Adaptive Regression Splines(MARS).This study presents a cutting-edge application of ensemble learning in geotechnical engineering and a reasonable methodology that allows engineers to determine the wall deflection in a fast,alternative way.展开更多
Data-driven approaches such as neural networks are increasingly used for deep excavations due to the growing amount of available monitoring data in practical projects.However,most neural network models only use the da...Data-driven approaches such as neural networks are increasingly used for deep excavations due to the growing amount of available monitoring data in practical projects.However,most neural network models only use the data from a single monitoring point and neglect the spatial relationships between multiple monitoring points.Besides,most models lack flexibility in providing predictions for multiple days after monitoring activity.This study proposes a sequence-to-sequence(seq2seq)two-dimensional(2D)convolutional long short-term memory neural network(S2SCL2D)for predicting the spatiotemporal wall deflections induced by deep excavations.The model utilizes the data from all monitoring points on the entire wall and extracts spatiotemporal features from data by combining the 2D convolutional layers and long short-term memory(LSTM)layers.The S2SCL2D model achieves a long-term prediction of wall deflections through a recursive seq2seq structure.The excavation depth,which has a significant impact on wall deflections,is also considered using a feature fusion method.An excavation project in Hangzhou,China,is used to illustrate the proposed model.The results demonstrate that the S2SCL2D model has superior prediction accuracy and robustness than that of the LSTM and S2SCL1D(one-dimensional)models.The prediction model demonstrates a strong generalizability when applied to an adjacent excavation.Based on the long-term prediction results,practitioners can plan and allocate resources in advance to address the potential engineering issues.展开更多
There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals,i.e.,the planar 2D convolution,the spherical 2D convolution and the spherical 1D convolution.The larg...There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals,i.e.,the planar 2D convolution,the spherical 2D convolution and the spherical 1D convolution.The largest drawback of both the planar and the spherical 2D FFT methods is that,due to the approximations in the kernel function,only inexact results can be achieved.Apparently,the reason is the meridian convergence at higher latitudes.As the meridians converge,the Δ φ ,Δ λ blocks do not form a rectangular grid,as is assumed in 2D FFT methods.It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function,but also causes an approximation error during the implementation of 2D FFT in computer.In order to meet the increasing need for precise determination of the vertical deflections,this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections.After having made a detailed comparison between the planar and the spherical 2D FFT formulae,we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method.And then,a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper.A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT.The second part of this paper is to discuss the influences of the spherical harmonic reference field,the limited capsize,and the singular integral on the computation of the vertical deflections.The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro_observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters.展开更多
Distance between the main land and island is so long that it is very difficult to precisely connect the height datum across the sea with the traditional method like the trigonometric leveling, or it is very expensive ...Distance between the main land and island is so long that it is very difficult to precisely connect the height datum across the sea with the traditional method like the trigonometric leveling, or it is very expensive and takes long time to implement the height transfer with the geopotential technique. We combine the data of GPS surveying, astro-geodesy and EGM2008 to precisely connect the orthometric height across the sea with the improved astronomical leveling method in the paper. The Qiongzhou Strait is selected as the test area for the height connection over the sea. We precisely determine the geodetic latitudes, longitudes, heights and deflections of the vertical for four points on both sides across the strait. Modeled deflections of the vertical along the height connecting routes over the sea are determined with EGM2008 model based on the geodetic positions and heights of the sea segmentation points from DNSC08MSS model. Differences of the measured and modeled deflections of the vertical are calculated at four points on both sides and linearly change along the route. So the deflections of the vertical along the route over the sea can be improved by the linear interpolation model. The results are also in accord with those of trigonometirc levelings. The practical case shows that we can precisely connect the orthometric height across the Qiongzhou Strait to satisfy the requirement of order 3 leveling network of China. The method is very efficient to precisely connect the height datum across the sea along the route up to 80 km.展开更多
The deflection of the vertical reflects the mass distribution and density anomaly of celestial bodies. Lunar deflections of the vertical include directional information of the Moon’s gravity field. SGM90d, recovered ...The deflection of the vertical reflects the mass distribution and density anomaly of celestial bodies. Lunar deflections of the vertical include directional information of the Moon’s gravity field. SGM90d, recovered from SELENE mission, revealed the lunar far side gravity field for the first time in history owes to 4-way Doppler data. Lunar deflections of the vertical and their meridional and prime vertical components are calculated from SGM90d, and then their global distributions are also given in the paper. The gradients of lunar deflections of the vertical are defined and computed as well. The correlations between the lunar deflections of the vertical and the lunar terrain have been fully discussed. Many different characteristics of lunar deflections of vertical have been found between the near side and the far side of the Moon, which may be caused from the lithospheric compensation and the uplifting of mantle.展开更多
This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end ...This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.展开更多
Islands and the mainland are separated by seas,and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands,resulting in different height systems on the m...Islands and the mainland are separated by seas,and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands,resulting in different height systems on the mainland and the islands.In this study,we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas.First,the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model(EGM),and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets.Second,we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points.Third,we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle.Finally,we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach.Using observed data of normal heights,ellipsoidal heights,and astrogeodetic vertical deflections referring to height sites in Qingdao,Shandong Province,we conducted a numerical experiment involving the normal height connection across sea regions.We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10.The distance of the height connection across the sea was approximately 10.5 km.According to China's official leveling specifications,the experimental results met the criterion of third-class leveling precision.展开更多
High repeatability of needle insertion experiments is essential to the needle-phantom interaction model validation.However,the influential factors governing the accuracy of the phantom and needle deformations have not...High repeatability of needle insertion experiments is essential to the needle-phantom interaction model validation.However,the influential factors governing the accuracy of the phantom and needle deformations have not been systematically studied.In this paper,the impact of influential factors,including phantom characteristic represented by the ratio of DMSO and thawing time(TT),needle properties represented by needle external diameter(NED)and operating factors such as needle insertion velocity(IV),insertion positions(IP)and repeated insertion times(RITs)are analyzed by orthogonal experiment design.The range calculation shows the most sensitive parameters to phantom deformations are RITs,IV and DMSO while the most sensitive parameters to needle deflection are DMSO,TT and NED.By variance analysis,the significant factors on maximum tissue deformation(MTD)are IV,followed by RITs,DMSO and IP.And NED and TT have nearly no significant impact on MTD.The significant sequence on maximum needle deflection(MND)is as follows:DMSO,TT and NED.Results show that,among all impacting factors,phantom deformation is susceptible to both material properties and operative factors while the needle deflection is more susceptible to material properties of the phantom,which can help researchers in related fields to conduct experiments in a more precise manner and better understand the needle-phantom interaction mechanism.展开更多
This paper deals with the research of accuracy of differential equations of deflections. The basic idea is as follows. Firstly, considering the boundary effect the meridian midsurface displacement u=0, thus we derive ...This paper deals with the research of accuracy of differential equations of deflections. The basic idea is as follows. Firstly, considering the boundary effect the meridian midsurface displacement u=0, thus we derive the deflection differential equations; secondly we accurately prove that by use of the deflection differential equations or the original differential equations the same inner forces solutions are obtained; finally, we accurately prove that considering the boundary effect the meridian surface displacement u = 0 is an exact solution. In this paper we give the singular perturbation solution of the deflection differential equations. Finally we check the equilibrium condition and prove the inner forces solved by perturbation method and the outer load are fully equilibrated. It shows that perturbation solution is accurate. On the other hand, it shows again that the deflection differential equation is an exact equation.The features of the new differential equations are as follows:1. The accuracies of the new differential equations and the original differential e-quations are the same.2. The new differential equations can satisfy the boundary conditions simply.3. It is advantageous to use perturbation method with the new differential equations.4 We may obtain the deflection expression(w)and slope expression (dw/da) by using the new differential equations.The new differential equations greatly simplify the calculation of spherical shell. The notation adopted in this paper is the same as that in Ref. [1]展开更多
The use of fiber reinforced polymer(FRP)bars to substitute the steel bars in internal reinforcement is now an alternative in some structures subjected by corrosion.The strength,stiffness and bond characteristics of FR...The use of fiber reinforced polymer(FRP)bars to substitute the steel bars in internal reinforcement is now an alternative in some structures subjected by corrosion.The strength,stiffness and bond characteristics of FRP bars are tested to understand their flexural behaviour.In this study is investigated the way of failure of beams reinforced internally with carbon FRP(CFRP)bars and their mechanical properties.Two sets of concrete beams reinforced with different diameters of CFRP bars are designed and tested under four-point loading methods.In general,beams reinforced with FRP bars show more deflections and greater values of crack width than beams reinforced with conventional steel,which is due to their low modulus of elasticity and general stiffness.In this paper is presented the calculation and comparison of deflection using different methods,such as ACI 440,CAN/CSA,Eurocode and experimental loading tests.The evaluation is done comparing the results of every method.This study is effective when we use beams with one layer of reinforcement.展开更多
The paper presents an improved technique of calculating total deflections of flexural reinforced concrete elements that takes discrete crack formation into account. The technique is based on determining the curvature ...The paper presents an improved technique of calculating total deflections of flexural reinforced concrete elements that takes discrete crack formation into account. The technique is based on determining the curvature of the cross section of reinforced concrete elements with cracks and fissures in the area between cracks. The curvature of the element is calculated using a non-linear function of the deformation of concrete under compression. Approximating dependency of concrete resistance on compression developed by one of the authors is presented. An algorithm of finding the curvature and formulas for calculating curvature and deflection are provided. The function of the curvature distribution along the length of a flexible element is proposed by the authors. The paper also presents the results of the author＇s experimental research. The characteristics of samples tested are described. The experimental research results of deflections of fiexural reinforced concrete elements made of conventional and high-strength concretes are presented. Comparison of the values calculated using the technique with those obtained from the experimental research as well as those calculated according to existing regulations in Russia, USA and Europe is drawn.展开更多
In this paper,a comparative analysis of two beams’deflections,one supported-embedded beam and a bi-supported beam,is presented.For such comparison,first the respective second-order linear Ordinary Differential Equati...In this paper,a comparative analysis of two beams’deflections,one supported-embedded beam and a bi-supported beam,is presented.For such comparison,first the respective second-order linear Ordinary Differential Equations(ODEs)were obtained.Along with the boundary conditions,there are two Boundary Value Problems(BVPs),making it possible to perform their numerical and analytical solutions.For numerical solutions,a Matlab algorithm was implemented based on the Finite Difference Method(FDM).The analytical solutions were also obtained for comparison with the numerical ones and with the validation method.In the end we analyzed the shapes of the elastic lines of the two beams caused by the loads coming from the weight of each one.展开更多
基金supported by the High-end Foreign Expert Introduction program(No.G20190022002)Chongqing Construction Science and Technology Plan Project(2019-0045)+1 种基金the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJZD-K201900102)The financial support is gratefully acknowledged。
文摘This paper adopts the NGI-ADP soil model to carry out finite element analysis,based on which the effects of soft clay anisotropy on the diaphragm wall deflections in the braced excavation were evaluated.More than one thousand finite element cases were numerically analyzed,followed by extensive parametric studies.Surrogate models were developed via ensemble learning methods(ELMs),including the e Xtreme Gradient Boosting(XGBoost),and Random Forest Regression(RFR)to predict the maximum lateral wall deformation(δhmax).Then the results of ELMs were compared with conventional soft computing methods such as Decision Tree Regression(DTR),Multilayer Perceptron Regression(MLPR),and Multivariate Adaptive Regression Splines(MARS).This study presents a cutting-edge application of ensemble learning in geotechnical engineering and a reasonable methodology that allows engineers to determine the wall deflection in a fast,alternative way.
基金supported by the National Natural Science Foundation of China(Grant No.42307218)the Foundation of Key Laboratory of Soft Soils and Geoenvironmental Engineering(Zhejiang University),Ministry of Education(Grant No.2022P08)the Natural Science Foundation of Zhejiang Province(Grant No.LTZ21E080001).
文摘Data-driven approaches such as neural networks are increasingly used for deep excavations due to the growing amount of available monitoring data in practical projects.However,most neural network models only use the data from a single monitoring point and neglect the spatial relationships between multiple monitoring points.Besides,most models lack flexibility in providing predictions for multiple days after monitoring activity.This study proposes a sequence-to-sequence(seq2seq)two-dimensional(2D)convolutional long short-term memory neural network(S2SCL2D)for predicting the spatiotemporal wall deflections induced by deep excavations.The model utilizes the data from all monitoring points on the entire wall and extracts spatiotemporal features from data by combining the 2D convolutional layers and long short-term memory(LSTM)layers.The S2SCL2D model achieves a long-term prediction of wall deflections through a recursive seq2seq structure.The excavation depth,which has a significant impact on wall deflections,is also considered using a feature fusion method.An excavation project in Hangzhou,China,is used to illustrate the proposed model.The results demonstrate that the S2SCL2D model has superior prediction accuracy and robustness than that of the LSTM and S2SCL1D(one-dimensional)models.The prediction model demonstrates a strong generalizability when applied to an adjacent excavation.Based on the long-term prediction results,practitioners can plan and allocate resources in advance to address the potential engineering issues.
文摘There exist three types of convolution formulae for the efficient evaluation of gravity field convolution integrals,i.e.,the planar 2D convolution,the spherical 2D convolution and the spherical 1D convolution.The largest drawback of both the planar and the spherical 2D FFT methods is that,due to the approximations in the kernel function,only inexact results can be achieved.Apparently,the reason is the meridian convergence at higher latitudes.As the meridians converge,the Δ φ ,Δ λ blocks do not form a rectangular grid,as is assumed in 2D FFT methods.It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function,but also causes an approximation error during the implementation of 2D FFT in computer.In order to meet the increasing need for precise determination of the vertical deflections,this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections.After having made a detailed comparison between the planar and the spherical 2D FFT formulae,we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method.And then,a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper.A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT.The second part of this paper is to discuss the influences of the spherical harmonic reference field,the limited capsize,and the singular integral on the computation of the vertical deflections.The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro_observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters.
基金supported by the National Natural Science Foundation of China (Grant No. 40974004)the National High-Technology Research and Development Program of China (863 Program,Grant No. 2009AA121405)+1 种基金the Key Laboratory of Surveying and Mapping Technology on Island and Reef of NASMG,China (Grant No. 2011A01)the Key Laboratory of Advanced Engineering Surveying of NASMG,China (Grant No. TJES1101)
文摘Distance between the main land and island is so long that it is very difficult to precisely connect the height datum across the sea with the traditional method like the trigonometric leveling, or it is very expensive and takes long time to implement the height transfer with the geopotential technique. We combine the data of GPS surveying, astro-geodesy and EGM2008 to precisely connect the orthometric height across the sea with the improved astronomical leveling method in the paper. The Qiongzhou Strait is selected as the test area for the height connection over the sea. We precisely determine the geodetic latitudes, longitudes, heights and deflections of the vertical for four points on both sides across the strait. Modeled deflections of the vertical along the height connecting routes over the sea are determined with EGM2008 model based on the geodetic positions and heights of the sea segmentation points from DNSC08MSS model. Differences of the measured and modeled deflections of the vertical are calculated at four points on both sides and linearly change along the route. So the deflections of the vertical along the route over the sea can be improved by the linear interpolation model. The results are also in accord with those of trigonometirc levelings. The practical case shows that we can precisely connect the orthometric height across the Qiongzhou Strait to satisfy the requirement of order 3 leveling network of China. The method is very efficient to precisely connect the height datum across the sea along the route up to 80 km.
文摘The deflection of the vertical reflects the mass distribution and density anomaly of celestial bodies. Lunar deflections of the vertical include directional information of the Moon’s gravity field. SGM90d, recovered from SELENE mission, revealed the lunar far side gravity field for the first time in history owes to 4-way Doppler data. Lunar deflections of the vertical and their meridional and prime vertical components are calculated from SGM90d, and then their global distributions are also given in the paper. The gradients of lunar deflections of the vertical are defined and computed as well. The correlations between the lunar deflections of the vertical and the lunar terrain have been fully discussed. Many different characteristics of lunar deflections of vertical have been found between the near side and the far side of the Moon, which may be caused from the lithospheric compensation and the uplifting of mantle.
文摘This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.
基金financially supported by the foundation of the Key Laboratory of Marine Environmental Survey Technology and Application,Ministry of Natural Resources,China (No. MESTA-2020-B006)the National Natural Science Foundation of China (No.41774001)
文摘Islands and the mainland are separated by seas,and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands,resulting in different height systems on the mainland and the islands.In this study,we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas.First,the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model(EGM),and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets.Second,we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points.Third,we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle.Finally,we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach.Using observed data of normal heights,ellipsoidal heights,and astrogeodetic vertical deflections referring to height sites in Qingdao,Shandong Province,we conducted a numerical experiment involving the normal height connection across sea regions.We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10.The distance of the height connection across the sea was approximately 10.5 km.According to China's official leveling specifications,the experimental results met the criterion of third-class leveling precision.
基金Supported by Zhejiang Provincial Natural Science Foundation of China(Grant No.LSD19H180004)National Major Scientific Research Instrument Development Project of China(Grant No.81827804)and Science Fund for Creative Group of NSFC(Grant No.51821903).
文摘High repeatability of needle insertion experiments is essential to the needle-phantom interaction model validation.However,the influential factors governing the accuracy of the phantom and needle deformations have not been systematically studied.In this paper,the impact of influential factors,including phantom characteristic represented by the ratio of DMSO and thawing time(TT),needle properties represented by needle external diameter(NED)and operating factors such as needle insertion velocity(IV),insertion positions(IP)and repeated insertion times(RITs)are analyzed by orthogonal experiment design.The range calculation shows the most sensitive parameters to phantom deformations are RITs,IV and DMSO while the most sensitive parameters to needle deflection are DMSO,TT and NED.By variance analysis,the significant factors on maximum tissue deformation(MTD)are IV,followed by RITs,DMSO and IP.And NED and TT have nearly no significant impact on MTD.The significant sequence on maximum needle deflection(MND)is as follows:DMSO,TT and NED.Results show that,among all impacting factors,phantom deformation is susceptible to both material properties and operative factors while the needle deflection is more susceptible to material properties of the phantom,which can help researchers in related fields to conduct experiments in a more precise manner and better understand the needle-phantom interaction mechanism.
文摘This paper deals with the research of accuracy of differential equations of deflections. The basic idea is as follows. Firstly, considering the boundary effect the meridian midsurface displacement u=0, thus we derive the deflection differential equations; secondly we accurately prove that by use of the deflection differential equations or the original differential equations the same inner forces solutions are obtained; finally, we accurately prove that considering the boundary effect the meridian surface displacement u = 0 is an exact solution. In this paper we give the singular perturbation solution of the deflection differential equations. Finally we check the equilibrium condition and prove the inner forces solved by perturbation method and the outer load are fully equilibrated. It shows that perturbation solution is accurate. On the other hand, it shows again that the deflection differential equation is an exact equation.The features of the new differential equations are as follows:1. The accuracies of the new differential equations and the original differential e-quations are the same.2. The new differential equations can satisfy the boundary conditions simply.3. It is advantageous to use perturbation method with the new differential equations.4 We may obtain the deflection expression(w)and slope expression (dw/da) by using the new differential equations.The new differential equations greatly simplify the calculation of spherical shell. The notation adopted in this paper is the same as that in Ref. [1]
文摘The use of fiber reinforced polymer(FRP)bars to substitute the steel bars in internal reinforcement is now an alternative in some structures subjected by corrosion.The strength,stiffness and bond characteristics of FRP bars are tested to understand their flexural behaviour.In this study is investigated the way of failure of beams reinforced internally with carbon FRP(CFRP)bars and their mechanical properties.Two sets of concrete beams reinforced with different diameters of CFRP bars are designed and tested under four-point loading methods.In general,beams reinforced with FRP bars show more deflections and greater values of crack width than beams reinforced with conventional steel,which is due to their low modulus of elasticity and general stiffness.In this paper is presented the calculation and comparison of deflection using different methods,such as ACI 440,CAN/CSA,Eurocode and experimental loading tests.The evaluation is done comparing the results of every method.This study is effective when we use beams with one layer of reinforcement.
文摘The paper presents an improved technique of calculating total deflections of flexural reinforced concrete elements that takes discrete crack formation into account. The technique is based on determining the curvature of the cross section of reinforced concrete elements with cracks and fissures in the area between cracks. The curvature of the element is calculated using a non-linear function of the deformation of concrete under compression. Approximating dependency of concrete resistance on compression developed by one of the authors is presented. An algorithm of finding the curvature and formulas for calculating curvature and deflection are provided. The function of the curvature distribution along the length of a flexible element is proposed by the authors. The paper also presents the results of the author＇s experimental research. The characteristics of samples tested are described. The experimental research results of deflections of fiexural reinforced concrete elements made of conventional and high-strength concretes are presented. Comparison of the values calculated using the technique with those obtained from the experimental research as well as those calculated according to existing regulations in Russia, USA and Europe is drawn.
文摘In this paper,a comparative analysis of two beams’deflections,one supported-embedded beam and a bi-supported beam,is presented.For such comparison,first the respective second-order linear Ordinary Differential Equations(ODEs)were obtained.Along with the boundary conditions,there are two Boundary Value Problems(BVPs),making it possible to perform their numerical and analytical solutions.For numerical solutions,a Matlab algorithm was implemented based on the Finite Difference Method(FDM).The analytical solutions were also obtained for comparison with the numerical ones and with the validation method.In the end we analyzed the shapes of the elastic lines of the two beams caused by the loads coming from the weight of each one.
