Regarding the scale effects on propeller's noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respec...Regarding the scale effects on propeller's noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respectively. The discrete line-spectrum noise and its standardized spectrum level scaling law, together with the total sound pressure level are analyzed. The non-cavitation noise predictions are completed by both the frequency domain method and the time domain method. As a fluctuated noise source, the time-dependent fluctuated pressure and normal velocity distribution on propeller blades are obtained by the unsteady Reynolds-averaged Navier-Stokes ( URANS ) simulation. Results show that the pressure coefficient distribution of three propellers on the 0.7R section is nearly superposed under the same advance ratio. The periodic thrust fluctuation of three propellers can exactly reflect the tonal components of the axial passing frequency (APF) and the blade passing frequency (BPF), and the fluctuation enhancement from the small to the middle propeller at the BPF is greater than that from the middle to the big one. By the two noise prediction methods, the increment of the total sound pressure level from the small to the big propeller differs by 2.49 dB. Following the standardized scaling law, the spectrum curves of the middle and big propellers are nearly the same while significantly differing from the small one. The increment of both the line-spectrum level and the total sound pressure increases with the increase in diameter. It is suggested that the model scale of the propeller should be as large as possible in engineering to reduce the prediction error of the empirical scalin~ law and weaken the scale effects.展开更多
The seismic behavior of skewed bridges has not been well studied compared to straight bridges. Skewed bridges have shown extensive damage, especially due to deck rotation, shear keys failure, abutment unseating and co...The seismic behavior of skewed bridges has not been well studied compared to straight bridges. Skewed bridges have shown extensive damage, especially due to deck rotation, shear keys failure, abutment unseating and column- bent drift. This research, therefore, aims to study the behavior of skewed and straight highway overpass bridges both with and without taking into account the effects of Soil-Structure Interaction (SSI) due to near-fault ground motions. Due to several sources of uncertainty associated with the ground motions, soil and structure, a probabilistic approach is needed. Thus, a probabilistic methodology similar to the one developed by the Pacific Earthquake Engineering Research Center (PEER) has been utilized to assess the probability of damage due to various levels of shaking using appropriate intensity measures with minimum dispersions. The probabilistic analyses were performed for various bridge configurations and site conditions, including sand ranging from loose to dense and clay ranging from soft to stiff, in order to evaluate the effects. The results proved a considerable susceptibility of skewed bridges to deck rotation and shear keys displacement. It was also found that SSI had a decreasing effect on the damage probability for various demands compared to the fixed-base model without including SSI. However, deck rotation for all types of the soil and also abutment unseating for very loose sand and soft clay showed an increase in damage probability compared to the fixed-base model. The damage probability for various demands has also been found to decrease with an increase of soil strength for both sandy and clayey sites. With respect to the variations in the skew angle, an increase in skew angle has had an increasing effect on the amplitude of the seismic response for various demands. Deck rotation has been very sensitive to the increase in the skew angle; therefore, as the skew angle increased, the deck rotation responded accordingly. Furthermore, abutment unseating showed an increasing trend due to an increase in skew angle for both fixed-base and SSI models.展开更多
A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to t...A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to the Shields parameter, and takes into account the effects of mass conservation, phase-lag, and asymmetric boundary layer development, which are important in skewed asymmetric flows but usually absent in classical models. The proposed model is validated by erosion depth and sheet flow layer thickness data in both steady and unsteady flows, and applied to a new instantaneous sediment transport rate formula. With higher accuracy than classical empirical models in steady flows, the new formula can also be used for instantaneous sediment transport rate prediction in skewed asymmetric oscillatory sheet flows.展开更多
It is critical to ensure the functionality of highway bridges after earthquakes to provide access to important facilities. Since the 1971 San Fernando earthquake, there has been a better understanding of the seismic p...It is critical to ensure the functionality of highway bridges after earthquakes to provide access to important facilities. Since the 1971 San Fernando earthquake, there has been a better understanding of the seismic performance of bridges. Nonetheless, there are no detailed guidelines addressing the performance of skewed highway bridges. Several parameters affect the response of skewed highway bridges under both service and seismic loads which makes their behavior complex. Therefore, there is a need for more research to study the effect of skew angle and other related factors on the performance of highway bridges. This paper examines the seismic performance of a three-span continuous concrete box girder bridge with skew angles from 0 to 60 degrees, analytically. Finite element (FE) and simplified beam-stick (BS) models of the bridge were developed using SAP2000. Different types of analysis were considered on both models such as: nonlinear static pushover, and linear and nonlinear time history analyses. A comparison was conducted between FE and BS, different skew angles, abutment support conditions, and time history and pushover analysis. It is shown that the BS model has the capability to capture the coupling due to skew and the significant modes for moderate skew angles. Boundary conditions and pushover load profile are determined to have a major effect on pushover analysis. Pushover analysis may be used to predict the maximum deformation and hinge formation adequately.展开更多
In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is...In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis (IDA) for fragility curves. Four different earthquake directions have been considered: -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.展开更多
MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center...MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center-scale cluster nodes.However,we observe that this approach can lead to uneven data distribution,which can result in skewed loads among reduce tasks,thus hamper performance of MapReduce systems.Moreover,worker nodes in MapReduce systems may differ in computing capability due to(1) multiple generations of hardware in non-virtualized data centers,or(2) co-location of virtual machines in virtualized data centers.The heterogeneity among cluster nodes exacerbates the negative effects of uneven data distribution.To improve MapReduce performance in heterogeneous clusters,we propose a novel load balancing approach in the reduce phase.This approach consists of two components:(1) performance prediction for reducers that run on heterogeneous nodes based on support vector machines models,and(2) heterogeneity-aware partitioning(HAP),which balances skewed data for reduce tasks.We implement this approach as a plug-in in current MapReduce system.Experimental results demonstrate that our proposed approach distributes work evenly among reduce tasks,and improves MapReduce performance with little overhead.展开更多
The skewed symmetry detection plays an improtant role in three-dimensional(3-D) reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detect...The skewed symmetry detection plays an improtant role in three-dimensional(3-D) reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detection can decrease the geometric constrains and the complexity of 3-D reconstruction. The detection technique for the quadric curve ellipse proposed by Sugimoto is improved to further cover quadric curves including hyperbola and parabola. With the parametric detection, the 3-D quadric curve projection matching is automatical- ly accomplished. Finally, the skewed symmetry surface of the quadric surface solid is obtained. Several examples are used to verify the feasibility of the algorithm and satisfying results can be obtained.展开更多
The objective was to gain proof of genome damage-repair induced mitotic slippage process (MSP) to 4n-diplochromosome skewed division-system, earlier suggested to have “cancer-deciding” consequences. Our damage-model...The objective was to gain proof of genome damage-repair induced mitotic slippage process (MSP) to 4n-diplochromosome skewed division-system, earlier suggested to have “cancer-deciding” consequences. Our damage-model showed two succeeding phases: molecular mutations for initiation of fitness-gained cells, and large chromosomal changes to aneuploidy from inherited DNA-breakage-repair inaccuracies. The mutations were gained while DNA-repair and DNA-replication, co-existed in the route to tetraploidy, a phenomenon also expressed for some existing unicellular organisms. These organisms also showed genome reductive, amitotic, meioticlike division, and was the origin of human genome conserved, self-inflicted 90° reorientation of the 4n nucleus relative to the cytoskeleton axis. In the in vitro DNA-damage model, this remarkable 4n-event deciding “flat-upright” cell-growth characteristics showed several consequences, for example, cancer-important, E-cadherin-β-catenin cell-to-cell adherence destruction, which gave diploid progeny cells, mobility freedom from cell contact inhibition, likely in renewal tissues. This 4n-skewed division-system with inheritance in progeny cells for repeat occurrences as mentioned for flat-up-right growth patterns is similar to claimed concepts of metaplasia-EMT/MET embryogenesis events in cancer evolution. A scrutiny of this literature, proof-wise invalidated this embryological concept by tetraploid 8C cells occurring in MET events and, was noted for small cell occurrence, i.e., diploidy from 4n-8C reductive division, an also event for tumor relapse cells, derived from genome damaging therapy agents. Pre-cancer hyperplasia reported MSP, cadherincatenin destruction and 90° perpendicularity to basal cell membrane. The DNA-damage-repair model can weed-out therapy-agents triggering 4n-skewed division. Cancer-control, beginning-information, is likely from mutational identity of the 4n derived fitness-gained cells.展开更多
An analytical model with essential parameters given by a two-phase numerical model is utilized to study the net boundary layer current and sediment transport under skewed asymmetric oscillatory sheet flows. The analyt...An analytical model with essential parameters given by a two-phase numerical model is utilized to study the net boundary layer current and sediment transport under skewed asymmetric oscillatory sheet flows. The analytical model is the first instantaneous type model that can consider phase-lag and asymmetric boundary layer development. The two-phase model supplies the essential phase-lead, instantaneous erosion depth and boundary layer development for the analytical model to enhance the understanding of velocity skewness and acceleration skewness in sediment flux and transport rate. The sediment transport difference between onshore and offshore stages caused by velocity skewness or acceleration skewness is shown to illustrate the determination of net sediment transport by the analytical model. In previous studies about sediment transport in skewed asymmetric sheet flows, the generation of net sediment transport is mainly concluded to the phase-lag effect.However, the phase-lag effect is shown important but not enough for the net sediment transport, while the skewed asymmetric boundary layer development generated net boundary layer current and mobile bed effect are key important in the transport process.展开更多
This article makes the first attempt in assessing the influence of active constrained layer damping(ACLD)treatment towards precise control of frequency responses of functionally graded skew-magneto-electroelastic(FGSM...This article makes the first attempt in assessing the influence of active constrained layer damping(ACLD)treatment towards precise control of frequency responses of functionally graded skew-magneto-electroelastic(FGSMEE)plates by employing finite element methods.The materials are functionally graded across the thickness of the plate in terms of modest power-law distributions.The principal equations of motion of FGSMEE are derived via Hamilton’s principle and solved using condensation technique.The effect of ACLD patches are modelled by following the complex modulus approach(CMA).Additionally,distinctive emphasis is laid to evaluate the influence of geometrical skewness on the attenuation capabilities of the plate.The accuracy of the current analysis is corroborated with comparison of previous researches of similar kind.Additionally,a complete parametric study is directed to understand the combined impacts of various factors like coupling fields,patch location,fiber orientation of piezoelectric patch in association with skew angle and power-law index.展开更多
In this paper, we report on an analytical solution for beam-type skewed highway bridges subjected to truck loading. To confirm the analysis derivation and the solution obtained, the moment and shear responses to the d...In this paper, we report on an analytical solution for beam-type skewed highway bridges subjected to truck loading. To confirm the analysis derivation and the solution obtained, the moment and shear responses to the design truck load are acquired using the analytical method for a number of typical US highway bridges and compared with those from numerical finite element method (FEM) analysis. In addition, the lateral distribution factors for moment and shear used in routine design are investigated based on comparison of the analytical approach and FEM. The analytical solution is shown in good agreement with the FEM result. Furthermore, the relevant provisions in the American Association of State Highway Transportation Officials' (AASHTO's) LRFD Bridge Design Specifications are also discussed here for comparison, particularly with respect to design application. It is observed that the design code specified load distribution factor may not predict well, especially for shear and/or severe skew.展开更多
Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely...Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.展开更多
基金The National Natural Science Foundation of China(No.51009144)
文摘Regarding the scale effects on propeller's noncavitation hydrodynamics and hydroacoustics, three similar 7bladed highly-skewed propellers in the wake flow are addressed with diameters of 250, 500 and 1 000 mm, respectively. The discrete line-spectrum noise and its standardized spectrum level scaling law, together with the total sound pressure level are analyzed. The non-cavitation noise predictions are completed by both the frequency domain method and the time domain method. As a fluctuated noise source, the time-dependent fluctuated pressure and normal velocity distribution on propeller blades are obtained by the unsteady Reynolds-averaged Navier-Stokes ( URANS ) simulation. Results show that the pressure coefficient distribution of three propellers on the 0.7R section is nearly superposed under the same advance ratio. The periodic thrust fluctuation of three propellers can exactly reflect the tonal components of the axial passing frequency (APF) and the blade passing frequency (BPF), and the fluctuation enhancement from the small to the middle propeller at the BPF is greater than that from the middle to the big one. By the two noise prediction methods, the increment of the total sound pressure level from the small to the big propeller differs by 2.49 dB. Following the standardized scaling law, the spectrum curves of the middle and big propellers are nearly the same while significantly differing from the small one. The increment of both the line-spectrum level and the total sound pressure increases with the increase in diameter. It is suggested that the model scale of the propeller should be as large as possible in engineering to reduce the prediction error of the empirical scalin~ law and weaken the scale effects.
文摘The seismic behavior of skewed bridges has not been well studied compared to straight bridges. Skewed bridges have shown extensive damage, especially due to deck rotation, shear keys failure, abutment unseating and column- bent drift. This research, therefore, aims to study the behavior of skewed and straight highway overpass bridges both with and without taking into account the effects of Soil-Structure Interaction (SSI) due to near-fault ground motions. Due to several sources of uncertainty associated with the ground motions, soil and structure, a probabilistic approach is needed. Thus, a probabilistic methodology similar to the one developed by the Pacific Earthquake Engineering Research Center (PEER) has been utilized to assess the probability of damage due to various levels of shaking using appropriate intensity measures with minimum dispersions. The probabilistic analyses were performed for various bridge configurations and site conditions, including sand ranging from loose to dense and clay ranging from soft to stiff, in order to evaluate the effects. The results proved a considerable susceptibility of skewed bridges to deck rotation and shear keys displacement. It was also found that SSI had a decreasing effect on the damage probability for various demands compared to the fixed-base model without including SSI. However, deck rotation for all types of the soil and also abutment unseating for very loose sand and soft clay showed an increase in damage probability compared to the fixed-base model. The damage probability for various demands has also been found to decrease with an increase of soil strength for both sandy and clayey sites. With respect to the variations in the skew angle, an increase in skew angle has had an increasing effect on the amplitude of the seismic response for various demands. Deck rotation has been very sensitive to the increase in the skew angle; therefore, as the skew angle increased, the deck rotation responded accordingly. Furthermore, abutment unseating showed an increasing trend due to an increase in skew angle for both fixed-base and SSI models.
基金supported by the National Natural Science Foundation of China (Grants 51609244, 11472156, and 51139007)the National Science-Technology Support Plan of China (Grant 2015BAD20B01)
文摘A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to the Shields parameter, and takes into account the effects of mass conservation, phase-lag, and asymmetric boundary layer development, which are important in skewed asymmetric flows but usually absent in classical models. The proposed model is validated by erosion depth and sheet flow layer thickness data in both steady and unsteady flows, and applied to a new instantaneous sediment transport rate formula. With higher accuracy than classical empirical models in steady flows, the new formula can also be used for instantaneous sediment transport rate prediction in skewed asymmetric oscillatory sheet flows.
基金Supported by:In part by the California Department of Transportation Under Caltrans Contract No.59A0503the Dept. of Civil and Environmental Engineering(UNR)
文摘It is critical to ensure the functionality of highway bridges after earthquakes to provide access to important facilities. Since the 1971 San Fernando earthquake, there has been a better understanding of the seismic performance of bridges. Nonetheless, there are no detailed guidelines addressing the performance of skewed highway bridges. Several parameters affect the response of skewed highway bridges under both service and seismic loads which makes their behavior complex. Therefore, there is a need for more research to study the effect of skew angle and other related factors on the performance of highway bridges. This paper examines the seismic performance of a three-span continuous concrete box girder bridge with skew angles from 0 to 60 degrees, analytically. Finite element (FE) and simplified beam-stick (BS) models of the bridge were developed using SAP2000. Different types of analysis were considered on both models such as: nonlinear static pushover, and linear and nonlinear time history analyses. A comparison was conducted between FE and BS, different skew angles, abutment support conditions, and time history and pushover analysis. It is shown that the BS model has the capability to capture the coupling due to skew and the significant modes for moderate skew angles. Boundary conditions and pushover load profile are determined to have a major effect on pushover analysis. Pushover analysis may be used to predict the maximum deformation and hinge formation adequately.
文摘In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis (IDA) for fragility curves. Four different earthquake directions have been considered: -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.
基金The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work is support- ed by National High-Tech Research and Development Plan of China under grants NO.2011AA01A204, and 2012AA01A306, National Natural Science Foundation of China under grant NO. 61202041, and NO.91330117.
文摘MapReduce has emerged as a popular computing model used in datacenters to process large amount of datasets.In the map phase,hash partitioning is employed to distribute data that sharing the same key across data center-scale cluster nodes.However,we observe that this approach can lead to uneven data distribution,which can result in skewed loads among reduce tasks,thus hamper performance of MapReduce systems.Moreover,worker nodes in MapReduce systems may differ in computing capability due to(1) multiple generations of hardware in non-virtualized data centers,or(2) co-location of virtual machines in virtualized data centers.The heterogeneity among cluster nodes exacerbates the negative effects of uneven data distribution.To improve MapReduce performance in heterogeneous clusters,we propose a novel load balancing approach in the reduce phase.This approach consists of two components:(1) performance prediction for reducers that run on heterogeneous nodes based on support vector machines models,and(2) heterogeneity-aware partitioning(HAP),which balances skewed data for reduce tasks.We implement this approach as a plug-in in current MapReduce system.Experimental results demonstrate that our proposed approach distributes work evenly among reduce tasks,and improves MapReduce performance with little overhead.
基金Supported by the National Natural Science Foundation of China(10377007)~~
文摘The skewed symmetry detection plays an improtant role in three-dimensional(3-D) reconstruction. The skewed symmetry depicts a real symmetry viewed from some unknown viewing directions. And the skewed symmetry detection can decrease the geometric constrains and the complexity of 3-D reconstruction. The detection technique for the quadric curve ellipse proposed by Sugimoto is improved to further cover quadric curves including hyperbola and parabola. With the parametric detection, the 3-D quadric curve projection matching is automatical- ly accomplished. Finally, the skewed symmetry surface of the quadric surface solid is obtained. Several examples are used to verify the feasibility of the algorithm and satisfying results can be obtained.
文摘The objective was to gain proof of genome damage-repair induced mitotic slippage process (MSP) to 4n-diplochromosome skewed division-system, earlier suggested to have “cancer-deciding” consequences. Our damage-model showed two succeeding phases: molecular mutations for initiation of fitness-gained cells, and large chromosomal changes to aneuploidy from inherited DNA-breakage-repair inaccuracies. The mutations were gained while DNA-repair and DNA-replication, co-existed in the route to tetraploidy, a phenomenon also expressed for some existing unicellular organisms. These organisms also showed genome reductive, amitotic, meioticlike division, and was the origin of human genome conserved, self-inflicted 90° reorientation of the 4n nucleus relative to the cytoskeleton axis. In the in vitro DNA-damage model, this remarkable 4n-event deciding “flat-upright” cell-growth characteristics showed several consequences, for example, cancer-important, E-cadherin-β-catenin cell-to-cell adherence destruction, which gave diploid progeny cells, mobility freedom from cell contact inhibition, likely in renewal tissues. This 4n-skewed division-system with inheritance in progeny cells for repeat occurrences as mentioned for flat-up-right growth patterns is similar to claimed concepts of metaplasia-EMT/MET embryogenesis events in cancer evolution. A scrutiny of this literature, proof-wise invalidated this embryological concept by tetraploid 8C cells occurring in MET events and, was noted for small cell occurrence, i.e., diploidy from 4n-8C reductive division, an also event for tumor relapse cells, derived from genome damaging therapy agents. Pre-cancer hyperplasia reported MSP, cadherincatenin destruction and 90° perpendicularity to basal cell membrane. The DNA-damage-repair model can weed-out therapy-agents triggering 4n-skewed division. Cancer-control, beginning-information, is likely from mutational identity of the 4n derived fitness-gained cells.
基金The National Natural Science Foundation of China under contract Nos 51609244 and 51779258
文摘An analytical model with essential parameters given by a two-phase numerical model is utilized to study the net boundary layer current and sediment transport under skewed asymmetric oscillatory sheet flows. The analytical model is the first instantaneous type model that can consider phase-lag and asymmetric boundary layer development. The two-phase model supplies the essential phase-lead, instantaneous erosion depth and boundary layer development for the analytical model to enhance the understanding of velocity skewness and acceleration skewness in sediment flux and transport rate. The sediment transport difference between onshore and offshore stages caused by velocity skewness or acceleration skewness is shown to illustrate the determination of net sediment transport by the analytical model. In previous studies about sediment transport in skewed asymmetric sheet flows, the generation of net sediment transport is mainly concluded to the phase-lag effect.However, the phase-lag effect is shown important but not enough for the net sediment transport, while the skewed asymmetric boundary layer development generated net boundary layer current and mobile bed effect are key important in the transport process.
文摘This article makes the first attempt in assessing the influence of active constrained layer damping(ACLD)treatment towards precise control of frequency responses of functionally graded skew-magneto-electroelastic(FGSMEE)plates by employing finite element methods.The materials are functionally graded across the thickness of the plate in terms of modest power-law distributions.The principal equations of motion of FGSMEE are derived via Hamilton’s principle and solved using condensation technique.The effect of ACLD patches are modelled by following the complex modulus approach(CMA).Additionally,distinctive emphasis is laid to evaluate the influence of geometrical skewness on the attenuation capabilities of the plate.The accuracy of the current analysis is corroborated with comparison of previous researches of similar kind.Additionally,a complete parametric study is directed to understand the combined impacts of various factors like coupling fields,patch location,fiber orientation of piezoelectric patch in association with skew angle and power-law index.
文摘In this paper, we report on an analytical solution for beam-type skewed highway bridges subjected to truck loading. To confirm the analysis derivation and the solution obtained, the moment and shear responses to the design truck load are acquired using the analytical method for a number of typical US highway bridges and compared with those from numerical finite element method (FEM) analysis. In addition, the lateral distribution factors for moment and shear used in routine design are investigated based on comparison of the analytical approach and FEM. The analytical solution is shown in good agreement with the FEM result. Furthermore, the relevant provisions in the American Association of State Highway Transportation Officials' (AASHTO's) LRFD Bridge Design Specifications are also discussed here for comparison, particularly with respect to design application. It is observed that the design code specified load distribution factor may not predict well, especially for shear and/or severe skew.
基金supported by the National Natural Science Foundation of China(12131015,12071422).
文摘Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic.