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Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary
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作者 Zhenliang HU Xueyang ZHANG Xianfang LI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第9期1573-1594,共22页
This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mecha... This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported. 展开更多
关键词 micro/nanoscale cantilever plate partially debonded bending fracture singular integral equation oscillatory singularity
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Experimental,Numerical,and Analytical Studies on the Bending of Mechanically Lined Pipe 被引量:1
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作者 WEI Wen-bin YUAN Lin +1 位作者 ZHOU Jia-sheng LIU Zheng 《China Ocean Engineering》 SCIE EI CSCD 2024年第2期221-232,共12页
Mechanically lined pipe(MLP)is often used for offshore oil and gas transport because of its low cost and corrosion resistance.During installation and operation,the pipe may undergo severe bending deformation,which cau... Mechanically lined pipe(MLP)is often used for offshore oil and gas transport because of its low cost and corrosion resistance.During installation and operation,the pipe may undergo severe bending deformation,which causes the liner to separate from the outer pipe and buckles,affecting the stability of the whole line.In this paper,the buckling response of MLP subjected to bending is investigated to clarify its bending characteristics by employing both experiments,numerical simulation,as theoretical methods.Two types of MLPs were manufactured with GB 45 carbon steel(SLP)and Al 6061(ALP)used as the outer pipe material,respectively.The hydraulic expansion and bending experiments of small-scale MLPs are conducted.In addition to the ovalized shape of the cross-section for the SLP specimens,the copper liner was found to wrinkle on the compressive side.In contrast,the liner of ALP remains intact without developing any wrinkling and collapse mode.In addition,a dedicated numerical framework and theoretical models were also established.It was found both the manufacturing and bending responses of the MLP can be well reproduced,and the predicted maximum moment and critical curvatures are in good agreement with the experimental results. 展开更多
关键词 lined pipe bending nonlinear ring theory BUCKLING PLASTICITY
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Effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on tensile and bending properties of high-Al-containing Mg alloys
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作者 Sumi Jo Gyo Myeong Lee +2 位作者 Jong Un Lee Young Min Kim Sung Hyuk Park 《Journal of Magnesium and Alloys》 SCIE EI CAS CSCD 2024年第2期779-793,共15页
This study investigates the effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on the uniaxial tensile and three-point bending properties of extruded Mg alloys containing high Al contents.The ext... This study investigates the effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on the uniaxial tensile and three-point bending properties of extruded Mg alloys containing high Al contents.The extruded Mg–9Al–1Zn–0.3Mn(AZ91)alloy contains lamellar-structured Mg_(17)Al_(12)discontinuous precipitates along the grain boundaries,which are formed via static precipitation during natural air cooling.The extruded Mg–11Al–1Zn–0.3Mn(AZ111)alloy contains spherical Mg_(17)Al_(12)precipitates at the grain boundaries and inside the grains,which are formed via dynamic precipitation during extrusion.Due to inhomogeneous distribution of precipitates,the AZ111 alloy consists of two different precipitate regions:precipitate-rich region with numerous precipitates and finer grains and precipitate-scarce region with a few precipitates and coarser grains.The AZ111 alloy exhibits a higher tensile strength than the AZ91 alloy because its smaller grain size and more abundant precipitates result in stronger grain-boundary hardening and precipitation hardening effects,respectively.However,the tensile elongation of the AZ111 alloy is lower than that of the AZ91 alloy because the weak cohesion between the dynamic precipitates and the matrix facilitates the crack initiation and propagation.During bending,a macrocrack initiates on the outer surface of bending specimen in both alloys.The AZ111 alloy exhibits higher bending yield strength and lower failure bending strain than the AZ91 alloy.The bending specimens of the AZ91 alloy have similar bending formability,whereas those of the AZ111 alloy exhibit considerable differences in bending formability and crack propagation behavior,depending on the distribution and number density of precipitates in the specimen.In bending specimens of the AZ111 alloy,it is found that the failure bending strain(ε_(f,bending))is inversely proportional to the area fraction of precipitates in the outer zone of bending specimen(A_(ppt)),with a relationship ofε_(f,bending)=–0.1A_(ppt)+5.86. 展开更多
关键词 Mg–Al alloy EXTRUSION bending Precipitation Microstructure
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Bending Failure Mode and Prediction Method of the Compressive Strain Capacity of A Submarine Pipeline with Dent Defects
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作者 HOU Fu-heng JIA Lu-sheng +3 位作者 CHEN Yan-fei ZHANG Qi ZHONG Rong-feng WANG Chun-sha 《China Ocean Engineering》 SCIE EI CSCD 2024年第4期636-647,共12页
A dent is a common type of defects for submarine pipeline.For submarine pipelines,high hydrostatic pressure and internal pressure are the main loads.Once pipelines bend due to complex subsea conditions,the compression... A dent is a common type of defects for submarine pipeline.For submarine pipelines,high hydrostatic pressure and internal pressure are the main loads.Once pipelines bend due to complex subsea conditions,the compression strain capacity may be exceeded.Research into the local buckling failure and accurate prediction of the compressive strain capacity are important.A finite element model of a pipeline with a dent is established.Local buckling failure under a bending moment is investigated,and the compressive strain capacity is calculated.The effects of different parameters on pipeline local buckling are analyzed.The results show that the dent depth,external pressure and internal pressure lead to different local buckling failure modes of the pipeline.A higher internal pressure indicates a larger compressive strain capacity,and the opposite is true for external pressure.When the ratio of external pressure to collapse pressure of intact pipeline is greater than 0.1,the deeper the dent,the greater the compressive strain capacity of the pipeline.And as the ratio is less than 0.1,the opposite is true.On the basis of these results,a regression equation for predicting the compressive strain capacity of a dented submarine pipeline is proposed,which can be referred to during the integrity assessment of a submarine pipeline. 展开更多
关键词 submarine pipeline dent defect bending load local buckling compressive strain capacity
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Bending Strength of Glass Materials under Strong Dynamic Impact and Its Strain Rate Effects
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作者 LIU Xiaogen QI Shuang +2 位作者 WEI Shaoshan WAN Detian JIN Chunxia 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS CSCD 2024年第6期1358-1364,共7页
Based on the structural characteristics of the high-speed loading tester,a four-point bending test device was designed to carry out the four-point bending strength test of glass under the action of static load and dif... Based on the structural characteristics of the high-speed loading tester,a four-point bending test device was designed to carry out the four-point bending strength test of glass under the action of static load and different impact velocities,and the formulae for calculating the maximum dynamic stress and strain rate of glass specimens under the action of impact loads were derived.The experimental results show that the bending strength values of the glass under dynamic impact loading are all higher than those under static loading.With the increase of impact speed,the bending strength value of glass specimens generally tends to increase,and the bending strength value increases more obviously when the impact speed exceeds 0.5 m/s or higher.By increasing the impact velocity,higher tensile strain rate of glass specimens can be obtained because the load action time becomes shorter.The bending strength of the glass material increases with its tensile strain rate,and when the tensile strain rate is between 0 and 2 s^(-1),the bending strength of the glass specimen grows more obviously with the strain rate,indicating that the glass bending strength is particularly sensitive to the tensile strain rate in this interval.As the strain rate increases,the number of cracks formed after glass breakage increases significantly,thus requiring more energy to drive the crack formation and expansion,and showing the strain rate effect of bending strength at the macroscopic level.The results of the study can provide a reference for the load bearing and structural design of glass materials under dynamic loading. 展开更多
关键词 glass materials strong dynamic impact bending strength strain rate effect dynamic enhancement factor
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Analysis of deformation mechanisms in magnesium single crystals using a dedicated four-point bending tester
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作者 Yutaka Yoshida Rikuto Izawa Kenji Ohkubo 《Journal of Magnesium and Alloys》 SCIE EI CAS CSCD 2024年第5期1911-1917,共7页
In this study,we explored the deformation mechanisms of Mg single crystals using a combination of scanning electron microscopy and electron backscattered diffraction in conjunction with a dedicated four-point bending ... In this study,we explored the deformation mechanisms of Mg single crystals using a combination of scanning electron microscopy and electron backscattered diffraction in conjunction with a dedicated four-point bending tester.We prepared two single-crystal samples,oriented along the<1120>and<1010>directions,to assess the mechanisms of deformation when the initial basal slip was suppressed.In the<1120>sample,the primary{1012}twin(T1)was confirmed along the<1120>direction of the sample on the compression side with an increase in bending stress.In the<1010>sample,T1 and the secondary twin(T2)were confirmed to be along the<1120>direction,with an orientation of±60°with respect to the bending stress direction,and their direction matched with(0001)in T1 and T2.This result implies that crystallographically,the basal slip occurs readily.In addition,the<1010>sample showed the double twin in T1 on the compression side and the tertiary twin along the<1010>direction on the tension side.These results demonstrated that the maximum bending stress and displacement changed significantly under the bend loading because the deformation mechanisms were different for these single crystals.Therefore,the correlation between bending behavior and twin orientation was determined,which would be helpful for optimizing the bending properties of Mg-based materials. 展开更多
关键词 Four-point bending Magnesium single crystal TWINNING Basal slip Scanning electron microscopy Electron backscatter diffraction
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A Light and Simplified Branch Bending Method for Young Pear Trees
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作者 Jintao XU Longfei LI +3 位作者 Minghui JI Huan LIU Lijuan GAO Baofeng HAO 《Plant Diseases and Pests》 2024年第2期19-21,共3页
Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with ... Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with wide source of raw materials,cheap price and simple operation,which is also suitable for the management of low-age branches in the process of high grafting and upgrading of traditional big trees. 展开更多
关键词 Pear tree Light and simplified Branch bending METHOD
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The Effects of the Longitudinal Axis of Loading upon Bending, Shear and Torsion of a Thin-Walled Cantilever Channel Beam
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作者 David W. A. Rees Abdelraouf M. Sami Alsheikh 《World Journal of Mechanics》 2024年第5期73-96,共24页
Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoreticall... Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section. 展开更多
关键词 Thin-Aluminium Channels Cantilever Beam bending Shear Torsion WARPING BIMOMENT Flexural Axis Centre of Twist CENTROID Shear Centre Torsional Stiffness Constrained Stress
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Multiresolution method for bending of plates with complex shapes
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作者 Jizeng WANG Yonggu FENG +2 位作者 Cong XU Xiaojing LIU Youhe ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第4期561-582,共22页
A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth... A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity. 展开更多
关键词 MULTIRESOLUTION generalized Coiflet wavelet integral collocation method irregular domain complex shape high accuracy plate bending
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Unified Solution Method of Rectangular Plate Elastic Bending 被引量:9
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作者 许琪楼 姬同庚 +2 位作者 姜锐 唐国明 姬鸿恩 《Journal of Southeast University(English Edition)》 EI CAS 2002年第3期241-248,共8页
The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition a... The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate. The latter can be solved by using the superposition principle. Making use of the recommended method, the bending of the plate with all kinds of... 展开更多
关键词 bending of elastic thin plate rectangular plate unified solution method
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无界域上具有记忆的非自治Plate方程随机吸引子的存在性
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作者 蒲武军 姚晓斌 《西北师范大学学报(自然科学版)》 CAS 2024年第3期115-126,共12页
研究无界域上一类具有衰退记忆和加性噪声的非自治Plate方程解的长时间行为.利用一致估计验证了解的拉回渐近紧性,获得了其随机吸引子的存在性.
关键词 随机吸引子 非自治plate方程 衰退记忆 加性噪声
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基于IP联合蛋白质组学探讨ENG互作蛋白在bEnd.3细胞中的作用
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作者 陈清杰 李奥迪 +4 位作者 季慧敏 孙艺瑄 蒋越 叶子奇 潘荣 《湖北科技学院学报(医学版)》 2024年第6期461-466,F0002,共7页
目的本研究拟筛选并验证在脑微血管内皮细胞(bEnd.3)中Endoglin(ENG)的互作蛋白及其作用。方法采用蛋白质组学和生物信息学技术鉴定并富集ENG互作蛋白,对这些互作蛋白进行亚细胞定位、GO功能注释、IPR注释和蛋白互作网络等分析。将以上... 目的本研究拟筛选并验证在脑微血管内皮细胞(bEnd.3)中Endoglin(ENG)的互作蛋白及其作用。方法采用蛋白质组学和生物信息学技术鉴定并富集ENG互作蛋白,对这些互作蛋白进行亚细胞定位、GO功能注释、IPR注释和蛋白互作网络等分析。将以上分析筛选出的ENG互作蛋白,采用免疫共沉淀(IP)实验、细胞免疫荧光(IF)和蛋白免疫印迹(WB)技术进行验证和对比,探究ENG互作蛋白在棕榈酸(PA)、基因沉默和过表达ENG处理bEnd.3细胞中的表达变化及作用。结果通过蛋白质组学分析,bEnd.3细胞中ENG互作蛋白在亚细胞定位分析中细胞骨架相关成分呈现出较高的占比;通过GO注释和IPR注释进一步发现,是细胞骨架中的中间纤维和微丝蛋白呈现较高的富集状态。ENG与细胞骨架蛋白互作热力图结果显示,与对照组相比,PA处理的bEnd.3细胞中微丝蛋白Filamin B(Flnb)数值显著降低。IP和IF结果显示,bEnd.3细胞中ENG与Flnb存在蛋白互作和共定位情况。WB结果显示,bEnd.3细胞在PA处理条件下,ENG和Flnb蛋白表达均下降;在ENG沉默条件下,Flnb蛋白随ENG表达的减少而降低;在ENG过表达条件下,Flnb蛋白随ENG表达的增加而升高。结论ENG互作蛋白广泛参与到多种相关的生物途径以及信号通路之中,ENG在bEnd.3细胞中与Flnb蛋白存在相互作用且二者具有共定位现象,ENG还能够调控PA处理的bEnd.3细胞Flnb蛋白表达水平。 展开更多
关键词 ENG Flnb 互作蛋白 bend.3 棕榈酸
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Electro-chemo-mechanical analysis of the effect of bending deformation on the interface of flexible solid-state battery 被引量:2
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作者 Yutao SHI Chengjun XU +2 位作者 Bingbing CHEN Jianqiu ZHOU Rui CAI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第2期189-206,共18页
Flexible solid-state battery has several unique characteristics including high flexibility,easy portability,and high safety,which may have broad application prospects in new technology products such as rollup displays... Flexible solid-state battery has several unique characteristics including high flexibility,easy portability,and high safety,which may have broad application prospects in new technology products such as rollup displays,power implantable medical devices,and wearable equipments.The interfacial mechanical and electrochemical problems caused by bending deformation,resulting in the battery damage and failure,are particularly interesting.Herein,a fully coupled electro-chemo-mechanical model is developed based on the actual solid-state battery structure.Concentration-dependent material parameters,stress-dependent diffusion,and potential shift are considered.According to four bending forms(k=8/mm,0/mm,-8/mm,and free),the results show that the negative curvature bending is beneficial to reducing the plastic strain during charging/discharging,while the positive curvature is detrimental.However,with respect to the electrochemical performance,the negative curvature bending creates a negative potential shift,which causes the battery to reach the cut-off voltage earlier and results in capacity loss.These results enlighten us that suitable electrode materials and charging strategy can be tailored to reduce plastic deformation and improve battery capacity for different forms of battery bending. 展开更多
关键词 solid-state battery electro-chemo-mechanical coupling model bending deformation PHASE-TRANSFORMATION plastic deformation
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NEW SOLUTION SYSTEM FOR CIRCULAR SECTOR PLATE BENDING AND ITS APPLICATION 被引量:15
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作者 Yao, W Zhong, WX Su, B 《Acta Mechanica Solida Sinica》 SCIE EI 1999年第4期307-315,共9页
Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So ... Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is effective. 展开更多
关键词 circular sector plate Hamiltonian system bending moment functions ANALOGY
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The symplectic eigenfunction expansion theorem and its application to the plate bending equation 被引量:5
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作者 黄俊杰 阿拉坦仓 王华 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第9期3616-3623,共8页
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite... This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner. 展开更多
关键词 plate bending equation symplectic eigenfunction expansion theorem infinite dimensional Hamiltonian operator analytical solution
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AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES 被引量:6
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作者 Guojun Nie Zheng Zhong 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第4期289-295,共7页
Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using ... Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials. 展开更多
关键词 two-directional functionally graded materials circular and annular plates axisym-metric bending semi-analytical numerical method integrated design
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Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements 被引量:4
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作者 B. Kanber O. Yavuz Bozkurt 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第4期355-365,共11页
In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based... In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results. 展开更多
关键词 Finite element method Transition plate elements Elasto-plastic analysis. plate bending problems
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On Feasibility of Variable Separation Method Based on Hamiltonian System for a Class of Plate Bending Equations 被引量:5
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作者 额布日力吐 阿拉坦仓 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期569-574,共6页
The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended e... The eigenfunction system of infinite-dimensional Hamiltonian operators appearing in the bending problem of rectangular plate with two opposites simply supported is studied. At first, the completeness of the extended eigenfunction system in the sense of Cauchy's principal value is proved. Then the incompleteness of the extended eigenfunction system in general sense is proved. So the completeness of the symplectic orthogonal system of the infinite-dimensional Hamiltonian operator of this kind of plate bending equation is proved. At last the general solution of the infinite dimensional Hamiltonian system is equivalent to the solution function system series expansion, so it gives to theoretical basis of the methods of separation of variables based on Hamiltonian system for this kind of equations. 展开更多
关键词 plate bending equation infinite-dimensioanl Hamiltonian operator eigenfunction system COMPLETENESS general solution
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Pure bending of simply supported circular plate of transversely isotropic functionally graded material 被引量:6
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作者 LI Xiang-yu DING Hao-jiang CHEN Wei-qiu 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第8期1324-1328,共5页
This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial d... This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM). 展开更多
关键词 Transversely isotropic Functionally graded materials (FGMs) Pure bending problem Simply supported circular plate Axisymmetric deformation
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SELF-INSTABILITY AND BENDING BEHAVIORS OF NANO PLATES 被引量:10
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作者 Zhiqiao Wang Yapu Zhao 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第6期630-643,共14页
This paper aims at investigating the size-dependent self-buckling and bending behaviors of nano plates through incorporating surface elasticity into the elasticity with residual stress fields. In the absence of extern... This paper aims at investigating the size-dependent self-buckling and bending behaviors of nano plates through incorporating surface elasticity into the elasticity with residual stress fields. In the absence of external loading, positive surface tension induces a compressive residual stress field in the bulk of the nano plate and there may be self-equilibrium states corresponding to the plate self-buckling. The self-instability of nano plates is investigated and the critical self-instability size of simply supported rectangular nano plates is determined. In addition, the residual stress field in the bulk of the nano plate is usually neglected in the existing literatures, where the elastic response of the bulk is often described by the classical Hooke's law. The present paper considered the effect of the residual stress in the bulk induced by surface tension and adopted the elasticity with residual stress fields to study the bending behaviors of nano plates without buckling. The present results show that the surface effects only modify the coefficients in corresponding equations of the classical Kirchhoff plate theory. 展开更多
关键词 nano plates self-buckling surface tension residual stress
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