The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to an...The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.展开更多
This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized function...This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.展开更多
The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion ...The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.展开更多
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
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
目的:探讨弯钳撬拔术在股骨近端髓内钉(proximal femoral nail antirotation,PFNA)内固定治疗难复性股骨粗隆间骨折中的应用效果。方法:选择2021年6月—2023年5月在罗定市中医院接受手术治疗的难复性股骨粗隆间骨折患者144例,用随机数...目的:探讨弯钳撬拔术在股骨近端髓内钉(proximal femoral nail antirotation,PFNA)内固定治疗难复性股骨粗隆间骨折中的应用效果。方法:选择2021年6月—2023年5月在罗定市中医院接受手术治疗的难复性股骨粗隆间骨折患者144例,用随机数字表法将患者分为对照组(n=72,接受切开复位PFNA内固定治疗)、观察组(n=72,接受弯钳撬拔PFNA内固定治疗)。对比两组手术基本情况、骨折愈合情况、髋关节功能评分、并发症发生情况。结果:两组手术时间比较,差异无统计学意义(P>0.05);观察组术中出血量较对照组少,差异有统计学意义(P<0.05)。观察组术后住院时间、负重开始时间、骨折愈合时间均较对照组短,差异均有统计学意义(P<0.05)。术后6个月,观察组髋关节功能评分较对照组高,差异有统计学意义(P<0.05)。两组术后6个月的髋关节功能优良率比较,差异无统计学意义(P>0.05)。两组并发症发生率比较,差异无统计学意义(P>0.05)。结论:弯钳撬拔PFNA内固定治疗难复性股骨粗隆间骨折较切开复位PFNA内固定治疗更具优势,在促进术后骨折愈合、恢复患侧髋关节功能方面的作用均较理想,且不会增加并发症,是一种优质的手术模式。展开更多
We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being ben...We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.展开更多
By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value ...By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.展开更多
Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are e...Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of shearing force is formulated by trigonometric series and used to determine the coefficients in above expansions. The computational resuits give the chord and span wise distributions of nomal and shear stress in the cover plate and the honeycomb core. At the same time, the attenuation of additional stress from fixed end to free end along the length of beam is shown clearly.展开更多
In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-valu...In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavelet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.展开更多
Compositionally graded composite of alumina-20%zirconia (volume fraction) was fabricated by using centrifugal casting incorporated with relatively thin slip. An EPMA analysis exhibited a nearly linear variation of the...Compositionally graded composite of alumina-20%zirconia (volume fraction) was fabricated by using centrifugal casting incorporated with relatively thin slip. An EPMA analysis exhibited a nearly linear variation of the alumina/zirconia ratio along the centrifugal direction; zirconia tended to accumulate in the bottom section, while alumina in the top section. Such a graded structure exhibited a considerably higher flexural strength when the alumina rich surface was subjected to a tensile stress than compositionally uniform composite of the same average composition. Fracture toughness measurement across the specimen thickness by indentation method revealed that the crack lengths along the vertical and horizontal directions were different. The anisotropy of the fracture toughness was accounted for by the variation of the residual stress across the specimen thickness.展开更多
基金supported by the National Natural Science Foundation of China(11302055)Heilongjiang Post-doctoral Scientific Research Start-up Funding(LBH-Q14046)
文摘The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.
文摘This paper discusses the mathematical modeling for the mechanics of solid using the distribution theory of Schwartz to the beam bending differential Equations. This problem is solved by the use of generalized functions, among which is the well known Dirac delta function. The governing differential Equation is Euler-Bernoulli beams with jump discontinuities on displacements and rotations. Also, the governing differential Equations of a Timoshenko beam with jump discontinuities in slope, deflection, flexural stiffness, and shear stiffness are obtained in the space of generalized functions. The operator of one of the governing differential Equations changes so that for both Equations the Dirac Delta function and its first distributional derivative appear in the new force terms as we present the same in a Euler-Bernoulli beam. Examples are provided to illustrate the abstract theory. This research is useful to Mechanical Engineering, Ocean Engineering, Civil Engineering, and Aerospace Engineering.
基金the National Natural Science Foundation of China(Nos.10472102,10725210 and 10432030)
文摘The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.
基金Project supported by the National Natural Science Foundation of China (No.10432030).
文摘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.
基金National Natural Science Foundation(No.19732020)the Doctoral Research Foundation of China
文摘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.
文摘目的:探讨弯钳撬拔术在股骨近端髓内钉(proximal femoral nail antirotation,PFNA)内固定治疗难复性股骨粗隆间骨折中的应用效果。方法:选择2021年6月—2023年5月在罗定市中医院接受手术治疗的难复性股骨粗隆间骨折患者144例,用随机数字表法将患者分为对照组(n=72,接受切开复位PFNA内固定治疗)、观察组(n=72,接受弯钳撬拔PFNA内固定治疗)。对比两组手术基本情况、骨折愈合情况、髋关节功能评分、并发症发生情况。结果:两组手术时间比较,差异无统计学意义(P>0.05);观察组术中出血量较对照组少,差异有统计学意义(P<0.05)。观察组术后住院时间、负重开始时间、骨折愈合时间均较对照组短,差异均有统计学意义(P<0.05)。术后6个月,观察组髋关节功能评分较对照组高,差异有统计学意义(P<0.05)。两组术后6个月的髋关节功能优良率比较,差异无统计学意义(P>0.05)。两组并发症发生率比较,差异无统计学意义(P>0.05)。结论:弯钳撬拔PFNA内固定治疗难复性股骨粗隆间骨折较切开复位PFNA内固定治疗更具优势,在促进术后骨折愈合、恢复患侧髋关节功能方面的作用均较理想,且不会增加并发症,是一种优质的手术模式。
基金supported by the 973 program (Grants 2012CB937500, 2013CB932604)the National Natural Science Foundation of China (Grants 51535005, 51472117, 11021262, 11172303, 11132011)the Fundamental Research Funds for the Central Universities (Grant NP2013309)
文摘We find by ab initio simulations that significant overall tensile strain can be induced by pure bending in a wide range of two-dimensional crystals perpendicular to the bending moment, just like an accordion being bent to open. This bending-induced tensile strain increases in a power law with bent curvature and can be over 20% in monolayered black phosphorus and transition metal dichalcogenides at a moderate curvature of but more than an order weaker in graphene and hexagon boron nitride. This accordion effect is found to be a quantum mechanical effect raised by the asymmetric response of chemical bonds and electron density to the bending curvature.
文摘By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.
文摘Restrained bending of thin-walled box beam with honeycomb core is analyzed on the basis of rigid profile assumption. The method of variable separation is applied and two ordinary differential governing equations are established and solved. The boundary conditions are satisfied rigorously and the solutions are expressed by means of eigen function expansions. The diagram of shearing force is formulated by trigonometric series and used to determine the coefficients in above expansions. The computational resuits give the chord and span wise distributions of nomal and shear stress in the cover plate and the honeycomb core. At the same time, the attenuation of additional stress from fixed end to free end along the length of beam is shown clearly.
文摘In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavelet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.
文摘Compositionally graded composite of alumina-20%zirconia (volume fraction) was fabricated by using centrifugal casting incorporated with relatively thin slip. An EPMA analysis exhibited a nearly linear variation of the alumina/zirconia ratio along the centrifugal direction; zirconia tended to accumulate in the bottom section, while alumina in the top section. Such a graded structure exhibited a considerably higher flexural strength when the alumina rich surface was subjected to a tensile stress than compositionally uniform composite of the same average composition. Fracture toughness measurement across the specimen thickness by indentation method revealed that the crack lengths along the vertical and horizontal directions were different. The anisotropy of the fracture toughness was accounted for by the variation of the residual stress across the specimen thickness.
