A Light and Simplified Branch Bending Method for Young Pear Trees

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.

Unified Solution Method of Rectangular Plate Elastic Bending

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...

Comparison study on calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949

In order to study the calculation methods of bending behavior of Chinese reinforced concrete beams from 1912 to 1949, tests on the mechanical performance of 66 rebars from different modem Chinese concrete buildings, the concrete compressive strength of 12 modem Chinese concrete buildings, and the concrete cover thickness of 9 modem Chinese concrete buildings are carried out; and the actual material properties and structural conformations of modem Chinese concrete buildings are obtained. Then, the comparison on calculation methods of bending behavior including the original Chinese calculation method, the present Chinese calculation method, the present American calculation method and the present European calculation method is studied. The results show that the original Chinese calculation method of bending behavior is based on the allowable stress calculation method, and the design safety factors are 3.55 to 4. 0. In term of the calculation area of longitudinal rebars of reinforced concrete beams, without considering earthquake action, the original Chinese structural calculation method is safer than the present Chinese structural calculation method, the present European structural calculation method, and the present American structural calculation method. The results can provide support for the structural safety assessments of modem Chinese reinforced concrete buildings.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT_VENANT BENDING

Using the single crack solution and the regular solution of plane harmonic function, the problem of Saint_Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross_section is not thin_walled, but of small torsion rigidity is proposed. Some numerical examples are given.

2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

A Numerical-analytic Method for Quickly Predicting Springback of Numerical Control Bending of Thin-walled Tube

Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process was put forward. The method is based on springback angle model derived using analytic method and simulation results from three-dimensional （3D） rigid-plastic finite element method （FEM）. The method is validated through comparison with experimental results. The features of the method are as follows： （1） The method is high in efficiency because it combines advantages of rigid-plastic FEM and analytic method. （2） The method is satisfactory in accuracy, since the field variables used in the model is resulting from 3D rigid-plastic FEM solution, and the effects both of axial force and strain neutral axis shift have been included. （3） Research on multi-factor effects can be carried out using the method due to its advantage inheriting from rigid-plastic FEM. The method described here is also of general significance to other bending processes.

Method of Semi Analytic Perturbation Weighted Residuals for Nonlinear Bending of Shallow Shells

The semi? analytic perturbation weighted residuals method was used to solve the nonlinear bending problem of shallow shells, and the fifth order B spline was taken as trial function to seek an efficient method for nonlinear bending problem of shallow shells. The results from the present method are in good agreement with those derived from other methods. The present method is of higher accuracy, lower computing time and wider adaptability. In addition, the design of computer program is simple and it is easy to be programmed.

BIMORPH-TYPE PIEZOELECTRIC THIN FILM BENDING ACTUATORS SYNTHESIZED BY HYDROTHERMAL METHOD

Lead zirconate titanium solid-solution (PZT) thin films with variousthickness are synthesized on titanium substrates by repeated hydrothermal treatments. Young modulus,electric-field-induced displacement and the density of the PZT film are measured respectively.Bimorph- type bending actuators are fabricated using these films. The model, which is used toanalyze the driving ability of bimorph-type bending actuators by hydrothermal method, is set up. Itcan be seen that the driving ability of bimorph-type bending actuators can be greatly improved byoptimizing the thickness of PZT thin film and substrate from the theoretical analysis results. Themeasured values are expected to agree with the theoretical values calculated by the above model.

Determining Atmospheric Boundary Layer Height with the Numerical Differentiation Method Using Bending Angle Data from COSMIC

This paper presents a new method to estimate the height of the atmospheric boundary layer(ABL) by using COSMIC radio occultation bending angle(BA) data. Using the numerical differentiation method combined with the regularization technique, the first derivative of BA profiles is retrieved, and the height at which the first derivative of BA has the global minimum is defined to be the ABL height. To reflect the reliability of estimated ABL heights, the sharpness parameter is introduced, according to the relative minimum of the BA derivative. Then, it is applied to four months of COSMIC BA data(January, April, July, and October in 2008), and the ABL heights estimated are compared with two kinds of ABL heights from COSMIC products and with the heights determined by the finite difference method upon the refractivity data. For sharp ABL tops(large sharpness parameters), there is little difference between the ABL heights determined by different methods, i.e.,the uncertainties are small; whereas, for non-sharp ABL tops(small sharpness parameters), big differences exist in the ABL heights obtained by different methods, which means large uncertainties for different methods. In addition, the new method can detect thin ABLs and provide a reference ABL height in the cases eliminated by other methods. Thus, the application of the numerical differentiation method combined with the regularization technique to COSMIC BA data is an appropriate choice and has further application value.

Numerical Method Based on Compatible Manifold Element for Thin Plate Bending

The typical quadrangular and triangular elements for thin plate bending based on Kirchhoff assumptions are the non- conforming elements with low computational accuracy and limitative application range in fmite element method（FEM）. Some compatible elements can be developed by the means of supplementing correction functions, increasing nodes in element or on the boundaries, expanding nodal degrees of freedom（DOF）, etc, but these elements are inconvenient to apply in practice for the high calculation complexity. In this paper, in order to overcome the defects of thin plate bending finite element, numerical manifold method（NMM） was introduced to solve thin plate bending deformation problem. Rectangular mesh was adopted as mathematical mesh to form f＇mite element cover system, and then 16-cover manifold element was proposed. Numerical manifold formulas were constructed on the basis of minimum potential energy principle, displacement boundary conditions are implemented by penalty function method, and all the element matrixes were derived in details. The 16-cover element has a simple calculation process for employing only the transverse displacement cover DOFs as the basic unknown variables, and has been proved to meet the requirements of completeness and full compatibility. As an application, the presented 16-cover element has been used to analyze bending deformation of square thin plate under different loads and boundary conditions, and the results show that numerical manifold method with compatible element, compared with finite element method, can improve computational accuracy and convergence greatly.

Swelling-induced finite bending of functionally graded pH-responsive hydrogels:a semi-analytical method

Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.

METHOD TO CALCULATE BENDING CENTER AND STRESS INTENSITY FACTORS OF CRACKED CYLINDER UNDER SAINT-VENANT BENDING

Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.

AN EXACT ELEMENT METHOD FOR BENDING OF NONHOMOGENEOUS THIN PLATES

In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

A SOLVING METHOD FOR A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS WITH AN APPLICATION TO THE BENDING PROBLEM OF A THICK PLATE

A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved, the mathematical role and physical nature of the theorem is interpreted briefly. As an example, the theorem is applied to solve the problem of thermo-force bending of a thick plate.

NONSINGULAR KERNEL BOUNDARY ELEMENT METHOD FOR THIN-PLATE BENDING PROBLEMS

In this paper, the nonsingular fundamental solutions were obtained from Fourier series under some given conditions. These solutions can be taken as the kernels of integral equation. So a new boundary element method was presented, with which all kinds of thin-plate bending problems can be solved, even with complicated loadings and sinuous boundaries. The calculation is much simpler and more accurate.

KIN SP:A boundary element method based code for single pile kinematic bending in layered soil

In high seismicity areas, it is important to consider kinematic effects to properly design pile foundations.Kinematic effects are due to the interaction between pile and soil deformations induced by seismic waves. One of the effect is the arise of significant strains in weak soils that induce bending moments on piles. These moments can be significant in presence of a high stiffness contrast in a soil deposit. The single pile kinematic interaction problem is generally solved with beam on dynamic Winkler foundation approaches(BDWF) or using continuous models. In this work, a new boundary element method(BEM)based computer code(KIN SP) is presented where the kinematic analysis is preceded by a free-field response analysis. The analysis results of this method, in terms of bending moments at the pile-head and at the interface of a two-layered soil, are influenced by many factors including the soil-pile interface discretization. A parametric study is presented with the aim to suggest the minimum number of boundary elements to guarantee the accuracy of a BEM solution, for typical pile-soil relative stiffness values as a function of the pile diameter, the location of the interface of a two-layered soil and of the stiffness contrast. KIN SP results have been compared with simplified solutions in literature and with those obtained using a quasi-three-dimensional(3D) finite element code.

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

ON MORTAR-TYPE TRUNC ELEMENT METHOD FOR PLATE BENDING PROBOEM

Wepresnet a brief introduction of applying the idea of mortar method to locally nonconforming TRUNC element for solving plate bending problem. At the interfaces, three mortar conditions, one for the value of solution in pointwise way, the other two for the normal and tangential derivatives of the solution in projection way, are provided to secure the global convergence. Afte some detailed analysis, we obtain that its error estimates in both energy norm and discrete H1 norm are optimal for u*∈H3(Ω)∩H2 0(Ω).

RATIONAL FINITE ELEMENT METHOD FOR ELASTIC BENDING OF REISSNER PLATES

In this paper; some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfect combination of the analytic methods and numeric methods, has been presented. This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures. What's more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.

Multiresolution method for bending of plates with complex shapes

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.