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1.
Based on elasticity theory, various two-dimensional (2D) equations and solutions for extensional deformation have been deduced
systematically and directly from the three-dimensional (3D) theory of thick rectangular plates by using the Papkovich–Neuber
solution and the Lur’e method without ad hoc assumptions. These equations and solutions can be used to construct a refined
theory of thick plates for extensional deformation. It is shown that the displacements and stresses of the plate can be represented
by the displacements and transverse normal strain of the midplane. In the case of homogeneous boundary conditions, the exact
solutions for the plate are derived, and the exact equations consist of three governing differential equations: the biharmonic
equation, the shear equation, and the transcendental equation. With the present theory a solution of these can satisfy all
the fundamental equations of 3D elasticity. Moreover, the refined theory of thick plate for bending deformation constructed
by Cheng is improved, and some physical or mathematical explanations and proof are provided to support our justification.
It is important to note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of nonhomogeneous
boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order
terms with respect to plate thickness. The correctness of the stress assumptions in the classic plane-stress problems is revised.
In an example it is shown that the exact or accurate solutions may be obtained by applying the refined theory deduced herein. 相似文献
2.
This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method. 相似文献
3.
从三维弹性力学基本方程出发,通过假设自由边的边界位移函数,建立了正交异性层合板的状态方程,给出了对边自由,对边简支矩形板的解析解.此解满足层合板的基本方程和层间连续条件.用本文的方法比较容易处理层合板的自由边.算例表明,数值结果具有较高的精度. 相似文献
4.
This paper studies the eigenfunction expansion method to solve the two-dimensional(2D) elasticity problems based on the stress formulation.The fundamentalsystem of partial differential equations of the 2D problems is rewritten as an upper tri-angular differential system based on the known results,and then the associated uppertriangular operator matrix matrix is obtained.By further research,the two simpler com-plete orthogonal systems of eigenfunctions in some space are obtained,which belong tothe two block operators arising in the operator matrix.Then,a more simple and conve-nient general solution to the 2D problem is given by the eigenfunction expansion method.Furthermore,the boundary conditions for the 2D problem,which can be solved by thismethod,are indicated.Finally,the validity of the obtained results is verified by a specificexample. 相似文献
5.
层状层电介质空间轴对称问题的状态空间解 总被引:15,自引:0,他引:15
从横观各向同性压电介质空间轴对称问题的基本方程出发,建立了压电介质空间轴对称问题的状态变量方程,对状态变量方程进行Hankel变换,得到以状态变量表示的单层压电介质在Hankel变换空间中的解,讨论了3种不同特征根的情况,利用提出的解得到了半无限压电体在垂直集中载荷和点电荷作出下的Boussinesq解。利用传递矩阵方法导出了多层压电介质空间轴对称问题解一般解析式。 相似文献
6.
According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed. 相似文献
7.
A theory of general solutions of plane problems is developed for the coupled equations in plane elasticity of two-dimensional
octagonal quasicrystals. In virtue of the operator method, the general solutions of the antiplane and inplane problems are
given constructively with two displacement functions. The introduced displacement functions have to satisfy higher order partial
differential equations, and therefore it is difficult to obtain rigorous analytic solutions directly and is not applicable
in most cases. In this case, a decomposition and superposition procedure is employed to replace the higher order displacement
functions with some lower order displacement functions, and accordingly the general solutions are further simplified in terms
of these functions. In consideration of different cases of characteristic roots, the general solution of the antiplane problem
involves two cases, and the general solution of the inplane problem takes three cases, but all are in simple forms that are
convenient to be applied. Furthermore, it is noted that the general solutions obtained here are complete in x
3-convex domains.
相似文献
8.
Summary A new meshless method is developed to analyze steady-state heat conduction problems with arbitrarily spatially varying thermal conductivity in isotropic and anisotropic materials. The analog equation is used to construct equivalent equations to the original differential equation so that a simpler fundamental solution of the Laplacian operator can be employed to take the place of the fundamental solutions related to the original governing equation. Next, the particular solution is approximated by using radial basis functions, and the corresponding homogeneous solution is solved by means of the virtual boundary collocation method. As a result, a new method fully independent of mesh is developed. Finally, several numerical examples are implemented to demonstrate the efficiency and accuracy of the proposed method. The numerical results show good agreement with the actual results.This work was supported by the National Natural Science Foundation of China (No. 10472082) and Australian Research Council. 相似文献
9.
N. I. Ostrosablin 《Journal of Applied Mechanics and Technical Physics》2013,54(6):971-988
A dynamic three-dimensional system of linear equations in terms of displacements of the theory of elasticity of transversely isotropic media is given explicit expressions for phase velocities and polarization vectors of plane waves. All the longitudinal normals are found. For some values of the elasticity moduli, the system of equations is reduced to a diagonal shape. For static equations, all the conditions of the system ellipticity are determined. Two new representations of displacements through potential functions that satisfy three independent quasi-harmonic equations are given. Constraints on elasticity moludi, at which the corresponding coefficients in these representations are real, different, equal, or complex, are determined. It is shown that these representations are general and complete. Each representation corresponds to a recursion (symmetry) operator, i.e., a formula of production of new solutions. 相似文献
10.
本文由横观各向同性的弹性力学方程出发,研究有限长圆柱体的自由振动问题。利用文献「1」的通解,将位移分量和应力分量分别表达成傅里叶-塞尔级数和双曲-贝塞尔级数的形式。通过边界条件和级数的正交关系,得到关于有限长圆柱自由振动频率的特征方程。利用数值方法求解特征根,从而得到圆柱体三维振动的自振频率。 相似文献
11.
Analytical solutions for some nonlinear evolution equations 总被引:1,自引:0,他引:1
IntroductionItiswell_knownthatmanyimportantdynamicsprocessescanbedescribedbyspecificnonlinearpartialdifferentialequations .Whenanonlinearpartialdifferentialequationisusedtodescribeaphysicalparameterthatshowssomekindsofpropagationoraggregationproperties,oneofthemostimportantphysicalmotivationsistosolvethepartialdifferentialequationwithacertaintypeoftravellingwavesolution .Inthepastseveraldecades,therehavebeenmanyattemptsinthisfieldbothbymathematiciansandphysicists[1]- [16 ],however,duetothecomp… 相似文献
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13.
In this paper, the (3+1)-dimensional KP equation is mainly discussed. Based on the Wronskian technique, the double Wronskian solution is established. Generating functions for matrix entries satisfy the linear system of partial differential equations involving free parameters. Rational, Matveev, and complexiton solutions are obtained by taking special cases in a general double Wronskian solution. 相似文献
14.
POINTFORCESOLUTIONFORATRANSVERSELYISOTROPICELASTICLAYERPOINTFORCESOLUTIONFORATRANSVERSELYISOTROPICELASTICLAYER¥DingHaojiang(丁... 相似文献
15.
This paper presents a general solution of the three-dimensional governing equations for the axisymmetric buckling problem of transversely isotropic media. The solution is expressed by a displacement function that satisfies a homogeneous fourth-order partial differential equation. Using this general solution, the axisymmetric buckling of circular and annular plates is investigated and exact solutions are obtained for appropriate boundary conditions. Numerical results are considered for clamped and simply supported circular and annular plates in comparison with existent results. 相似文献
16.
IntroductionAsymplecticsystematicmethodology[1- 3]forelasticitywasestablishedbyZhongWan_xie .Hepresentedcreativelythedualvectorsandthesymplecticorthogonalrelationshipandopenedaworkplatformparalleledtothetraditionalelasticity[4 - 9].AnewdualvectorandanewdualdifferentialmatrixLwerepresentedforasymplecticsystematicmethodologyfortwo_dimensionalelasticityandaneworthogonalrelationshipwasdiscoveredforisotropicplaneproblems[4 ]byLuoJian_hui.Theneworthogonalrelationshipisgeneralizedfororthotropicelas… 相似文献
17.
In this paper, an analytical solution is developed to determine deformations and stresses in circular disks made of functionally
graded materials subjected to internal and/or external pressure. Taking mechanical properties of the materials of circular
disks to be linear variations, the governing equation is derived from basic equations of axisymmetric, plane stress problems
in elasticity. By transforming the governing equation into a hypergeometric equation, an accurate analytical solution of deformations
and stresses in circular disks is obtained. The comparison with the numerical solution indicates that both approaches give
very agreeable results, indicating correctness of the proposed analytical solution. The obtained analytical solution is employed
to determine the radial displacement and stresses in circular disks subjected to external pressure, internal pressure, and
internal and external pressure, respectively. How the radius ratio of circular disks affects deformations and stresses is
also investigated. 相似文献
18.
加权残数配点法解正交各向异性板的积分方程 总被引:1,自引:0,他引:1
本文推导了一般各向异性板弯曲的积分方程,运用加权残数配点法求解了正交各向异性板弯曲的积发方程,本文将部分配点取在边界上,另一部分配点取在域外,只用关于找度的基本积分方程,而不用关于转角的补充积分方程,简化了方程求解和计算程序,由于正交各向异性板没有争析形式的、实用的基本解,本文提出了两种新的近似基本解;加权双三角级数;广义各向同性板解析形式的基本解和加权双三角级数的叠加,算例表明,本文提出的解法和近似基本解适用于各类边界条件的正交各向异性板,具有简单、可靠、精度高等优点。 相似文献
19.
Nowadays,thecurrenttheoriesofplatesandshells,suchasKirchhoff’sthinplatetheoryandReissner’smoderatelythickplatetheoryetc.,aree... 相似文献
20.