This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish d...This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.展开更多
In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solutio...In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.展开更多
Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonaliza...Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.展开更多
Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionles...Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.展开更多
A weight double trigonometric series is presented as an approximate fundamental solution for orthotropic plate.Integral equation of orthotropic plate bending is solved by a new method, which only needs one basic bound...A weight double trigonometric series is presented as an approximate fundamental solution for orthotropic plate.Integral equation of orthotropic plate bending is solved by a new method, which only needs one basic boundary integral Eq., puts one fictitious boundary outside plate domain. Examples show that the approximate fundamental solution and solving method proposed in this paper are simple, reliable and quite precise. And they are applicable for various boundary conditions.展开更多
This paper reports the results of experimental research the longitudinal stiffeners in an orthotropic plated bridge deck on concerning the connection between the deck plate and the web of a microscopic scale. An impor...This paper reports the results of experimental research the longitudinal stiffeners in an orthotropic plated bridge deck on concerning the connection between the deck plate and the web of a microscopic scale. An important number of test specimens of a weld are studied with the help of a video microscope, to detect the efficiency of the root of the weld. The second part of the paper is concerned with parametric analysis of the lack of weld penetration by using accurate finite element modelling. The results demonstrate that the weld quality often required can not always be assured, which surely has important consequence on the stresses in the weld and the fatigue resistance.展开更多
In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported r...In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under in-plane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.展开更多
A generalized homotopy-based Coiflet-type wavelet method for solving strongly nonlinear PDEs with nonhomogeneous edges is proposed.Based on the improvement of boundary difference order by Taylor expansion,the accuracy...A generalized homotopy-based Coiflet-type wavelet method for solving strongly nonlinear PDEs with nonhomogeneous edges is proposed.Based on the improvement of boundary difference order by Taylor expansion,the accuracy in wavelet approximation is largely improved and the accumulated error on boundary is successfully suppressed in application.A unified high-precision wavelet approximation scheme is formulated for inhomogeneous boundaries involved in generalized Neumann,Robin and Cauchy types,which overcomes the shortcomings of accuracy loss in homogenizing process by variable substitution.Large deflection bending analysis of orthotropic plate with forced boundary moments and rotations on nonlinear foundation is used as an example to illustrate the wavelet approach,while the obtained solutions for lateral deflection at both smally and largely deformed stage have been validated compared to the published results in good accuracy.Compared to the other homotopy-based approach,the wavelet scheme possesses good efficiency in transforming the differential operations into algebraic ones by converting the differential operators into iterative matrices,while nonhomogeneous boundary is directly approached dispensing with homogenization.The auxiliary linear operator determined by linear component of original governing equation demonstrates excellent approaching precision and the convergence can be ensured by iterative approach.展开更多
In this work,a non-classical analytical approach for buckling analysis of partially cracked generally orthotropic plate is proposed under the thermal domain.The derivation for the governing equation is based on the no...In this work,a non-classical analytical approach for buckling analysis of partially cracked generally orthotropic plate is proposed under the thermal domain.The derivation for the governing equation is based on the non-classical approach using Kirchhoff’s thin plate theory and the modified couple stress theory.The effect of fibre orientation on critical buckling temperature is incorporated by considering the coefficients of mutual influence.Line spring model is applied with some modifications to formulate all the crack terms while the thermal effects are introduced in form of thermal in-plane moments and forces.The final governing equation is solved using Galerkin’s method and the relation for critical buckling temperature as affected by fibre orientation is obtained.The variation of critical buckling temperature as affected by fibre orientation for different values of crack length,crack location and length scale parameter is presented.Also,the effect of fibre orientation on fundamental frequency under the thermal domain is analysed.展开更多
When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certa...When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certain viscoelastic characteristic in a high temperature environment. In this paper, a laminated orthotropic rectangular plate with viscoelastic interfaces, described by the Kelvin-Voigt model, is considered. A power series expansion technique is adopted to approximate the time-variation of various field quantities. Results indicate that the response of the laminated plate with viscoelastic interfaces changes remarkably with time, and is much different from that of a plate with spring-like or viscous interfaces.展开更多
An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates.The coefficients of the polynomial function were determined by uniaxial test results.Buckling intera...An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates.The coefficients of the polynomial function were determined by uniaxial test results.Buckling interaction and failure interaction formulae under combined axial tension/compression and shear loads were established.Based on the uniaxial load test results of orthotropic plates,the buckling load and bearing capacity under any proportion of the combined loads could be predicted by using the proposed interaction formulae.The buckling interaction curves and failure envelopes predicted by the proposed interaction formulae were in excellent agreement with the test results.展开更多
In this paper, ihe probleins of nonlinear unsymmeirucal bending for cylindricallyorthotropic circular plale are sludied by using “ the method of two-variabie”￣[1], and theuniformly valid asympiotic soluiions of Nth...In this paper, ihe probleins of nonlinear unsymmeirucal bending for cylindricallyorthotropic circular plale are sludied by using “ the method of two-variabie”￣[1], and theuniformly valid asympiotic soluiions of Nth-order .lor ε_1 and Mth-order for ε_2 areobiained展开更多
In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturba...In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbation'[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained.展开更多
A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simpl...A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.展开更多
The fundamental solutions of the orthotropic thick plates taking into account the transverse shear deformation are derived by means of Hrmander's operator method and a plane-wave decomposition of the Dirac δ-func...The fundamental solutions of the orthotropic thick plates taking into account the transverse shear deformation are derived by means of Hrmander's operator method and a plane-wave decomposition of the Dirac δ-function in this papey.The boundary integral equations of the thick plates have been formulated which are adapted to arbitrary boundary conditions and plane forms.The numerical calculation of the fundamental solutions is discussed in detail.Some numerical examples are analyzed with BEM.展开更多
To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the met...To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.展开更多
It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this ...It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this paper is to verify the effect of radius on the materal properties According to the flat stress-strain relation the values of material properties E E andwhich are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.展开更多
Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bendin...Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.展开更多
By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate wi...By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.展开更多
In this Paper we study the recursive equations under the recursive boundary conditions for W_(nm),nm, v_(nm) and ψ_(nm)(n=0.1.2...N:m=1.2...M. which derivedby the two-variable method ￣[3] in the preceding paper￣[1]...In this Paper we study the recursive equations under the recursive boundary conditions for W_(nm),nm, v_(nm) and ψ_(nm)(n=0.1.2...N:m=1.2...M. which derivedby the two-variable method ￣[3] in the preceding paper￣[1]. We then solve these problems by using the method of regular perturbation￣[2]. and the uniformly valid asymptotic solution is obtained. Lastly we consider a particular example i. e the bending problems of the axisymmetrical circular plate by using the mixed perurbation method and compare our results with the exact solution found in Ret [ 5 ]. They are similarly coincided.展开更多
基金supported by the National Natural Science Foundation of China (10772039 and 10632030)the National Basic Research Program of China (973 Program) (2010CB832704)
文摘This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation.Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space.The operator matrix of the equation set is proven to be a Hamilton operator matrix.Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition.There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions,with opposite sides simply supported and opposite sides clamped.Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given.Analytical solutions using two examples are presented to show the use of the new methods described in this paper.To verify the accuracy and convergence,a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method,the Levy method and the new method.Results show that the new technique has good accuracy and better convergence speed than other methods,especially in relation to internal forces.A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods,with solutions compared to those produced by the Galerkin method.
文摘In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.
文摘Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.
基金Project supported by the National Natural Science Foundation of China (No.10572049)
文摘Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.
文摘A weight double trigonometric series is presented as an approximate fundamental solution for orthotropic plate.Integral equation of orthotropic plate bending is solved by a new method, which only needs one basic boundary integral Eq., puts one fictitious boundary outside plate domain. Examples show that the approximate fundamental solution and solving method proposed in this paper are simple, reliable and quite precise. And they are applicable for various boundary conditions.
文摘This paper reports the results of experimental research the longitudinal stiffeners in an orthotropic plated bridge deck on concerning the connection between the deck plate and the web of a microscopic scale. An important number of test specimens of a weld are studied with the help of a video microscope, to detect the efficiency of the root of the weld. The second part of the paper is concerned with parametric analysis of the lack of weld penetration by using accurate finite element modelling. The results demonstrate that the weld quality often required can not always be assured, which surely has important consequence on the stresses in the weld and the fatigue resistance.
文摘In this paper, applying perturbation method to von Karman-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, the postbuckling behavior of simply supported rectangular orthotropic plates under in-plane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.
基金supported by the National Natural Science Foundation of China(Grant No.11902189)。
文摘A generalized homotopy-based Coiflet-type wavelet method for solving strongly nonlinear PDEs with nonhomogeneous edges is proposed.Based on the improvement of boundary difference order by Taylor expansion,the accuracy in wavelet approximation is largely improved and the accumulated error on boundary is successfully suppressed in application.A unified high-precision wavelet approximation scheme is formulated for inhomogeneous boundaries involved in generalized Neumann,Robin and Cauchy types,which overcomes the shortcomings of accuracy loss in homogenizing process by variable substitution.Large deflection bending analysis of orthotropic plate with forced boundary moments and rotations on nonlinear foundation is used as an example to illustrate the wavelet approach,while the obtained solutions for lateral deflection at both smally and largely deformed stage have been validated compared to the published results in good accuracy.Compared to the other homotopy-based approach,the wavelet scheme possesses good efficiency in transforming the differential operations into algebraic ones by converting the differential operators into iterative matrices,while nonhomogeneous boundary is directly approached dispensing with homogenization.The auxiliary linear operator determined by linear component of original governing equation demonstrates excellent approaching precision and the convergence can be ensured by iterative approach.
文摘In this work,a non-classical analytical approach for buckling analysis of partially cracked generally orthotropic plate is proposed under the thermal domain.The derivation for the governing equation is based on the non-classical approach using Kirchhoff’s thin plate theory and the modified couple stress theory.The effect of fibre orientation on critical buckling temperature is incorporated by considering the coefficients of mutual influence.Line spring model is applied with some modifications to formulate all the crack terms while the thermal effects are introduced in form of thermal in-plane moments and forces.The final governing equation is solved using Galerkin’s method and the relation for critical buckling temperature as affected by fibre orientation is obtained.The variation of critical buckling temperature as affected by fibre orientation for different values of crack length,crack location and length scale parameter is presented.Also,the effect of fibre orientation on fundamental frequency under the thermal domain is analysed.
基金Project supported by the National Natural Science Foundation of China (No. 10432030) and NCET.
文摘When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certain viscoelastic characteristic in a high temperature environment. In this paper, a laminated orthotropic rectangular plate with viscoelastic interfaces, described by the Kelvin-Voigt model, is considered. A power series expansion technique is adopted to approximate the time-variation of various field quantities. Results indicate that the response of the laminated plate with viscoelastic interfaces changes remarkably with time, and is much different from that of a plate with spring-like or viscous interfaces.
文摘An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates.The coefficients of the polynomial function were determined by uniaxial test results.Buckling interaction and failure interaction formulae under combined axial tension/compression and shear loads were established.Based on the uniaxial load test results of orthotropic plates,the buckling load and bearing capacity under any proportion of the combined loads could be predicted by using the proposed interaction formulae.The buckling interaction curves and failure envelopes predicted by the proposed interaction formulae were in excellent agreement with the test results.
文摘In this paper, ihe probleins of nonlinear unsymmeirucal bending for cylindricallyorthotropic circular plale are sludied by using “ the method of two-variabie”￣[1], and theuniformly valid asympiotic soluiions of Nth-order .lor ε_1 and Mth-order for ε_2 areobiained
文摘In this paper,under the non-uniformtransverse load,the problems of nonlinear bending for orthotropic rectangular plate are studied by using'the method of twovariable'[1]and 'the method of mixing perturbation'[2].The uniformly valid asymptotic solutions of Nth-order for ε1 and Mth-order for ε2 for ortholropic rectangular plale with four clamped edges are oblained.
文摘A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.
基金The project supported by National Natural Science Foundation of China
文摘The fundamental solutions of the orthotropic thick plates taking into account the transverse shear deformation are derived by means of Hrmander's operator method and a plane-wave decomposition of the Dirac δ-function in this papey.The boundary integral equations of the thick plates have been formulated which are adapted to arbitrary boundary conditions and plane forms.The numerical calculation of the fundamental solutions is discussed in detail.Some numerical examples are analyzed with BEM.
文摘To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.
文摘It has been been reported that the reduced stiffness of non-homogeneous cylindricallyorthotrpic circular plate varing exponentially with radius r is obtained by using thebending theory of a simple beamThe aim of this paper is to verify the effect of radius on the materal properties According to the flat stress-strain relation the values of material properties E E andwhich are the functions of radius r are obtained.Compared with the experimentalvalues the analytical values of the material properties are in essential agreement withtem.
文摘Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.
文摘By using “the method of modified two-variable”,“the method of mixing perturbation” and introducing four small parameters,the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied.And the uniformly valid asymptotic solution of Nth-order for ε_1 and Mth-order for ε_2 of the deflection functions and stress function are obtained.
文摘In this Paper we study the recursive equations under the recursive boundary conditions for W_(nm),nm, v_(nm) and ψ_(nm)(n=0.1.2...N:m=1.2...M. which derivedby the two-variable method ￣[3] in the preceding paper￣[1]. We then solve these problems by using the method of regular perturbation￣[2]. and the uniformly valid asymptotic solution is obtained. Lastly we consider a particular example i. e the bending problems of the axisymmetrical circular plate by using the mixed perurbation method and compare our results with the exact solution found in Ret [ 5 ]. They are similarly coincided.
