The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical ...The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method （FEM） is developed to obtain the temperature stress of the bi-modulus struc- tures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM proce- dure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.展开更多
The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equa...The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of tile problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green＇s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.展开更多
In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of ser...In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.展开更多
Differential equations of free/forc ed vibrations of stepped rectangular thin plates on Winkler's foundation are estab lished by using singular functions, and their general solutions are also solved for expressi...Differential equations of free/forc ed vibrations of stepped rectangular thin plates on Winkler's foundation are estab lished by using singular functions, and their general solutions are also solved for expression of vibration mode function and frequency equations on usual suppo rts derived with W operator, as well as forced responses of such plates unde r different_type loads disc ussed with Fourier expansion of generalized functions.展开更多
Differential equations of free/forced vibrations of n_step one_way thin rectangular plates subjected to in_plane tensile/compressive force in y_direction on Winkler's foundation are established by using singular f...Differential equations of free/forced vibrations of n_step one_way thin rectangular plates subjected to in_plane tensile/compressive force in y_direction on Winkler's foundation are established by using singular functions, their general solutions solved for, expression of vibration mode function and frequency equation on usual supports derived with W operator. Influence functions for various cases deduced here may also be used to solve problems of static buckling or stability for beams and plates in relevant circumstances.展开更多
Differential equations of free forced vibrations of one -way rectangular stepped thin plated on Winkler 's foundation are established by using singular functions ,their general solutions are solved :exprssion of ...Differential equations of free forced vibrations of one -way rectangular stepped thin plated on Winkler 's foundation are established by using singular functions ,their general solutions are solved :exprssion of vibration mode function and frequency equations on usual supports are derived from W operator :forced responses of such plates under different -type loads are discussed with generalized functions .展开更多
Serious uneven settlement of the tunnel may directly cause safety problems.At this stage,the deformation of the tunnel is predicted and analyzed mainly by numerical simulation,while the commonly used finite element me...Serious uneven settlement of the tunnel may directly cause safety problems.At this stage,the deformation of the tunnel is predicted and analyzed mainly by numerical simulation,while the commonly used finite element method(FEM)uses low-order continuous elements.Therefore,the accuracy of tunnel settlement prediction is not enough.In this paper,a method is proposed to study the vertical deformation of the tunnel by using the combination of isogeometric analysis(IGA)and Bézier extraction operator.Compared with the traditional IGA method,this method can be easily integrated into the existing FEM framework,and ensure the same accuracy.A numerical example of an elastic foundation beam subjected to uniformly distributed load and an engineering example of an equivalent elastic foundation beamof the tunnel are given.The results show that the solution of the IGA method is closer to the theoretical solution of the initial-parameter method than the FEM,and the accuracy and reliability of the proposedmodel are verified.Moreover,it not only provides some theoretical support for the longitudinal design of the tunnel,but also provides a new way for the application and popularization of IGA in tunnel engineering.展开更多
A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the founda...A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.展开更多
This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations using the Generalized Differential Quadrature (GDQ) method...This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations using the Generalized Differential Quadrature (GDQ) method. The analyses are worked out considering the First-order Shear Deformation Theory (FSDT) for the above mentioned moderately thick structural elements. The effect of the shell curvatures is included from the beginning of the theory formulation in the kinematic model. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Simple Rational Bézier curves are used to define the meridian curve of the revolution structures. The discretization of the system by means of the GDQ technique leads to a standard linear problem for the static analysis and to a standard linear eigenvalue problem for the dynamic analysis. Comparisons between the present formulation and the Reissner-Mindlin theory are presented. Furthermore, GDQ results are compared with those obtained by using commercial programs. Very good agreement is observed. Finally, new results are presented in order to investtigate the effects of the Winkler modulus, the Pasternak modulus and the inertia of the elastic foundation on the behavior of laminated shells of revolution.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11072143 and11272200)
文摘The materials with different moduli in tension and compression are called bi-modulus materials. Graphene is such a kind of materials with the highest strength and the thinnest thickness. In this paper, the mechanical response of the bi-modulus beam subjected to the temperature effect and placed on the Winkler foundation is studied. The differential equations about the neutral axis position and undetermined parameters of the normal strain of the bi-modulus foundation beam are established. Then, the analytical expressions of the normal stress, bending moment, and displacement of the foundation beam are derived. Simultaneously, a calculation procedure based on the finite element method （FEM） is developed to obtain the temperature stress of the bi-modulus struc- tures. It is shown that the obtained bi-modulus solutions can recover the classical modulus solution, and the results obtained by the analytical expressions, the present FEM proce- dure, and the traditional FEM software are consistent, which verifies the accuracy and reliability of the present analytical model and procedure. Finally, the difference between the bi-modulus results and the classical same modulus results is discussed, and several reasonable suggestions for calculating and optimizing the certain bi-modulus member in practical engineering are presented.
文摘The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of tile problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green＇s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.
文摘In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.
文摘Differential equations of free/forc ed vibrations of stepped rectangular thin plates on Winkler's foundation are estab lished by using singular functions, and their general solutions are also solved for expression of vibration mode function and frequency equations on usual suppo rts derived with W operator, as well as forced responses of such plates unde r different_type loads disc ussed with Fourier expansion of generalized functions.
文摘Differential equations of free/forced vibrations of n_step one_way thin rectangular plates subjected to in_plane tensile/compressive force in y_direction on Winkler's foundation are established by using singular functions, their general solutions solved for, expression of vibration mode function and frequency equation on usual supports derived with W operator. Influence functions for various cases deduced here may also be used to solve problems of static buckling or stability for beams and plates in relevant circumstances.
文摘Differential equations of free forced vibrations of one -way rectangular stepped thin plated on Winkler 's foundation are established by using singular functions ,their general solutions are solved :exprssion of vibration mode function and frequency equations on usual supports are derived from W operator :forced responses of such plates under different -type loads are discussed with generalized functions .
基金support fromthe National Natural Science Foundation of China (52079128).
文摘Serious uneven settlement of the tunnel may directly cause safety problems.At this stage,the deformation of the tunnel is predicted and analyzed mainly by numerical simulation,while the commonly used finite element method(FEM)uses low-order continuous elements.Therefore,the accuracy of tunnel settlement prediction is not enough.In this paper,a method is proposed to study the vertical deformation of the tunnel by using the combination of isogeometric analysis(IGA)and Bézier extraction operator.Compared with the traditional IGA method,this method can be easily integrated into the existing FEM framework,and ensure the same accuracy.A numerical example of an elastic foundation beam subjected to uniformly distributed load and an engineering example of an equivalent elastic foundation beamof the tunnel are given.The results show that the solution of the IGA method is closer to the theoretical solution of the initial-parameter method than the FEM,and the accuracy and reliability of the proposedmodel are verified.Moreover,it not only provides some theoretical support for the longitudinal design of the tunnel,but also provides a new way for the application and popularization of IGA in tunnel engineering.
文摘A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.
文摘This work presents the static and dynamic analyses of laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations using the Generalized Differential Quadrature (GDQ) method. The analyses are worked out considering the First-order Shear Deformation Theory (FSDT) for the above mentioned moderately thick structural elements. The effect of the shell curvatures is included from the beginning of the theory formulation in the kinematic model. The solutions are given in terms of generalized displacement components of points lying on the middle surface of the shell. Simple Rational Bézier curves are used to define the meridian curve of the revolution structures. The discretization of the system by means of the GDQ technique leads to a standard linear problem for the static analysis and to a standard linear eigenvalue problem for the dynamic analysis. Comparisons between the present formulation and the Reissner-Mindlin theory are presented. Furthermore, GDQ results are compared with those obtained by using commercial programs. Very good agreement is observed. Finally, new results are presented in order to investtigate the effects of the Winkler modulus, the Pasternak modulus and the inertia of the elastic foundation on the behavior of laminated shells of revolution.
