According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam e...According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.展开更多
Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are considered.It is shown that these equations have solutions on subspaces of the polynomial,...Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are considered.It is shown that these equations have solutions on subspaces of the polynomial,exponential ortrigonometric form defined by linear nth-order ordinary differential equations with constant coefficients for n=4,...,9.Several examples of exact solutions are presented.展开更多
We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bek...We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking＇s area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L^3 as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.展开更多
A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impu...A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impulsive loads.Considering the rate strengthening and thermal softening effects on member impact behavior,a modified Cowper-Symonds model for constructional steels is utilized.The element displacement field is built upon the superposition of GBT cross-section deformation modes,so arbitrary deformations such as cross-section distortions,local buckling and warping shear can all be involved by the proposed model.The amplitude function of each cross-section deformation mode is approximated by the cubic non-uniform B-spline basis functions.The Kirchhoff s thin-plate assumption is utilized in the construction of the bending related displacements.The Green-Lagrange strain tensor and the second Piola-Kirchhoff(PK2)stress tensor are employed to measure deformations and stresses at any material point,where stresses are assumed to be in plane-stress state.In order to verify the effectiveness of the proposed GBT model,three numerical cases involving impulsive loading of the thin-walled parts are given.The GBT results are compared with those of the Ls-Dyna shell finite element.It is shown that the proposed model and the shell finite element analysis has equivalent accuracy in displacement and stress.Moreover,the proposed model is much more computationally efficient and structurally clearer than the shell finite elements.展开更多
基金Specialized Research Fund for the Doctoral Program of Higher Education (No.20070247002)
文摘According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Northwest University Graduate Innovation and Creativity Funds under Grant No.07YZZ15
文摘Classification and reduction of the generalized fourth-order nonlinear differential equations arising from theliquid films are considered.It is shown that these equations have solutions on subspaces of the polynomial,exponential ortrigonometric form defined by linear nth-order ordinary differential equations with constant coefficients for n=4,...,9.Several examples of exact solutions are presented.
基金Supported by the National Natural Science Foundation of China under Grant No.10573004
文摘We discuss the entropy of the Garfinkle-Horowitz-Strominger dilaton black hole by using the thin film brick-wall model, and the entropy obtained is proportional to the horizon area of the black hole confirming the Bekenstein-Hawking＇s area-entropy formula. Then, by comparing with the original brick-wall method, we find that the result obtained by the thin film method is more reasonable avoiding some drawbacks, such as little mass approximation, neglecting logarithm term, and taking the term L^3 as a contribution of the vacuum surrounding the black hole, and the physical meaning of the entropy is more clearer.
基金The National Natural Science Foundation of China(No.51078229)the Specialized Research Fund for the Doctoral Program of Higher Education(o.20100073110008)
文摘A nonlinear explicit dynamic finite element formulation based on the generalized beam theory(GBT)is proposed and developed to simulate the dynamic responses of prismatic thin-walled steel members under transverse impulsive loads.Considering the rate strengthening and thermal softening effects on member impact behavior,a modified Cowper-Symonds model for constructional steels is utilized.The element displacement field is built upon the superposition of GBT cross-section deformation modes,so arbitrary deformations such as cross-section distortions,local buckling and warping shear can all be involved by the proposed model.The amplitude function of each cross-section deformation mode is approximated by the cubic non-uniform B-spline basis functions.The Kirchhoff s thin-plate assumption is utilized in the construction of the bending related displacements.The Green-Lagrange strain tensor and the second Piola-Kirchhoff(PK2)stress tensor are employed to measure deformations and stresses at any material point,where stresses are assumed to be in plane-stress state.In order to verify the effectiveness of the proposed GBT model,three numerical cases involving impulsive loading of the thin-walled parts are given.The GBT results are compared with those of the Ls-Dyna shell finite element.It is shown that the proposed model and the shell finite element analysis has equivalent accuracy in displacement and stress.Moreover,the proposed model is much more computationally efficient and structurally clearer than the shell finite elements.
