In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, ...In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.展开更多
The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral...The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral deflection including second-order effects,the relationship of force versus displacement is established. In the formulation of finite element method (FEM),the stiffness matrix developed has the same accuracy with the solution of exact differential equations. The proposed tangent stiffness matrix will degenerate into the Bernoulli-Euler beam without the effects of shear deformation. The critical buckling force can be determined from the determinant element assemblage by FEM. The equivalent stiffness matrix constructed by the topmost deflection and slope is established by static condensation method,and then a recurrence formula is proposed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.展开更多
This paper presents a novel stiffness prediction method for periodic beam-like structures based on the two-scale equivalence at different strain states.The macroscopic fields are achieved within the framework of Timos...This paper presents a novel stiffness prediction method for periodic beam-like structures based on the two-scale equivalence at different strain states.The macroscopic fields are achieved within the framework of Timoshenko beam theory,while the microscopic fields are obtained by the newly constructed displacement form within the framework of three-dimensional(3D)elasticity theory.The new displacement form draws lessons from that in the asymptotic homogenization method(AHM),but the present field governing equations or boundary conditions for the first two order influence functions are constructed and very different from the way they were defined in the AHM.The constructed displacement form,composed of one homogenized and two warping terms,can accurately describe the deformation mode of beam-like structures.Then,with the new displacement form,the effective stiffness is achieved by the equivalence principle of macro-and microscopic fields.The finite element formulations of the proposed method are presented,which are easy to implement.Numerical examples validate that the present method can well predict both diagonal and coupling stiffness of periodic composite beams.展开更多
基金Sponsored by the Subsidization Plan for Outstanding Young Teacher of Ministry of Education
文摘In order to understand mechanical characters and find out a calculating method for preflex beams used in particular bridge engineering projects, two types of simply supported preflex beams with variable crosssection, preflex beam with alterative web depth and preflex beam with aherative steel flange thickness, are dis- cussed on how to achieve the equivalent moment of inertia and Young＇ s modulus. Additionally, methods of cal- culating the equivalent bending stiffness and post-cracking deflection are proposed. Results of the experiments on 6 beams agree well with the theoretical analysis, which proves the correctness of the proposed formulas.
基金Sponsored by the National Key Technology Research and Development Program (Grant No.2006BAJ12B03-2)
文摘The tangent stiffness matrix of Timoshenko beam element is applied in the buckling of multi-step beams under several concentrated axial forces with elastic supports. From the governing differential equation of lateral deflection including second-order effects,the relationship of force versus displacement is established. In the formulation of finite element method (FEM),the stiffness matrix developed has the same accuracy with the solution of exact differential equations. The proposed tangent stiffness matrix will degenerate into the Bernoulli-Euler beam without the effects of shear deformation. The critical buckling force can be determined from the determinant element assemblage by FEM. The equivalent stiffness matrix constructed by the topmost deflection and slope is established by static condensation method,and then a recurrence formula is proposed. The validity and efficiency of the proposed method are shown by solving various numerical examples found in the literature.
基金supported by the China Postdoctoral Science Foundation(Grant No.2021T140040)the National Natural Science Foundation of China(Grant Nos.12002019 and 11872090).
文摘This paper presents a novel stiffness prediction method for periodic beam-like structures based on the two-scale equivalence at different strain states.The macroscopic fields are achieved within the framework of Timoshenko beam theory,while the microscopic fields are obtained by the newly constructed displacement form within the framework of three-dimensional(3D)elasticity theory.The new displacement form draws lessons from that in the asymptotic homogenization method(AHM),but the present field governing equations or boundary conditions for the first two order influence functions are constructed and very different from the way they were defined in the AHM.The constructed displacement form,composed of one homogenized and two warping terms,can accurately describe the deformation mode of beam-like structures.Then,with the new displacement form,the effective stiffness is achieved by the equivalence principle of macro-and microscopic fields.The finite element formulations of the proposed method are presented,which are easy to implement.Numerical examples validate that the present method can well predict both diagonal and coupling stiffness of periodic composite beams.
