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.
