Study On Analogue Slab Method Of Box-shaped Hollow Floor Based On Asymptotic Homogenization Method

As a new type of floor,cast-in-place concrete hollow floor has the advantages of light weight,convenient construction and low cost.The thin-walled hollow box is widely used in the construction of practical engineering projects because of its remarkable characteristics such as large hollow ratio,low reinforcement ratio and saving more reinforced concrete.At present,the research on thin-walled box hollow floor at home and abroad mostly adopts scale test and numerical simulation to study its deformation and internal force characteristics;The macroscopic equivalent elastic modulus of hollow floor has typical anisotropic characteristics,and its macroscopic(coarse-scale)equivalent elastic modulus is directly affected by the structure and material parameters of local(small-scale)hollow box.However,the multi-scale method is seldom used to analyze the mechanical properties of box hollow beamless floor.In this paper,the coarse-scale equivalent elastic modulus of thin-walled box hollow floor is calculated by using the self-developed multi-scale analysis software(AHMP),which is completely different from the traditional analogue slab method.The influence of the small-scale characteristics of hollow floor on the equivalent elastic quantity of hollow floor is analyzed.The modulus calculated by multi-scale method is used in the calculation of quasi plate method,and the concept of multi-scale analog slab method(MASM)is formed;This paper also uses the traditional analogue slab method and direct finite element model method to analyze the coarse scale deformation and internal force characteristics of hollow floor,and compares the results with the multi-scale analogue slab method,which verifies the applicability and accuracy of the multi-scale analogue slab method in the design of hollow floor.The main work and conclusions are as follows:(1)The representative volume elements(RVE)of box type hollow floor with different void ratios are established.The equivalent elastic constants of RVE are calculated by AHMP,which are converted into young’s modulus,Poisson’s ratio and shear modulus required by analogue slab method,Then the deformation and internal force of hollow floor are calculated by analogue slab method,The design process of "multi-scale analogue slab method" is formed;Compared with the results of the equivalent method in the analogue slab method,the results of the three methods have the same change trend,and the values are within the reasonable error range,which proves that the multi-scale method is reasonable and effective to calculate the design parameters such as young’s modulus of the box hollow floor.(2)The deflection and deformation of hollow box floor under three boundary conditions and uniform load are calculated by the technical specification method(analogue slab method),direct finite element method and multi-scale analogue slab method.The results show that the deflection calculation value based on multi-scale analogue slab method is close to the theoretical calculation value and the actual deformation value of hollow floor,which can accurately simulate the vertical deformation of the original structure.(3)Seven groups of anisotropic material parameters of RVE of box hollow floor with different hollow ratio are calculated by using AHMP.The equivalent solid plate finite element models are established respectively under the boundary conditions of four simply supported,four fixed and four corner point supports.The numerical simulation is carried out to analyze the influence of hollow ratio and boundary conditions on the internal force and deformation of hollow floor.