Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the...Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.展开更多
By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist ...By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.展开更多
基金Project supported by the China Postdoctoral Science Foundation(No.2018M630167)
文摘Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.
文摘By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.
