ANALYTICAL STUDY ON OPTIMAL STIFFNESS DISTRIBUTION OF BEND-SHEAR STRUCTURES CONSIDERING LOAD DISTRIBUTION

For structures subjected to external excitation, the weak layers can be avoided and the bearing capacity and safety can be improved if all the damage degrees or the relative displacements of each story are the same, i.e., the uniform damage or uniform deformation occurs. It is significant to carry out structural optimization with uniform damage as the optimization objective. The bend-shear structure is simplified as a continuous variable cross-section cantilever. The assumed cross section functions include the forms of a natural exponential function and a power function. The external excitation such as earthquake effects and wind loads are idealized to three load modes, that is, the uniform distribution, the inverted triangle distribution and the inertia correlation distribution. According to the uniform deformation criterion, to make the second derivative of the absolute displacement curve of the structure equals zero is taken as the optimization target. The continuous displacement equation is established and the optimization results are discussed. The analytical solution of the optimal stiffness and the cross section distribution of the bend-shear structure is obtained. According to the theoretical and numerical results, the uniform damage can be realized if the cross section function is taken as power function, and the optimal distributions of stiffness and cross sections are different for different load distribution modes. The accuracy and the practicability of the analytical solution is verified by static-dynamic analysis based on the finite element method.