This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial d...This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).展开更多
This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory.The cracked section is modeled by a massless elastic rotational spring.It is a...This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory.The cracked section is modeled by a massless elastic rotational spring.It is assumed that material properties follow exponential distributions through the beam thickness.The differential quadrature(DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions.The effects of the material gradient,crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail.展开更多
基金Project (Nos. 10472102 and 10432030) supported by the NationalNatural Science Foundation of China
文摘This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).
基金supported by the National Natural Science Foundation of China (Grant No. 11002019)Ph.D. Programs Foundation of the Ministry of Education of China (Grant No. 20100009120018)the Fundamental Research Funds for the Central Universities (Grant No. 2009JBM073)
文摘This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory.The cracked section is modeled by a massless elastic rotational spring.It is assumed that material properties follow exponential distributions through the beam thickness.The differential quadrature(DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions.The effects of the material gradient,crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail.
