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
Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material ...Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.展开更多
The fast excitation system of a composite magnetic controllable reactor is introduced. In this excitation system, a bidirectional function (i.e. fast forward excitation and backward forcible demagnetization) is avai...The fast excitation system of a composite magnetic controllable reactor is introduced. In this excitation system, a bidirectional function (i.e. fast forward excitation and backward forcible demagnetization) is available, which can significantly improve the response speed, performances, and application scope of magnetic controllable reactor.展开更多
By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three...By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three-dimensional point–load and patch–load Green’s functions for stresses and displacements are given in line-integral representations.The formulation includes a complete set of transformed stress–potential and displacement–potential relations,with utilizing Fourier series and Hankel transforms.As illustrations,the present Green’s functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green’s functions.Because of complicated integrand functions,the integrals are evaluated numerically and for numerical computation of the integrals,a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration.Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions.Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green’s functions that the effect of degree of variation of material properties will be recognized.展开更多
This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches f...This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.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The National Key Research and Development Program of China(No.2017YFC0307604)the Talent Foundation of China University of Petroleum(No.Y1215042)
文摘Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.
文摘The fast excitation system of a composite magnetic controllable reactor is introduced. In this excitation system, a bidirectional function (i.e. fast forward excitation and backward forcible demagnetization) is available, which can significantly improve the response speed, performances, and application scope of magnetic controllable reactor.
文摘By virtue of a complete set of two displacement potentials,an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented.Three-dimensional point–load and patch–load Green’s functions for stresses and displacements are given in line-integral representations.The formulation includes a complete set of transformed stress–potential and displacement–potential relations,with utilizing Fourier series and Hankel transforms.As illustrations,the present Green’s functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green’s functions.Because of complicated integrand functions,the integrals are evaluated numerically and for numerical computation of the integrals,a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration.Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions.Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green’s functions that the effect of degree of variation of material properties will be recognized.
基金supported by the National Natural Science Foundation of China(No.11471292)
文摘This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.