Elastic And Steady-state Thermoelastic Analysis Of Polar Orthotropic Functionally Graded Materials With Symmetric Structures

As a class of new designable composite materials,functionally graded materials are widely used in aerospace engineering,nuclear energy reactor,turbine motors,and civil engineering etc.According to its characteristics of the preparation process,functionally graded materials is rarely be isotropic materials.Therefore,the elastic and steady-state thermoelastic problems of polar orthotropic functionally graded with axis(spherical)symmetry structures are studied from a more practical point of view in this paper.Firstly,we consider the elastic modulus of polar orthotropic functionally graded sandwich circular ring,and assume the transition layer vary continuously with power-law model along the radial direction.Introducing the stress function,the plane stress problem is converted into solving an Euler equations of the stress function.Numerical results show that the increase of the gradient index and the orthotropy index can reduce the radial displacement and radial stresses in the structure,and the maximum value of the circumferential stress may be located on the contact surface between the transition layer and the outer layer,which never occurs in homogeneous materials.Secondly,the steady-state thermoelastic analysis of polar orthotropic functionally graded hollow spheres is performed under consideration of two different typical boundary conditions.On the one hand,it is assumed that the physical properties of materials change along the radial direction as a power-law model.By introducing the stress function,an analytical solution of the thermoelastic field is obtained.On the other hand,from the more practical point of view,using the integral equation method to transform the problem into solving a Fredholm integral equation about the radial thermal stress for the case of arbitrary gradient change.Compared with the analytic solution of the power-law model,the validity and accuracy of the integral equation method are verified.The influences of the gradient index and the orthotropy index on the thermoelastic fields are analyzed by numerical examples.The results show that under the action of steady-state temperature field,the increasing of the gradient index can reduce the thermal stress of structure,while the increasing of the orthotropy index will improve the thermal stress of structure for two boundary conditions of the inner and outer boundaries free and the inner boundary free,the outer boundary fixed boundary.Finally,the steady-state thermoelastic analysis of polar orthotropic functionally graded uniform rotating disk with variable thickness under thermal mechanical loading is carried out.The problem is transformed into solving an Euler equation about the radial displacement,the analytic solution of thermal elastic field of structure under the change of power-law model is derived.For the case of arbitrary gradient variation,using the integral equation method we obtain the numerical solution of the thermoelastic field.The accuracy of the integral equation method is verified by comparing the numerical solution with the analytical solution.The influences of the gradient index,orthotropy index,thickness index and rotation angular velocity on the temperature field and thermoelastic fields of structure are analyzed.The results show that under the action of steady-state temperature field,the thermal stress of inner and outer surfaces in variable thickness disc shows the opposite change with the gradient index,and the maximum value of the thermal stress increases with the increase of the gradient index,that is,the possibility of damage increases.