Study On Analytical Solutions Of Functionally Graded Beams Based On Theory Of Different Moduli In Tension And Compression

Smart materials and structures is widely used in large-scale civil engineering health monitoring and disaster warning systems, such as carbon fiber implanted in the concrete, in order to make the concrete member have self enhancement, diagnosis, healing and regulation functions, it will greatly affect the structure and design interdisciplinary development applications. In recent years, the features of smart material and structure itself, also draw more and more attention of the academia and engineering field, and in this paper, we consider the smart structure materials with two distinct features which are different tension and compression properties and functional gradient. The different characteristics in pull and pressure are exist in all engineering materials including graphite, glass, metal alloys, ceramics, and a basic property of certain composite materials, the introduction of different compressive and tensile cause computational complexity, engineering analysis is usually downplayed. Functional gradient materials is generally composed of two different performance of composite materials, due to the volume of its constituent materials in a continuous space position change, thus material macro characteristics show the nature of the change of gradient. Functionally graded material eliminates the obvious interface materials, which help to alleviate thermal stress and it is widely applied in various fields when it was first put forward. In light of the current study of functionally graded structures without considering the different characteristics of tension and compression, the paper work has a certain practical significance.Around these problems, this paper carried out the following work:① In view of the pure bending problem, based on the simplified mechanics model on subsection area, we get the solutions of stress and displacement of different tension and compression modulus of functionally graded beams in one dimensional solutions and two-dimensional solutions; then we analysis the flat section assumption and the feasibility in using one dimensional solution in shallow beam case.② In view of the lateral force bending problem, firstly the assumption is given and proved that shear stress does not contribute to neutral layer, and then we also establish the subsection simplified mechanics model; respectively we solve the stress and displacement of elastic mechanics on concentrated force on end of cantilever beam and uniform load on the upper surface on cantilever beam.③ Based on numerical analysis, through the finite element software Marc, we has carried on the numerical analysis under uniformly distributed load of different tension and compression modulus of functionally graded beams. We made a comparison with finite element analysis results and the analytical solution and verify the effectiveness of the analytical work in this paper.④ By changing the material of function gradient index, we analyze emphatically deformation of the beam when the material of tension zone and compressive zone are tend to be rigid or flexible; then discuss the change of the stress and displacement of beam when material modulus in compression zone is greater than the tensile area or tensile area is greater than the pressure zone. The results showed that: the introduction of different tension and compression moduli, will significantly change the mechanical response of the structure.In this paper, we innovatively put the introduction of different compressive and tensile properties into functionally graded structure in the calculation and analysis, considering different tension and compression characteristics helps to excavate potential material mechanics, which has the certain theory reference significance on the detailed analysis and design of smart materials and structure...