Analysis Of The Static Mechanical Behavior Of Fiber-Reinforced Functionally Graded Material Beams

Functionally graded material (FGM) is a new type of non-uniform composite materials, which is produced according to a specific technique from two or more kind materials with different properties through certain design procedure so that it can make the material components change continuously in the gradient direction and eliminate the non-continuity of the physical material properties, or avoid the internal interfaces. By continuously adding reinforced fiber materials in the base and make the distribution of the fibers to be non-uniform in the transverse direction we can obtain the fiber-reinforced functionally graded material beam which can content specific load requirements. In this dissertation, the static bending mechanical behavior of fiber-reinforced functionally graded material beam were mainly analyzed and the bending response of the externally constraint beams under different transverse loadings were discussed. Main work of this dissertation is formed of the following three parts:1. Based on the Euler-Bernoulli beam theory, the static bending of fiber reinforced functional gradient materials beam is studied. Linear transformative relationship between the static bending solutions of fiber reinforced FGM beams and the corresponding homogenous beams is analyzed by the segmented discrete method. Under the simply supported-simply supported (S-S), clamped-clamped(C-C) and clamped-free(C-F) end constraints, the static analytical bending solutions of the SiC/Ti fiber reinforced functional graded materials beam were presented.2. Based on the Euler-Bernoulli beam theory, the bending response of the externally constraint beams under transverse load is discussed. By assuming that the stresses of the beam and the external constrains are less than their proportional limits, the analytical formulation of axial force of the externally reinforcing bars and normal stress in the cross section of the beam was derived by considering the externally reinforcing bars are pre-stressed or not pre-stressed under given transverse load. Influences of the parameters of the stiffness, the position and pre-stress of the externally reinforcing bars on the stress and deformation of the beam were discussed. The results show that the eccentric arrangement of externally reinforcing bars pre-stressed can effectively reduce the maximum tensile stress of the beam. The results can provide references for the study and design of the brittle material beam.3. Based on the above analysis, the static bending of fiber reinforced functional graded materials Timoshenko beam was further studied. Firstly, linear transformative relationship between the static bending solutions of homogenous Timoshenko beams and the homogenous Euler-Bernoulli beams is analyzed. Then, based on the linear transformative relationship between the static bending solutions of homogenous Timoshenko beams and the fiber reinforced functional gradient materials Timoshenko beam, the bending solution of fiber reinforced non-uniform Timoshenko beams with external constrains was derived by the solution of homogenous Euler-Bernoulli beams. So that, the solutions of static bending of fiber-reinforced functionally graded Timoshenko beams with external constrains can be transformed into that of the homogeneous Euler-Bernoulli beams under the same loads and boundary conditions.