Analysis Of Elasticity-Viscoplasticity On Curved Beam

The mechanics properties of the engineering materials are actually very complex, and always relate to many enviromental factors, such as properties of loads, the velocity of acting, time, temperature, as well as electricity, magnetism, radialization and so on. Strictly speaking, in fact, generally it is very difficult to try to make fixedly constant provisions of mechanics properties and describe mechanics properties of any engineering materials completely as they are, also it is unnecessary in the meantime. Therefore putting forward the ideal model of science and building up reasonable constitutive relation is very important.The elastic-viscoplastic theory is more close to the engineering practice, with a great deal of applications of the modern aviation, aerospace and other engineering materials, there will be higher and higher request to characteristic of engineering materials, as well as there will be requirement to reflect true characteristic of engineering materials more truly. There will provide very extensive foreground for development and application of the theory of elasticity-viscoplasticity. Theory of elasticity-viscoplasticity have many important academic and practical meaning in many field of engineering.This paper first adopt theory of elasticity to deduce analytical solution of curved beam under vertical uniform distributing loads. In consideration of elastic stage, it settles for principle of superposition, so translate the curved beam of complicated loads state into a few instances of under stress, carry on analysing respectively, construct stress function to satisfy boundary condition of every instances reasonably, calculate analysitical solution of curved beam. In the meantime use ANSYS to analyse mechanical properties of curved beam under vertical uniform distribution loads, contrast the results of analytical solution with the results of ANSYS, the results are consistent.Seond contrast the analytical solution of pure bending curved beam of elasticity-plasticity with numerical solution of ANSYS, the results indicate that in the state of elasticity-plasticity, the numerical solution of ANSYS satisfies boundary condition of inner and outer surface of curved beam basically. Radial stress affects yielding of plasticity very small, yielding of plasticity is mainly produced by tangential stress. There is obvious stress concentration in the field of action of loads, result in fluctuation of the data of ANSYS.Last use theory of elasticity-viscoplasticity to deduce analytical solution of elasticity-viscoplasticity of pure bending curved beam, from analytical solution of curved beam, it can conclude that in the definite time frame, when coefficient of viscosit is constant, the stress of curved beam decreases with increase of time gradually, at last decreases to some a constant; When the time is constant, with increase of coefficient of viscosit, stress of curved beam increase gradually. In the definite time frame, effects produced by coefficient of viscosit on stress of curved beam is quite obvious. If modulus of elasticity of materials is very high, coefficient of viscosity is very small, the effects produced by time factor are very small, viscosity can be ignored. When coefficient of viscosit equal to zero, the solution of elasticity-viscoplasticity can be degenerated into the solution of elasticity-plasticity of curved beam.