Axisymmetrical Problems in Theory of Elasticity
Zhu Bofang · 2018
An axisymmetrical stress problem often appears in the engineering of shaft, pressure vessel, and machine manufacturing. If all the geometry, constraint conditions, and loads of an elastic body are axisymmetrical, it is necessary to analyze only one cross section. This chapter discusses the relation between stresses and strains. For axisymmetrical problem, there may be four independent initial strain components. If the geometrical shape of an elastic body is axisymmetrical, but the load is not axisymmetrical, such as the wind load and earthquake load, it may express the load in 𝜃 direction by Fourier series. Taking advantage of the axisymmetrical shape of the body, the three-dimensional problem can be transformed into a set of two-dimensional problems that are easier to solve. Although the computing mesh is two-dimensional, there are three displacement parameters and three loading parameters at each node, which is different from the plane problems in the theory of elasticity.