Axisymmetric Solids

This chapter treats the analysis of solids with axial symmetry. Thus, only solids with geometrical and material properties independent of the circumferential coordinate θ are considered (Figure 7.1). This property allows the inherent 3D behaviour of a solid to be expressed with a much simpler 2D model.

If the loading is also axisymmetric, the displacement vector has only two components in the radial and axial directions. The analysis of axisymmetric solid structures by the FEM is not difficult and follows very similar steps to those explained in the previous chapters for plane elasticity problems. For arbitrary non-axisymmetric loading a full 3D analysis is needed. However, even in these cases the axial symmetry of the structure allows important simplifications to be introduced. For instance, the loading can be expanded in Fourier series and the effect of each harmonic term can be evaluated by a simpler 2D analysis. The final result is obtained by adding the contributions from the different 2D solutions. This avoids costly 3D computations. This chapter focuses only on the analysis of axisymmetric solids under axisymmetric loading. Axisymmetric solids under arbitrary loading will be studied in Volume 2 [On].