Nonlinear deformation of axisymmetrically loaded rotation shell based on FEM with different variants of definitional equations

Abstract

A curvilinear finite element of the median line of an axisymmetrically loaded shell of revolution with a stiffness matrix of $8{\times} 8$ size is used when choosing nodal unknowns in the form of displacements and their first derivatives is used. The constitutive equations at the loading step are implemented in two versions. In the first version, the relations of the deformation theory of plasticity are used, which consist of expressions for the elastic and plastic parts. The relationships between strain increments and stress increments were determined by differentiating the equations used. In the second version, the hypothesis of separation of the deformation into elastic and plastic parts was not used. The constitutive equations developed by the authors are obtained on the basis of the hypothesis of the proportionality of the components of the deviators of the stress increments and the components of the deviators of the increments of deformations with the coefficient of proportionality as a function of the chord modulus of the deformation diagram. An example of calculation showing the effectiveness of the developed algorithm is presented.

Keywords

• shell of revolution
• strain tensor
• displacement vector
• finite element
• loading step
• physical nonlinearity
• stress