A Mixed StressDisplacement Approach Model of Homogeneous Shells for Elastodynamic Problems

الملخص EN

This paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems.

The model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems.

In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate.

The stress approximation coincides with the static version of SAM-H when dynamic effects are neglected.

The generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified.

The generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler–Lagrange equation which includes pertinently Hellinger–Reissner functional.

In the constitutive equations, Poisson’s effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H.

To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid.

In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load.

The results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations.

In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes.

Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.