A Stress Approach Model of Moderately Thick, Homogeneous Shells

Axel Fernando Domínguez Alvarado,Alberto Díaz Díaz

doi:10.1155/2018/6141683

Axel Fernando Domínguez Alvarado, Alberto Díaz Díaz

Open Access

https://doi.org/10.1155/2018/6141683

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Abstract

This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones. The model starts from an original stress polynomial approximation which involves the generalized forces and verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. Hellinger-Reissner functional and Reissner’s variational method are applied to determine the generalized fields and equations. The generalized forces and displacements are the same as those obtained in a classical, moderately thick shell model (CS model). The equilibrium and constitutive equations have some differences from those of a CS model, mainly in consideration of applied stress vectors at the upper and lower faces of the shell and the stiffness matrices. Another feature of the SAM-H model is the inclusion of the Poisson’s effect of out-of-plane normal stresses on in-plane strains. As a first application example to test the accuracy of the model, the case of a pressurized hollow sphere is considered. The analytical results of stresses and displacements of the SAM-H and CS models are compared to those of an exact 3D resolution. In this example, SAM-H model proves to be much more accurate than the CS model and its approximation of the normal out-of-plane stress is very precise. Finally, an implementation of the SAM-H model equations in a finite element software is performed and a case study is analyzed to show the advantages of using the SAM-H model.

Highlights

In structural engineering, models of plates and shells are necessary for carrying out reliable predictions of displacements and stresses without the excessive computational cost of three-dimensional solid finite element calculations
This paper presents the theoretical development of a new model of shells called SAM-H (Stress Approach Model of Homogeneous shells) and adapted for linear elastic shells, from thin to moderately thick ones
To test the accuracy of SAM-H model, its results are compared to those obtained with (i) solid finite elements (SFE) available in COMSOL Multiphysics; (ii) the classical shell model (CS model); its equations are implemented in COMSOL Multiphysics in a similar manner to how SAM-H equations were treated; (iii) MITC6 shell finite elements [33] available in COMSOL Multiphysics

Summary

Introduction

Models of plates and shells are necessary for carrying out reliable predictions of displacements and stresses without the excessive computational cost of three-dimensional solid finite element calculations. Stress approximation and the simplicity of the model: the 3D equilibrium equations and the stress boundary conditions at the shell faces are verified, with the same number of generalized forces, moments, strains, and displacements as the linear elastic version of the classical model of general moderately thick shells proposed by Reddy [19]. Another originality of the model resides on taking into account and distinguishing the effect of stress vectors applied at the inner and outer faces of the shell. The stress approximation will lead to 5 generalized displacements (3 displacements and 2 rotations)

Stress Approximation

Generalized Fields and Equations

Results and Discussion

Conclusions

Alternative Form of the Generalized Constitutive Equations