The finite element analysis of curved structures (arches, shells) has always presented great difficulty. In fact, in recent years, many researchers have soundly investigated the meaning of the poor convergence rate and the locking phenomena exhibited by the traditional displacement approaches. Nevertheless, selective or reduced integration methods and multi-field variational formulations have proved capable of overcoming these difficulties. In this paper the problem is discussed once more, starting from the basic idea that for a rod it is always possible to set up internal force fields, which pointwise satisfy exactly the indefinite equilibrium equations. The use of a finite set of stress parameters (for instance, the stress resultant components) to describe the internal force is well documented in the technical literature. Unfortunately these studies are all focussed on a particular arch geometry, without a systematic generalization. This limitation can be overcome through the substitution of the axis line by a cubic B-spline approximated one. The proposed method allows an easy and systematic generation of the mentioned equilibrated stress resultant field. In this way it is possible to compute exactly (apart from the numerical integration error) the flexibility matrix, or according to the classical works of Pian, the curved beam stiffness matrix directly. The paper ends with some technically relevant numerical experiments, which illustrate the good performances of the proposed model, independently of the shape and aspect ratio of the arch, even with one element. © 1989.
A new hybrid F.E. model for arbitrarily curved beam-I. Linear analysis
TRALLI, Antonio Michele
1989
Abstract
The finite element analysis of curved structures (arches, shells) has always presented great difficulty. In fact, in recent years, many researchers have soundly investigated the meaning of the poor convergence rate and the locking phenomena exhibited by the traditional displacement approaches. Nevertheless, selective or reduced integration methods and multi-field variational formulations have proved capable of overcoming these difficulties. In this paper the problem is discussed once more, starting from the basic idea that for a rod it is always possible to set up internal force fields, which pointwise satisfy exactly the indefinite equilibrium equations. The use of a finite set of stress parameters (for instance, the stress resultant components) to describe the internal force is well documented in the technical literature. Unfortunately these studies are all focussed on a particular arch geometry, without a systematic generalization. This limitation can be overcome through the substitution of the axis line by a cubic B-spline approximated one. The proposed method allows an easy and systematic generation of the mentioned equilibrated stress resultant field. In this way it is possible to compute exactly (apart from the numerical integration error) the flexibility matrix, or according to the classical works of Pian, the curved beam stiffness matrix directly. The paper ends with some technically relevant numerical experiments, which illustrate the good performances of the proposed model, independently of the shape and aspect ratio of the arch, even with one element. © 1989.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.