Numerical implementation of composite Koiter shells including membrane/bending coupling coefficientsImplémentation numérique des coques composites de Koiter prenant en considération les coefficients de couplage membrane/flexions

We propose a way for determining the generalized coefficients of rigidity – some of which are membrane/bending coupling coefficients – which appear in the deformation energy of the Koiter model of thin shells. This is concerned with a heterogeneous material in the thickness direction. A new program to compute these coefficients is implemented in the finite element code Modulef, in order to simulate problems of thin multilayered shells with linearly elastic anisotropic layers. We propose an example of an inhibited multilayered thin shell, with hyperbolic middle surface, involving a composite material with unidirectional fibres. To cite this article: H. Ranarivelo, C. R. Mecanique 330 (2002) 273–278.     

Uniqueness in the Cauchy problem for the Koiter shell

We present the uniqueness in the Cauchy problem for the Koiter shell where the model is described by the Riemannian geometry. The Carleman estimates are established by the Bochner technique which yields the uniqueness for the Koiter shell.     

Koiter壳动力学方程解的存在性和唯一性

用Galerkin方法研究了Koiter壳动力学方程,得到了解的存在性与唯一性结果。     

MIXED FINITE ELEMENT METHODS BASED ON RIESZ-REPRESENTING OPERATORS FOR THE SHELL PROBLEM

1. IntroductionAs far as the shell problem is concerned, [l] established a mixed formulation in the clas-sical W that the K-ellipticity and the lnfSup condition are introduced. Unfortunately it isvery dndcult to construct ndxed elemellts simultaneously satisfying the K-ellipticity and theInfSup conditionI2], which are indeed prerequisites Of the stability and the convergence. Inaddition, the indefiniteness of the resulting linear algebraic system complicates the solutionalgorithIn.ffecentl…     

An eigenanalysis-based bifurcation indicator proposed in the framework of a reduced-order modeling technique for non-linear structural analysis

The Koiter–Newton method is a reduced order modeling technique which allows us to trace efficiently the entire equilibrium path of a non-linear structural analysis. In the framework of buckling the method is capable to handle snap-back and snap-through phenomena but may fail to predict reliably bifurcation branches along the equilibrium path. In this contribution we extend the original Koiter–Newton approach with a reliable and accurate bifurcation indicator which is based on an eigenanalysis of the reduced order tangent stiffness matrix. The proposed indicator has a negligible numerical effort since all computations refer to the reduced order model which is typically of very small dimension. The extension allows the identification of bifurcation points and a tracing of corresponding bifurcation branches in each sector of the equilibrium path. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with several examples.     

Load carrying capacity of systems within a global safety perspective. Part I. Robustness of stable equilibria under imperfections

The problem of the practical stability of structures is addressed in a modern way by considering the effects of both static and dynamic perturbations. The major historical contributions, due to Euler, Koiter and Thompson, are reviewed and illustrated by an archetypal model permitting to highlight the main mechanical and dynamical points. It is found that a global approach is necessary for a reliable safety estimation, especially in the neighborhood of (static) critical loads. Considering that the admissible load threshold has to account for robustness to finite perturbations, the Koiter critical load must be lowered, obtaining the so called Thompson critical load. It is shown how these two thresholds share some properties (e.g., both depend in a sensitive way on imperfections, which must be known for practical calculations), while having a deep different meaning: the former is related to static imperfections, and requires only a local analysis, while the latter is related to dynamical imperfections, and requires a global analysis. It is shown that P^crit_Euler≥P^crit_Koiter≥P^crit_Thompson, i.e., that the advancement of knowledge leads to a lower estimation of the actual critical load.     

Existence and uniqueness of the solution to the viscoelastic equations for Koiter shells

In this paper, we consider the linearly viscoelastic equations for Koiter shells. The existence and uniqueness of the solution are proved by Galerkin method.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE VISCOELASTIC EQUATIONS FOR KOITER SHELLS

In this paper,we consider the linearly viscoelastic equations for Koiter shells. Also,we prove the existence and uniqueness of the solution by Galerkin method.     

Load carrying capacity of systems within a global safety perspective. Part II. Attractor/basin integrity under dynamic excitations

The effects of the dynamic excitation on the load carrying capacity of mechanical systems are investigated with reference to the archetypal model addressed in Part I, which permits to highlight the main ideas without spurious mechanical complexities. First, the effects of the excitation on periodic solutions are analyzed, focusing on bifurcations entailing their disappearance and playing the role of Koiter critical thresholds. Then, attractor robustness (i.e., large magnitude of the safe basin) is shown to be necessary but not sufficient to have global safety under dynamic excitation. In fact, the excitation strongly modifies the topology of the safe basins, and a dynamical integrity perspective accounting for the magnitude of the solely compact part of the safe basin must be considered. By means of extensive numerical simulations, robustness/erosion profiles of dynamic solutions/basins for varying axial load and dynamic amplitude are built, respectively. These curves permit to appreciate the practical reduction of system load carrying capacity and, upon choosing the value of residual integrity admissible for engineering design, the Thompson practical stability. Dwelling on the effects of the interaction between axial load and lateral dynamic excitation, this paper supports and, indeed, extends the conclusions of the companion one, highlighting the fundamental role played by global dynamics as regards a reliable estimation of the actual load carrying capacity of mechanical systems.