The Finite Element Method in Thin Shell Theory: Application to Arch Dam Simulations

Bernadou, Michel; Boisserie, Jean-Marie

doi:10.1007/978-1-4684-9143-2

Cited by 36 publications

(26 citation statements)

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“…The Galerkin method of this work is equally efficient to implement for models incorporating the fixed-edge boundary conditions (6), 'almost fixed' boundary conditions, or the simply supported edge conditions (7). The method is demonstrated for the fixed-edge and simply supported conditions while modifications to adapt the method to 'almost fixed' can be found in References 27 and 28.…”

Section: Boundary Conditionsmentioning

confidence: 97%

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Spline approximation of thin shell dynamics

Rosario

Smith

1997

Int. J. Numer. Meth. Engng.

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SUMMARYA spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flü gge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material non-homogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.1997 by John Wiley & Sons, Ltd.

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Section: Boundary Conditionsmentioning

confidence: 97%

“…To illustrate, we consider the eigenvalue problem (10) with the simply-supported boundary conditions (7). One form of the natural vibration modes for this case is…”

Section: Modal Solution-simply Supported Boundary Conditions Constanmentioning

confidence: 99%

Spline approximation of thin shell dynamics

Rosario

Smith

1997

Int. J. Numer. Meth. Engng.

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“…)is a bilinear continuous symmetric coercive form on V,o. So equation (3.4) has one and only one solution (see [6], [7], [12]). …”

Section: = E~ X H~(to)mentioning

confidence: 99%

“…More recently mathematicians started working on that problem, and obtained some knowledge on how the usual models can be found expending the threedimensional model in power series in thickness, and neglecting one term on another [10], [12]. Also, numerical analysis on shells using finite elements is becoming standard [2], [3], [4], [5], [6], [9], [11].…”

Section: Introductionmentioning

confidence: 99%

Optimal design of midsurface of shells: Differentiability proof and sensitivity computation

Chenais

1987

Appl Math Optim

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Abstract. We suppose that a shell submitted to a given load (self-weight or wind, for instance), has to resist as well as possible towards given criteria. We aim at the following problem: Is it possible to find an optimal design of the midsurface of the shell with respect to this criteria?This problem can be worked using gradient-type algorithms. In this paper we work on the differentiability proof and numerical computation of the gradient.For a given shape of the midsurface, we consider that the shell works in linear elastic conditions. We use the Budiansky-Sanders model for elastic shells, from which we get the displacement field in the shell. The criteria to be minimized are supposed to depend on the shape directly, and also through the displacement field. In this paper, we prove that the displacement field depends on the shape in a Frrchet-differentiable manner (for an appropriate topology on the set of admissible shapes). Then we give a way to compute the gradient of a given criteria from a theoretical point of view and from a numerical point of view.This allows us to use descent-type methods of optimization. They will lead to shapes which react better and better. Notice that we know nothing about convergence of these methods, the existence and unicity of a theoretical optimal solution. But from a practical point of view, it is quite interesting to be able to modify a given shape to obtain a better one.

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“…A very interesting alternative to the approximation of thin shell problems by conforming methods [2,3] is given by the use of fiat plate elements E9, 10]. With no doubt, such flat element methods are very popular among industrial people.…”

Section: Introductionmentioning

confidence: 99%