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h p -FEM for three-dimensional elastic plates

Monique Dauge, Christoph Schwab (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this work, we analyze hierarchic h p -finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the h p -FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the h p -discretization is consistent with the three-dimensional solution to any power of ε in the energy...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary conditions depend on parameters ε, α, β and the...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

Homogenization of thin piezoelectric perforated shells

Marius Ghergu, Georges Griso, Houari Mechkour, Bernadette Miara (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We rigorously establish the existence of the limit homogeneous constitutive law of a piezoelectric composite made of periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. We deal with an extension of the Koiter shell model in which the three curvilinear coordinates of the elastic displacement field and the electric potential are coupled. By letting the size of the microstructure going to zero and by using the periodic unfolding method combined...

hp-FEM for three-dimensional elastic plates

Monique Dauge, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we analyze hierarchic hp-finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the hp-FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in...

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