A new hybrid explicit/implicit in-plane-out-of-plane separated representation for the solution of dynamic problems defined in plate-like domains

Abstract

The present paper extends in-plane-out-of-plane separated representations successfully used for addressing fully 3D model solutions defined in plate-like domain, to dynamics. Common time integration are performed using explicit or implicit strategies. Even if the implementation of implicit integration schemes into a 3D in-plane-out-of-plane separated representation does not imply major difficulties, the use of explicit integration preferable in many applications becomes a tricky issue. In fact the mesh employed for discretizing the out-of-plane dimension (thickness) determines the maximum time-step ensuring stability. In this paper we introduce a new efficient hybrid explicit/implicit in-plane-out-ofplane separated representation for dynamic problems defined in plate-like domains that allows computing 3D solutions with the stability constraint exclusively determined by the coarser in-plane discretization.

Proper Generalized Decomposition with time adaptive space separation for transient wave propagation problems in separable domains

“…This formulation is applicable when the spatial domain Ω is separable [32]. In 2D, it limits the study to rectangular domains Ω = Ω x × Ω y , and in 3D to domains with an extrusion direction Ω = Ω x y × Ω z (plate, cylinder etc.).…”

“…The same methodology can be used for deriving the operators associated to the elastodynamic problem studied in Section 3.4. More details regarding the manipulation of a multi-component displacement field u = (u, v) within a PGD framework can be found in [32].…”

A minimally-intrusive fully 3D separated plate formulation in computational structural mechanics

“…The in-plane-out-of-plane separated representation was applied in our former works to efficiently solve 3D elastic problems in plate geometries [2][3][4]. The elastic problem was defined in a plate domain…”

On the coupling of local 3D solutions and global 2D shell theory in structural mechanics

“…Then, using the constitutive equation and the separated representation of both the trial and test displacements and the corresponding strains, the separated representation constructor proceeds as described in [3]. The procedure was easily generalized to the case of elastic problems defined in shell geometries [8] and also extended to dynamics in [9]. However the proposed in-plane-out-of-plane separated representation remains too intrusive to be implemented in structural mechanics commercial softwares that instead, propose a variety of plate and shell elements.…”