Abstract
The current paper presents enhancement introduced to the elasto-viscoplastic shell formulation, which serves as a theoretical base for the finite element code EPSA (Elasto-Plastic Shell Analysis) [1–3]. The shell equations used in EPSA are modified to account for transverse shear deformation, which is important in the analysis of thick plates and shells, as well as composite laminates. Transverse shear forces calculated from transverse shear strains are introduced into a rate-dependent yield function, which is similar to Iliushin's yield surface expressed in terms of stress resultants and stress couples [12]. The hardening rule defined by Bieniek and Funaro [4], which allows for representation of the Bauschinger effect on a moment-curvature plane, was previously adopted in EPSA and is used here in the same form. Viscoplastic strain rates are calculated, taking into account the transverse shears. Only non-layered shells are considered in this work.
Highlights
Our objective is to introduce transverse shear strains and forces into the elasto-viscoplastic model of shell behavior, formulated within the finite element code EPSA
The problems are selected to challenge new features introduced into the finite element code EPSA, i.e., representation of shear deformation and shear forces in the elasto-viscoplastic shell model
In “case a” the vertical displacement caused by bending and shear actions is approximated correctly. This confirms that EPSA features reliable representation of transverse shear deformation and can be used successfully to model the elasto-plastic behavior of thick plates, shells, and beams
Summary
Our objective is to introduce transverse shear strains and forces into the elasto-viscoplastic model of shell behavior, formulated within the finite element code EPSA. In our formulation, we use the following hypothesis: plane sections originally perpendicular to the middle surface remain plane after deformation but not perpendicular to the middle surface (Fig. 1). From this hypothesis, we deduce that bending displacements u and v along x and y directions are:. Some types of loading conditions, cause significant shear forces, regardless of the thickness of the structure An example of such a loading condition is a concentrated bending moment applied at mid-span of the beam, plate, or shell (Fig. 2).
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