About linear and quadratic ‘Solid-Shell’ elements at large deformations

SUMMARYIn this work the recently proposed Reduced Enhanced Solid-Shell (RESS) finite element, based on the enhanced assumed strain (EAS) method and a one-point quadrature integration scheme, is extended in order to account for large deformation elastoplastic thin-shell problems. One of the main features of this finite element consists in its minimal number of enhancing parameters (one), sufficient to circumvent the well-known Poisson and volumetric locking phenomena, leading to a computationally efficient performance when compared to other 3D or solid-shell enhanced strain elements. Furthermore, the employed numerical integration accounts for an arbitrary number of integration points through the thickness direction within a single layer of elements. The EAS formulation comprises an additive split of the Green-Lagrange material strain tensor, making the inclusion of nonlinear kinematics a straightforward task. A corotational coordinate system is used to integrate the constitutive law and to ensure incremental objectivity. A physical stabilization procedure is implemented in order to correct the element's rank deficiencies. A variety of shell-type numerical benchmarks including plasticity, large deformations and contact are carried out, and good results are obtained when compared to well-established formulations in the literature.

Section: Elastoplastic Analysis Of a Simply Supported Plate With Presmentioning

confidence: 98%

A new one‐point quadrature enhanced assumed strain (EAS) solid‐shell element with multiple integration points along thickness—part II: nonlinear applications

Sousa

Cardoso

Valente

et al. 2006

“…The plate is subjected to a deformation-dependent uniform pressure. It has been studied in References [2,6,62,84,85] and combines the bending e orts at the ÿrst stages of the analysis and membrane e orts at the latter stages. The plate has dimensions 508 × 508 × 2:54.…”

Section: Non-linear Problemsmentioning

confidence: 99%

Analysis of 3D problems using a new enhanced strain hexahedral element

Areias¹,

Sá²,

Curnis³

et al. 2003

119

SUMMARYThe now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell ÿnite elements, is here explored in a versatile 3D low-order element which is identiÿed as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including ÿnite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent sti ness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several ÿnite strain tests. Some examples involve ÿnite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples.

“…This example has been treated in a number of references, including shell and solid-shell formulations and adopting a variety of mesh topologies (see, for instance References [28,61,78,[83][84][85][86]). About Figure 4, and following the previous references, the total length of the plate is 2L = 508, with thickness a = 2.54 consistent unities.…”

Section: Elasto-plastic Analysis Of a Simply-supported Platementioning

confidence: 99%

“…For each simulation just two Gauss points along thickness direction are employed, as for a higher interpolation order the same results were obtained. For comparison, Reference [78] adopts five Gauss points along thickness direction, while References [85,86] use six integration points. About boundary and loading conditions, displacements along the OZ direction are restrained on the outer edges, while a deformation dependent pressure load p = f × p 0 is applied on one side of the shell, for a nominal load level of p 0 = 10 −2 .…”

Section: Elasto-plastic Analysis Of a Simply-supported Platementioning

confidence: 99%

Enhanced transverse shear strain shell formulation applied to large elasto‐plastic deformation problems

Valente

Parente

Jorge

et al. 2004

SUMMARYIn this work, a previously proposed Enhanced Assumed Strain (EAS) finite element formulation for thin shells is revised and extended to account for isotropic and anisotropic material non-linearities. Transverse shear and membrane-locking patterns are successfully removed from the displacement-based formulation. The resultant EAS shell finite element does not rely on any other mixed formulation, since the enhanced strain field is designed to fulfil the null transverse shear strain subspace coming from the classical degenerated formulation. At the same time, a minimum number of enhanced variables is achieved, when compared with previous works in the field. Non-linear effects are treated within a local reference frame affected by the rigid-body part of the total deformation. Additive and multiplicative update procedures for the finite rotation degrees-of-freedom are implemented to correctly reproduce mid-point configurations along the incremental deformation path, improving the overall convergence rate. The stress and strain tensors update in the local frame, together with an additive treatment of the EAS terms, lead to a straightforward implementation of non-linear geometric and material relations. Accuracy of the implemented algorithms is shown in isotropic and anisotropic elasto-plastic problems.