. Developments on the 'RESS' element were motivated by the following reasons: first, solid-shell elements automatically incorporate the normal stress along the thickness direction, which makes them more suitable for the simulations with double-sided contact than their shell counterparts; second, they have only translational degrees of freedom, which alleviates some difficulties associated with formulating complex shell formulations using nodal rotations; third, general constitutive models can be used and a reformulation for plane-stress conditions is not necessary. was developed for one single-layer shell structure with reduced in-plane and multiple integration points along the thickness direction of the shell. The formulation consists of several combinations of well-known techniques to ameliorate locking problems as is the case of the enhanced assumed strain (EAS) method. However, the proposed 'RESS' solid shell did not consider the transverse shear components of hourglass (or physical stabilization) parts. This negligence produces a slightly flexible behavior of the element, but it can also cause the appearance of hourglass modes for several non-linear applications including large rigid body rotations. Sometimes, the negligence brings a non-positive-definite status on the stiffness matrix. In order to overcome such drawbacks, a modified assumed natural strain (ANS) method considering the top and bottom surfaces of the element was incorporated for the transverse shear components. At the same time, new hourglass strains for the membrane field were constructed based on the stabilization vectors of Liu et al. (Comput. Meth. Appl. Mech. Engng 1998; 154:69). With these modifications, the improved element (called 'M-RESS') passes both the membrane and bending patch tests and performs with remarkable stability and accuracy in sheet-forming simulations.

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.

SUMMARYAccuracy and efficiency are the main features expected in finite element method. In the field of loworder formulations, the treatment of locking phenomena is crucial to prevent poor results. For threedimensional analysis, the development of efficient and accurate eight-node solid-shell finite elements has been the principal goal of a number of recent published works. When modelling thin-and thickwalled applications, the well-known transverse shear and volumetric locking phenomena should be conveniently circumvented. In this work, the enhanced assumed strain method and a reduced in-plane integration scheme are combined to produce a new eight-node solid-shell element, accommodating the use of any number of integration points along thickness direction. Furthermore, a physical stabilization procedure is employed in order to correct the element's rank deficiency. Several factors contribute to the high computational efficiency of the formulation, namely: (i) the use of only one internal variable per element for the enhanced part of the strain field; (ii) the reduced integration scheme; (iii) the prevention of using multiple elements' layers along thickness, which can be simply replaced by any number of integration points within a single element layer. Implementation guidelines and numerical results confirm the robustness and efficiency of the proposed approach when compared to conventional elements well-established in the literature.

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SUMMARYIn the last decade, one-point quadrature shell elements attracted many academic and industrial researchers because of their computational performance, especially if applied for explicit finite element simulations. Nowadays, one-point quadrature finite element technology is not only applied for explicit codes, but also for implicit finite element simulations, essentially because of their efficiency in speed and memory usage as well as accuracy. In this work, one-point quadrature shell elements are combined with the enhanced assumed strain (EAS) method to develop a finite element formulation for shell analysis that is, simultaneously, computationally efficient and more accurate. The EAS method is formulated to alleviate locking pathologies existing in the stabilization matrices of one-point quadrature shell elements.An enhanced membrane field is first constructed based on the quadrilateral area coordinate method, to improve element's accuracy under in-plane loads. The finite element matrices were projected following the work of Wilson et al. (Numerical and Computer Methods in Structural Mechanics, Fenven ST et al. (eds). Academic Press: New York, 1973; 43-57) for the incompatible modes approach, but the present implementation led to more accurate results for distorted meshes because of the area coordinate method for quadrilateral interpolation.The EAS method is also used to include two more displacement vectors in the subspace basis of the mixed interpolation of tensorial components (MITC) formulation, thus increasing the dimension of the null space for the transverse shear strains. These two enhancing vectors are shown to be fundamental for the Morley skew plate example in particular, and in improving the element's transverse shear locking behaviour in general.