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Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and constant stresses ensures satisfaction of the patch test and convergence of the method in case of linear elasticity. However, this does not hold in the case of large deformations. By analytic derivation of the element eigenvalues in large strain states additional orthogonality conditions can be derived, leading to a stable formulation, regardless of the magnitude of deformations. Proposes a new element based on a consistent formulation of the enhanced gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation and does not exhibit hour‐glassing for large deformations.

This paper is concerned with the performance of shell finite elements, well established in locking‐free computations with linear constitutive laws, in the case of non‐linear elastic material behaviour. Specifically enhanced strain elements are focused on. It is shown that the element behaviour depends on the resulting form of the stress tensor. Phenomenological models for highly non‐linear and elastically deforming rubber, like that of Odgen, are compared with the statistical‐based constitutive model developed by Arruda and Boyce. Whereas computations with the Odgen or any equivalent phenomenological model prove unstable, the behaviour of the enhanced elements, when the statistical model is applied, is shown to be superior. The behaviour is attributed to the mathematical form of the resulting stress tensor.

An efficient algorithm to estimate the large elasto‐plastic strains encountered in thin sheet metal forming parts has been continuously developed by the authors since 1987. The algorithm is based on a finite element discretization of the known final shape. In this paper a new simple triangular shell element with constant membrane and bending strains is presented using discrete Kirchhoff constraints. The expressions of the internal force vector and logarithmic strains through the thickness are derived. Two applications are considered to discuss the validity and efficiency of the numerical procedure.

HAVING discussed in the standard longhand notation the main ideas and methods for the calculation of redundant structures on the basis of forces as unknowns we now turn our attention to the matrix formulation of the analysis. Consider a system consisting of s structural elements with a total number n of redundancies which may be forces (stresses), moments or any generalized forces. We select a basic system by ‘cutting’ a number r of redundancies where r<n. Thus, the simple idea of a statically determinate basic system (r=n) is but a particular case of our investigations.

Presents recent advances obtained by the authors in the development of enhanced strain finite elements for finite deformation problems. Discusses two options, both involving simple modifications of the original enhancement strategy of the deformation gradient as proposed in previous works. The first new strategy is based on a full symmetrization of the original enhanced interpolation fields; the second involves only the transposed part of these fields. Both modifications lead to a significant improvement of the performance in problems involving high compressive stresses, showing in particular a mode‐free response, while maintaining a simple and efficient (strain driven) numerical implementation. Demonstrates these properties with a number of numerical benchmark simulations, including a complete modal analysis of the elements.

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test. By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved. A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

As known from nearly incompressible elasticity, selective reduced integration (SRI) is a simple and effective method of overcoming the volumetric locking problem in 2D and 3D solid elements. This method of finite elastoviscoplasticity is discussed as are its well‐known limitations. In this context, an isochoric‐volumetric decoupled material behavior is assumed and thus the additive deviatoric‐volumetric decoupling of the consistent algorithmic moduli tensor is essential. By means of several numerical examples, the performance of elements using selective reduced integration is demonstrated and compared to the performance of other elements such as the enhanced assumed strain elements. It is shown that a minor modification, with little numerical effort, leads to rather robust element behaviour. The application of this process to so‐called solid‐shell elements for thin‐walled structures is also discussed.

The general theory of the cut‐out and modification analysis is reviewed and extended for a structure involving primary, secondary and tertiary redundancies. Some important points of practical application are illustrated on simple examples and the influence of the form chosen for the unassembled flexibility matrix is discussed. The question of the selection and number of actual cuts which will simulate a given major cut‐out is treated in general and illustrated on a simple type of structure.