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In order to optimize production and save material, numerical simulation is becoming more and more used in industrial forging processes.

Methods that use spatial gradients of enthalpy to evaluate effective specific heats and capture latent heat effects in phase change problems have been used successfully in finite element formulations based on linear interpolation. In view of the greater geometrical flexibility and efficiency of biquadratic isoparametric elements, it is of interest to assess the use of the methods with these elements. In comparisons with an accurate semi‐analytic solution for a test problem, it is shown that the enthalpy gradient methods with quadratic interpolation are prone to error. A new procedure is proposed that uses bilinear sub‐elements for enthalpy, formed by subdivision of the biquadratic temperature elements. This is shown to be accurate and robust, for phase change intervals as small as 0.02°C.

A procedure presented for displaying variables in colour on an isoparametric surface. It utilizes isoparametric interpolation functions to produce continuous colour variations on the surface. It can also be employed on standard printers for non‐colour displays.

The paper aims to propose two new 8-node quadrilateral membrane elements with good distortion tolerance for the modified couple stress elasticity based on the unsymmetric finite element method (FEM).

The nodal rotation degrees of freedom (DOFs) are introduced into the virtual work principle and constrained by the penalty function for approximating the test functions of the physical rotation and curvature. Therefore, only the C0 continuity instead of C1 continuity is required for the displacement during the element construction. The first unsymmetric element assumes the test functions of the displacement and strain using the standard 8-node isoparametric interpolations, while these test functions in the second model are further enhanced by the nodal rotation DOFs. Besides, the trial functions in these two elements are constructed based on the stress functions that can a priori satisfy related governing equations.

The benchmark tests show that both the two elements can efficiently simulate the size-dependent plane problems, exhibiting good numerical accuracies and high distortion tolerances. In particular, they can still exactly reproduce the constant couple stress state when the element shape deteriorates severely into the degenerated triangle. Moreover, it can also be observed that the second element model, in which the linked interpolation technique is used, has better performance than the first one, especially in capturing the steep gradients of the physical rotations.

As the proposed new elements use only three DOFs per node, they can be readily incorporated into the existing finite element (FE) programs. Thus, they are of great benefit to analysis of size-dependent membrane behaviors of micro/nano structures.

A mixed approach to large strain elastoplastic problems is presented in a somewhat different way to that usually used within the context of the additive split of the rate of deformation tensor into an elastic and plastic part. A non‐linear extended mixed variational equation, in which the Jacobian of the deformation gradient and the pressure part of the stress tensor appear as additional independent variables, is introduced. This equation is then linearized in the accordance with the Newton‐Raphson method to obtain the system of linear equations which represent the basis of the mixed finite element procedure. For the case of a bilinear isoparametric interpolation of the displacement field, and for piece‐wise constant pressure and Jacobian, simplified expressions, differing from similar expressions corresponding to mixed finite element implementations, are obtained. The effectiveness of the proposed mixed approach is demonstrated by means of two examples.

To obtain error estimates for 3D consistent boundary‐flux approximations.

Isoparametric approach is used for constructing finite‐element approximations.

This research study presents a convergence analysis of 3D boundary‐flux approximations. Error estimates are proved for the approximate solutions of the problem under consideration.

General results for a consistent boundary‐flux problem are obtained for all 3D domains with Lipschitz‐continuous boundary. This investigation will be continued studying combined effect of curved boundaries and isoparametric numerical integration. An optimal refined strategy with respect to algorithmic aspects for solving 3D boundary‐flux problem also will be considered.

The obtained results enable engineers to calculate the flux across the curved boundaries using finite element method (FEM).

The paper presents an isoparametric finite‐element method for a 3D consistent boundary‐flux problem in domains with complex geometry. The work is addressed to the possible‐related fields of interest of postgraduate students and specialists in fluid mechanics and numerical analysis.

In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.

Two isoparametric Lagrangian shallow shell elements are presented: a 4‐node element QUAD4 and a 9‐node element QUAD9. These elements are based on Mindlin/Reissner plate elements as described in a series of papers. These elements are sophisticated by adding conventional membrane stiffness and membrane‐bending coupling terms based on Maguerre's approximate shallow shell theory. This results in double curved shell elements which originally possess severe membrane locking behaviour. This defect is overcome in the same way as the shear locking problem is solved.

The formulation and programming of the six‐node, curved isoparametric triangle in plane stress is presented. This is intended to fill an apparent vacuum in the open finite element literature.

We describe a visual method—stress band plots—for displaying the stress solution within a two‐dimensional finite element mesh. The stress band plots differ from conventional stress contour plots because stress band plots display unaveraged stresses (the stresses are computed directly from the solution variables) and stress discontinuities in the finite element solution are directly displayed. Stress band plots are useful in judging the accuracy of a finite element solution, in the comparison of different finite element solutions and during mesh refinement. These uses are demonstrated in an axisymmetric pressure vessel analysis.