Search results

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

The use of enhanced strains leads to an improved performance of low order finite elements. A modified Hu‐Washizu variational formulation with orthogonal stress and strain functions is considered. The use of orthogonal functions leads to a formulation with B (overline) ‐strain matrices which avoids numerical inversion of matrices. Depending on the choice of the stress and strain functions in Cartesian or natural element coordinates one can recover, for example, the hybrid stress element P‐S of Pian‐Sumihara or the Trefftz‐type element QE2 of Piltner and Taylor. With the mixed formulation discussed in this paper a simple extension of the high precision elements P‐S and QE2 to general non‐linear problems is possible, since the final computer implementation of the mixed element is very similar to the implementation of a displacement element. Instead of sparse B‐matrices, sparse B (overline) ‐matrices are used and the typical matrix inversions of hybrid and mixed methods can be avoided. The two most efficient four‐node B (overline) ‐elements for plane strain and plane stress in this study are denoted B (overline)(x, y)‐QE4 and B (overline)(ξ, η)‐QE4.

The purpose of this paper is to compare mechanical response of polypropylene in multi‐cycle tensile tests with strain‐controlled and mixed deformation programs and to develop constitutive equations that describe quantitatively the experimental data.

Multi‐cycle tensile tests are performed on isotactic polypropylene with strain‐controlled (oscillations between fixed maximum and minimum strains) and mixed (oscillations between a fixed maximum strain and the zero minimum stress) programs. A constitutive model is derived in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and its parameters are found by fitting observations. The effect of damage accumulation of material parameters is analyzed numerically.

The model predicts accurately mechanical behavior of polypropylene in tests with numbers of cycles strongly exceeding those used to determine its parameters. In the regime of developed damage, material constants in the stress‐strain relations are independent of deformation program.

A novel constitutive model is derived in cyclic viscoelastoplasticity of semicrystalline polymers and comparison of its adjustable parameters is performed for different deformation programs.

This paper focuses on the development of a new class of eight‐node solid finite elements, suitable for the treatment of volumetric and transverse shear locking problems. Doing so, the proposed elements can be used efficiently for 3D and thin shell applications. The starting point of the work relies on the analysis of the subspace of incompressible deformations associated with the standard (displacement‐based) fully integrated and reduced integrated hexahedral elements. Prediction capabilities for both formulations are defined related to nearly‐incompressible problems and an enhanced strain approach is developed to improve the performance of the earlier formulation in this case. With the insight into volumetric locking gained and benefiting from a recently proposed enhanced transverse shear strain procedure for shell applications, a new element conjugating both the capabilities of efficient solid and shell formulations is obtained. Numerical results attest the robustness and efficiency of the proposed approach, when compared to solid and shell elements well‐established in the literature.

The objective of this work is to develop an element technology to recover the plane stress response without any plane stress specific modifications in the large strain regime. Therefore, the essential feature of the proposed element formulation is an interface to arbitrary three‐dimensional constitutive laws. The easily implemented and computational cheap four‐noded element is characterized by coarse mesh accuracy and the satisfaction of the plane stress constraint in a weak sense. A number of example problems involving arbitrary small and large strain constitutive models demonstrate the excellent performance of the concept pursued in this work.

Incremental sheet forming represents a promising process in the manufacturing of metallic components, particularly its variant known as single point incremental forming (SPIF). The purpose of this paper is to test and validate the results coming from numerical simulation of SPIF processes using the reduced enhanced solid‐shell formulation, when compared to the solid finite elements available in ABAQUS software. The use of SPIF techniques in the production of small batch components has a potential wide application in fields such as rapid prototyping and biomechanical devices.

Incremental forming processes differ from conventional stamping by not using a press and by requiring a lower number of tools, since no dedicated punches and dies are necessary, which lowers the overall production costs. In addition, it shows relative simplicity and flexible setup for complex parts, when compared with conventional technologies. However, the low speed of production and low‐dimensional accuracy levels are still the main obstacles for a wider application of this technique in the context of large production batches.

In this sense, the use of numerical simulation tools based on the finite element method (FEM) can provide a better understanding of the process' peculiarities. However, there are differences on using distinct finite element formulations, regarding accuracy as well as CPU times during simulations, which can be prohibitive in some cases.

Aiming to provide sounding improvements in these two fields (robustness and cost effectiveness of FEM solutions), the present work encloses a preliminary study about some relevant parameters in the FEM simulation of SPIF. Special focus is given to the use of solid‐shell and solid finite elements, for the sake of generality in modelling, as well as implicit solution schemes for the sake of accuracy. Finally, results coming from both experimental data and commercial FEM packages are compared to those obtained by a reliable and cost‐effective solid‐shell finite element formulation developed and implemented by the authors.

The purpose of this paper is to investigate the application of the element‐free Galerkin (EFG) method to the simulation of metal forming processes and to propose a strategy to deal with volumetric locking problem in this context.

The J₂ elastoplastic material model, employed in the work, assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and incorporates a non‐linear isotropic hardening response. The constitutive model is written in terms of the rotated Kirchhoff stress and the logarithmic strain measure. A Total Lagrangian formulation of the problem is considered in order to improve the computational performance of the proposed algorithm. The imposition of the essential boundary conditions and also of the unilateral contact with friction condition are made by the application of the Augmented Lagrangian method. Here, aspects related to the volumetric locking are investigated and an F‐bar approach is applied.

The results show that the proposed approach presents no volumetric locking phenomenon when using the mean dilation approach. Moreover, differently from finite element approximations, no hour‐glass instabilities in the deformation pattern are observed, avoiding in this way the need to devise additional stabilization procedures in the proposed procedure.

This paper demonstrates the implementation and validation of the mean dilation approach, in the scope of the EFG, which was successful in coping with the volumetric locking phenomena and presented no hour‐glass instabilities in the problem cases considered in this work.

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.

This study applies asymmetric rather than conventional symmetric analysis to advance theory in occupational psychology. The study applies systematic case-based analyses to model complex relations among conditions (i.e., configurations of high and low scores for variables) in terms of set memberships of managers. The study uses Boolean algebra to identify configurations (i.e., recipes) reflecting complex conditions sufficient for the occurrence of outcomes of interest (e.g., high versus low financial job stress, job strain, and job satisfaction). The study applies complexity theory tenets to offer a nuanced perspective concerning the occurrence of contrarian cases – for example, in identifying different cases (e.g., managers) with high membership scores in a variable (e.g., core self-evaluation) who have low job satisfaction scores and when different cases with low membership scores in the same variable have high job satisfaction. In a large-scale empirical study of managers (n = 928) in four (contextual) segments of the farm industry in New Zealand, this study tests the fit and predictive validities of set membership configurations for simple and complex antecedent conditions that indicate high/low core self-evaluations, job stress, and high/low job satisfaction. The findings support the conclusion that complexity theory in combination with configural analysis offers useful insights for explaining nuances in the causes and outcomes to high stress as well as low stress among farm managers. Some findings support and some are contrary to symmetric relationship findings (i.e., highly significant correlations that support main effect hypotheses).