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Article
Publication date: 13 June 2016

Feifei Zhang, Jieshi Chen and Jun Chen

– The purpose of this paper is to analyze theoretically the influence of normal stress on the formability of aluminum alloy sheets in non-linear strain paths.

Abstract

Purpose

The purpose of this paper is to analyze theoretically the influence of normal stress on the formability of aluminum alloy sheets in non-linear strain paths.

Design/methodology/approach

Four loading modes of non-linear strain paths are investigated in detail to consider the effect of normal stress on formability of aluminum alloy sheets.

Findings

Results show that the influence of normal stress in the first stage can be ignored. However, the normal stress in the second stage enhances the formability of aluminum alloy sheets obviously. Besides, the normal stress in the second stage is found to have larger effect on forming limit stress than that in the first stage.

Research limitations/implications

Maybe more experiment data should be obtained to support the theoretical findings.

Originality/value

This current study provides a better understanding of normal stress effect on the formability of aluminum alloy sheets in non-linear strain paths. Since the reacting stage of normal stress play important roles in normal stress effect on the formability of aluminum alloy sheets, the insight obtained in this paper will help to judge the instability of aluminum alloy sheets in complex forming processes with normal stress reacting on the sheet or tube.

Details

Engineering Computations, vol. 33 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 1987

T.K. Hellen and W.S. Blackburn

A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are…

Abstract

A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are reviewed, classified broadly into two groups, as domain integrals and virtual crack extension techniques. In addition to considerations of how such quantities may be calculated by finite elements, assessment methods of conducting the actual incremental analyses are described.

Details

Engineering Computations, vol. 4 no. 1
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 June 1997

Jaroslav Mackerle

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…

6041

Abstract

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.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 November 1996

Félix Darve

Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of…

Abstract

Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of liquefaction and its modelling by constitutive relations. Discusses this modelling in relation to the questions of stability and uniqueness. Considers the signs of three scalar quantities: the work of second order, the determinant of the symmetric part of the tangent constitutive tensor and the determinant of the tensor itself. Concludes that the liquefaction path is situated inside a potentially unstable domain and that in some cases this path reaches some states of loss of uniqueness, which are essentially bifurcation points.

Details

Engineering Computations, vol. 13 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1996

Itaru Mutoh, Shiro Kato and Y. Chiba

Presents an alternative lower bound to the elastic buckling collapse of thin shells of revolution, in comparison with results from geometrically non‐linear elastic analysis. The…

Abstract

Presents an alternative lower bound to the elastic buckling collapse of thin shells of revolution, in comparison with results from geometrically non‐linear elastic analysis. The numerical finite element method is based on axisymmetric rotational shell elements whose strain‐displacement relations are described by Koiter’s small finite deflection theory, with displacements expanded circumferentially using a Fourier series. First, compares the reduced stiffness linear analysis, based on the buckling equation without incremental linear in‐plane energy components corresponding to the lowest eigenmode (for a particular cylindrical shell under external pressure), with the results obtained by Batista and Croll. Second, the non‐linear astatic (quasi‐static) elastic analysis to clamped spherical caps under uniform external pressure is carried out in order to compare the results from a reduced stiffness analysis from viewpoints of not only buckling loads, but also total potential energy. Argues that the astatic buckling loads may relate to reductions due to a specific imperfection effect on elastic buckling collapses.

Details

Engineering Computations, vol. 13 no. 2/3/4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 7 November 2019

Vijay Kumar Polimeru and Arghadeep Laskar

The purpose of this study is to evaluate the effectiveness of two-dimensional (2D) cyclic softened membrane model (CSMM)-based non-linear finite element (NLFE) model in predicting…

Abstract

Purpose

The purpose of this study is to evaluate the effectiveness of two-dimensional (2D) cyclic softened membrane model (CSMM)-based non-linear finite element (NLFE) model in predicting the complete non-linear response of shear critical bridge piers (with walls having aspect ratios greater than 2.5) under combined axial and reversed cyclic uniaxial bending loads. The effectiveness of the 2D CSMM-based NLFE model has been compared with the widely used one-dimensional (1D) fiber-based NLFE models.

Design/methodology/approach

Three reinforced concrete (RC) hollow rectangular bridge piers tested under reversed cyclic uniaxial bending and sustained axial loads at the National Centre for Research on Earthquake Engineering (NCREE) Taiwan have been simulated using both 1D and 2D models in the present study. The non-linear behavior of the bridge piers has been studied through various parameters such as hysteretic loops, energy dissipation, residual drift, yield load and corresponding drift, peak load and corresponding drift, ultimate loads, ductility, specimen stiffness and critical strains in concrete and steel. The results obtained from CSMM-based NLFE model have been critically compared with the test results and results obtained from the 1D fiber-based NLFE models.

Findings

It has been observed from the analysis results that both 1D and 2D simulation models performed well in predicting the response of flexure critical bridge pier. However, in the case of shear critical bridge piers, predictions from 2D CSMM-based NLFE simulation model are more accurate. It has, thus, been concluded that CSMM-based NLFE model is more accurate and robust to simulate the complete non-linear behavior of shear critical RC hollow rectangular bridge piers.

Originality/value

In this study, a novel attempt has been made to provide a rational and robust FE model for analyzing shear critical hollow RC bridge piers (with walls having aspect ratios greater than 2.5).

Details

Engineering Computations, vol. 37 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1986

W.W. Bird and J.B. Martin

An algorithm is described for the incremental solution of elastic—plastic finite element analysis using a piecewise holonomic constitutive law based on a von Mises yield…

Abstract

An algorithm is described for the incremental solution of elastic—plastic finite element analysis using a piecewise holonomic constitutive law based on a von Mises yield condition. The holonomic assumption effectively converts each incremental problem into a non‐linear elastic—plastic problem. The algorithm is iterative, substituting the non‐linear strain potential by a quadratic potential at each iteration, and convergence is proved. The algorithm has been implemented into a finite element program as a series of secant modulus approximations, and results for a variety of problems are given. The rate of convergence is fairly slow, but the algorithm can be very easily programmed as an extension of an elastic program, and may have value as an independent method of determining incremental elastic—plastic solutions.

Details

Engineering Computations, vol. 3 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 May 2001

Stefan Schwarz and Ekkehard Ramm

The present contribution deals with the sensitivity analysis and optimization of structures for path‐dependent structural response. Geometrically as well as materially non‐linear

1142

Abstract

The present contribution deals with the sensitivity analysis and optimization of structures for path‐dependent structural response. Geometrically as well as materially non‐linear behavior with hardening and softening is taken into account. Prandtl‐Reuss‐plasticity is adopted so that not only the state variables but also their sensitivities are path‐dependent. Because of this the variational direct approach is preferred for the sensitivity analysis. For accuracy reasons the sensitivity analysis has to be consistent with the analysis method evaluating the structural response. The proposed sensitivity analysis as well as its application in structural optimization is demonstrated by several examples.

Details

Engineering Computations, vol. 18 no. 3/4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1988

J.B. Martin and W.W. Bird

This paper considers the classical problem of the deformation of an elastic‐plastic body subjected to a prescribed history of loading. Attention is focused on the basis for the…

Abstract

This paper considers the classical problem of the deformation of an elastic‐plastic body subjected to a prescribed history of loading. Attention is focused on the basis for the time discretization of the problem for numerical solution. It is suggested that this discretization can be achieved consistently by conceiving of the problem as a sequence of holonomic, or non‐linear elastic, problems. Complementary work bounds can be given, in special circumstances, for increasing numbers of time steps. The holonomic problem for a single time step is a non‐linear mathematical programming problem: it is shown that the conventional Newton‐Raphson algorithm used in elastic‐plastic finite element analysis can be interpreted as an iterative procedure for finding the least value of the holonomic potential work functional.

Details

Engineering Computations, vol. 5 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 1 March 1989

Eddy Pramono and Kaspar Willam

Numerical solutions in computational plasticity are severely challenged when concrete and geomaterials are considered with non‐regular yield surfaces, strain‐softening and…

Abstract

Numerical solutions in computational plasticity are severely challenged when concrete and geomaterials are considered with non‐regular yield surfaces, strain‐softening and non‐associated flow. There are two aspects that are of immediate concern within load steps which are truly finite: first, the iterative corrector must assure that the equilibrium stress state and the plastic process variables do satisfy multiple yield conditions with corners, Fi(σ, q) = 0, at discrete stages of the solution process. To this end, a reliable return mapping algorithm is required which minimizes the error of the plastic return step. Second, the solution of non‐linear equations of motion on the global structural level must account for limit points and premature bifurcation of the equilibrium path. The current paper is mainly concerned with the implicit integration of elasto‐plastic hardening/softening relations considering non‐associated flow and the presence of composite yield conditions with corners.

Details

Engineering Computations, vol. 6 no. 3
Type: Research Article
ISSN: 0264-4401

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