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Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain state. Hence, this study aims how to effectively evaluate the multiaxial random/variable amplitude fatigue life.

Recent studies on critical plane method under multiaxial random/variable amplitude loading are reviewed, and the computational framework is clearly presented in this paper.

Some basic concepts and latest achievements in multiaxial random/variable amplitude fatigue analysis are introduced. This review summarizes the research status of four main aspects of multiaxial fatigue under random/variable amplitude loadings, namely multiaxial fatigue criterion, method for critical plane determination, cycle counting method and damage accumulation criterion. Particularly, the latest achievements of multiaxial random/variable amplitude fatigue using critical plane methods are classified and highlighted.

This review attempts to provide references for further research on multiaxial random/variable amplitude fatigue and to promote the development of multiaxial fatigue from experimental research to practical engineering application.

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.

An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues.

SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS.

The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

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.

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.

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.

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

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.

In Simo and Taylor, the classical radial return algorithm of Wilkins and Krieg and Key for plane strain and three‐dimensional J2‐flow theory, is extended to the case of plane stress. In three dimensions (or plane strain), enforcement of the discrete consistency condition reduces to a simple radial scaling of the trial stress onto the yield surface; i.e., the return map is radial. In plane stress, on the other hand, the return map, that restores the trial stress back to the yield surface, is constrained to remain in the plane stress subspace, and thus no longer reduces to a simple radial scaling. The determination of the final stress point from the trial stress now involves the solution by Newton's method of a non‐linear scalar equation, referred to as the discrete consistency equation in what follows, that yields the discrete consistency parameter λn+>0. The requirement that λn+>1 be positive is a direct consequence of the discrete Kuhn‐Tucker optimality conditions.

The paper aims to shed some light on the effect of the notch/crack‐tip stresses and their role on the cyclic plasticity and crack growth behavior in compression‐compression fatigue.

Compression precracking was studied using 2D finite element analysis for CT specimen. The final crack length and the shape of the crack front were compared with those obtained experimentally.

It has been found that cyclic plasticity and stress redistribution govern the observed fatigue crack growth behavior in compression‐compression precracking. Only the internal stress corresponding to P_max shows a significant redistribution with the crack extension whereas the stress corresponding P_min is not affected by the increase of crack length.

This results are limited to Mode I cracking.

It supports that two thresholds, ΔK^th and K_max^th, govern the fatigue crack behavior. When the contribution from the internal tensile stress is not big enough to make K_max exceed K_max^th the crack will self arrest.

It has been found that cyclic plasticity and stress redistribution govern the observed fatigue crack growth behavior in compression‐compression precracking. The comparison of the numerical results with experimental data in terms of final crack length and crack front shape indicated a fair agreement.

In this paper an interface is derived between arbitrary three‐dimensional material laws and finite elements which include special stress conditions. The mechanical models of beams and shells are usually based upon zero‐stress conditions. This requires a material law respecting the stress condition for each finite element formulation. Complicated materials, e.g. finite strain models are often described in the 3D‐continuum. Considering the zero‐stress condition requires a reformulation of these material laws, which is often complicated. The subject of this paper is to incorporate physically non‐linear 3D‐material laws in beam and shell elements. To this effect a local algorithm will be developed to condense an arbitrary 3D‐material law with respect to the zero‐stress condition. The algorithm satisfies the stress condition at each integration point on the element level.

Stress state has a major influence on different phenomena, namely those involving diffusion and plastic deformation (like crack closure and high‐temperature fatigue crack growth, void formation or ductile fracture). The isolation of plane stress and plane strain states is crucial in fundamental studies of material behavior. The isolation of plane stress state is achieved with thin specimens, whilst the isolation of plane strain state is usually done increasing the thickness or introducing lateral grooves. The purpose of this paper is to propose a specimen geometry able to isolate the plane strain state, based on the standard M(T) geometry.

A numerical study was carried out aiming at obtaining a stress triaxiality parameter, h, as a function of different geometrical features of the specimen, such as the notch radius, notch depth and specimen thickness.

Results show that a pure plane strain state is achievable (i.e. 97 percent of specimen thickness has h>0.97) if a specimen with optimized geometrical features is used, which corresponds to a notch radius of 0.5 mm, a notch depth of 1 mm and a total specimen thickness of 12.56 mm.

This type of specimen geometry is a simple and efficient alternative to other common approaches used to obtain pure plain strain conditions for experimental purposes.

THE importance of the aircraft engine supercharger is being emphasized by the increasing demands for high altitude performance in the present war. Centrifugal stresses of considerable magnitude are induced in the supercharger impeller by reason of the high rotative speeds necessary to obtain the desired pumping effect. A speed of 20,000 r.p.m. is not uncommon for an impeller of 12 in. outside diameter and over. Consequently, a knowledge of the centrifugal stresses constitutes a basic design consideration. Unfortunately, a direct determination of these stresses is not an easy matter.

Purpose − The purpose of this paper is to propose a novel and simple strategy for construction of hybrid‐“stress function” plane element. Design/methodology/approach − First, a complementary energy functional, in which the Airy stress function is taken as the functional variable, is established within an element for analysis of plane problems. Second, 15 basic analytical solutions (in global Cartesian coordinates) of the stress function are taken as the trial functions for an 8‐node element, and meanwhile, 15 unknown constants are then introduced. Third, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of the displacements along element edges, which are interpolated by element nodal displacements. Finally, the whole system can be rewritten in terms of element nodal displacement vector. Findings − A new hybrid element stiffness matrix is obtained. The resulting 8‐node plane element, denoted as analytical trial function (ATF‐Q8), possesses excellent performance in numerical examples. Furthermore, some numerical defects, such as direction dependence and interpolation failure, are not found in present model. Originality/value − This paper presents a new strategy for developing finite element models exhibits advantages of both analytical and discrete method.