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Design engineers use the term load path to describe, in general terms, the way in which loads path through a structure from the points of application to the points where they are reacted. In contrast, stress trajectories are more clearly identified by the direction of the principal stress vectors at a point. The first author proposed a simple definition of the term load path in 1995 and proposed procedures to determine load paths from two‐dimensional finite element solutions. In this paper, the concept of load paths will be further explored and related to stress trajectories and Michell structures. The insight given when determining the load transfer near a pin‐loaded hole will be demonstrated. In addition a cantilevered beam will be considered and an introduction to plotting load paths in three‐dimensional structures is given.

The present work aims to reveal the effect of deposition paths on transient temperature, transient stress, residual stress and residual warping in the electron beam freeform fabrication (EBF) process.

Six typical deposition paths were involved in the finite element (FE) simulations of EBF process by implementing a specially written program.

The results showed that the deposition path had a remarkable influence on heat transfer and transient temperature distribution in the scanning process, resulting in different residual stress and residual warping after cooling to room temperature. The largest and smallest temperature gradients were obtained from the zigzag and alternate-line paths, respectively. Meanwhile, the temperature gradient decreased with the increase of deposited layers. The optimum deposition path, namely, the alternate-line pattern, was determined with respect to the residual stress and residual warping.

Although some researcher revealed the importance of deposition path through FE analysis and experimental observation, their studies were usually confined within one type of deposition pattern. A complete investigation of typical deposition paths and comparison among them are still lacking in literature. To address the aforementioned gap, the present work started by extensive FE simulations of EBF process involving six representative deposition paths, namely, the alternate-line, zigzag, raster, inside-out spiral, outside-in spiral and Hilbert. For each deposition path, the transient temperature field, residual stress and residual deformation were obtained to optimize the deposition path.

The determination of load paths is an essential element of structural design. Load paths provide insight into the way the structure is performing its prescribed function. They can also indicate possibilities for shape optimization and the effect of component modification or damage. They are relatively easy to define in simple structures such as trusses which comprise a finite number of clearly defined members which carry only axial load. The load path is given simply by tracing the higher axial loads through the structure. However, for continua such as plates or solids, there is currently no systematic procedure for determining the path of load from the point of application to the constrained boundaries. This paper addresses the problem of defining the path of loads in plates with geometric discontinuities and in simple joints. The theory associated with the determination of the load path is first introduced, and then integrated into a finite element package to provide pictorial contours.

This paper aims to present a simplified solution method for the elasto-plastic consolidation problem under different stress paths.

First, a double-yield-surface model is introduced as the constitutive model framework, and a partial derivative coefficient sequence is obtained by using numerical approximation using Gauss nuclear function to construct a discretization constitutive model which can reflect the influence of different stress paths. Then, the model is introduced to Biot’s consolidation theory. Volumetric strain of each step as the right-hand term, the continuity equation is simplified as a Poisson equation and the fundamental solution is derived by the variable separation method. Based on it, a semi-analytical and semi-numerical method is presented and implemented in a finite element program.

The method is a simplified solution that is more convenient than traditional coupling stiffness matrix method. Moreover, the consolidation of the semi-infinite foundation model is analyzed. It is shown that the numerical method is sufficiently stable and can reflect the influence of stress path, loading distribution width and some other factors on the deformation of soil skeleton and pore water pressure.

Original features of this research include semi-numerical semi-analytical consolidation method; pore water pressure and settlements of different stress paths are different; maximum surface uplift at 3.5a; and stress path is the main influence factor for settlement when loading width a > 10 m.

The purpose of this paper is to present an investigation of the effect of different gravity conditions on the penetration mechanism using the two-dimensional Distinct Element Method (DEM), which ranges from high gravity used in centrifuge model tests to low gravity incurred by serial parabolic flight, with the aim of efficiently analyzing cone penetration tests on the lunar surface.

Seven penetration tests were numerically simulated on loose granular ground under different gravity conditions, i.e. one-sixth, one-half, one, five, ten, 15 and 20 terrestrial gravities. The effect of gravity on the mechanisms is examined with aspect to the tip resistance, deformation pattern, displacement paths, stress fields, stress paths, strain and rotation paths, and velocity fields during the penetration process.

First, under both low and high gravities, the penetration leads to high gradients of the value and direction of stresses in addition to high gradients in the velocity field near the penetrometer. In addition, the soil near the penetrometer undergoes large rotations of the principal stresses. Second, high gravity leads to a larger rotation of principal stresses and more downward particle motions than low gravity. Third, the tip resistance increases with penetration depth and gravity. Both the maximum (steady) normalized cone tip resistance and the maximum normalized mean (deviatoric) stress can be uniquely expressed by a linear equation in terms of the reciprocal of gravity.

This study investigates the effect of different gravity conditions on penetration mechanisms by using DEM.

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.

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.

The analysis, carried out for this publication, concerned checking the nature of mating of gear wheels with different load conditions. The computation was made applying FEM in Abaqus 6.10-1 program and concerned spur gears in dual-power-path gears made of ABS. The same geometrical models, material parameters and boundary conditions were assumed for all the analysed stages of the computation. However, the values of torque transmitted from active wheels to passive wheel of the gearing were changed. The paper aims to discuss these issues.

Observing changes of stress levels for toothed wheel and pinions allows to state that for relatively low load values, bending stresses at tooth root change proportionally to the change of the applied load.

Values of contact stresses on mating teeth flanks were also defined for the most loaded part of the dual-power-path gearing, namely for a pinion. In case of contact stresses, it was observed that together with constant increase of torque value, the values of stresses change but the nature of these changes is not proportional to the applied load. Out of all the analysed variants, the most favourable, from the point of view of durability, was the situation in initial (theoretical) model with regular power division on all mating wheels.

Conclusions drawn as a result of numerical computation are helpful in defining the nature of work of dual-power-path gearing in different load conditions and will be compared to results of stand tests of the analysed gearing.

Fibre-reinforced additive manufacturing (FRAM) with short and continuous fibres yields light and stiff parts and thus increasing industry acceptance. High material anisotropy and specific manufacturing constraints shift the focus towards design for AM (DfAM), particularly on toolpath strategies. Assessing the design-property-processing relations of infill patterns is fundamental to establishing design guidelines for FRAM.

Subject to the DfAM factors performance, economy and manufacturability, the efficacy of two conventional infill patterns (grid and concentric) was compared with two custom strategies derived from the medial axis transformation (MAT) and guided by the principal stresses (MPS). The recorded stiffness and strength, the required CPU and print time, and the degree of path undulation and effective fibre utilisation (minimum printable fibre length) associated with each pattern, served as assessment indices for different case studies. Moreover, the influence of material anisotropy was examined, and a stiffness-alignment index was introduced to predict a pattern’s performance.

The highest stiffnesses and strengths were recorded for the MPS infill, emphasising the need for tailoring print paths rather than using fixed patterns. In contrast to the grid infill, the concentric infill offered short print times and reasonable utilisation of continuous fibres. The MAT-based infill yielded an excellent compromise between the three DfAM factors and experimentally resulted in the best performance.

This constitutes the first comprehensive investigation into infill patterns under DfAM consideration for FRAM, facilitating design and processing choices.

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.