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Proposes an automatic adaptive meshing scheme. Error in strain energy is directly obtained through strain energy density function (SED). Versatility of this function, in comparison with that of others, is looked at in detail. Mesh enrichment method consists of a series of h‐refinement steps and concludes with a single p‐refinement step. Adds that an examination of the accuracy of the element used in the refinement procedure is made. This scheme has been implemented in ZATILAN, a FE code developed in the Department of the Mechanical Engineering of the University of the Basque Country.

Accordingly to the recent multi-scale model proposed by Sih and Tang, different orders of stress singularities are related to different material dependent boundary conditions associated with the interaction between the V-notch tip and the material under the remotely applied loading conditions. This induces complex three-dimensional stress and displacement fields in the proximity of the notch tip, which are worthy of investigation. The paper aims to discuss these issues.

Starting from Sih and Tang’s model, in the present contribution the authors propose some analytical expressions for the calculation of the strain energy density (SED) averaged over a control volume embracing the V-notch tip. The expressions vary as a function of the different boundary conditions. Dealing with the specific crack case, the results from the analytical frame are compared with those determined numerically under linear-elastic hypotheses, by applying different constraints to the through-the-thickness crack edges in three-dimensional discs subjected to Mode III loading. Free-free and free-clamped cases are considered.

Due to three-dimensional effects, the application of a nominal Mode III loading condition automatically provokes coupled Modes (I and II). Not only the intensity of the induced modes but also their degree of singularity depend on the applied conditions on the crack flanks. The variability of local SED through the thickness of the disc is analysed by numerical analyses and compared with the theoretical trend.

The capability of the SED to capture the combined three-dimensional effects is discussed in detail showing that this parameter is particularly useful when the definition of the stress intensity factors (SIFs) is ambiguous or the direct comparison between SIFs with odd dimensionalities is not possible.

The purpose of this paper is to develop a heuristic method for topology optimization of a continuum with bi-modulus material which is frequently occurred in practical engineering.

The essentials of this model are as follows: First, the original bi-modulus is replaced with two isotropic materials to simplify structural analysis. Second, the stress filed is adopted to calculate the effective strain energy densities (SED) of elements. Third, a floating reference interval of SED is defined and updated by active constraint. Fourth, the elastic modulus of an element is updated according to its principal stresses. Final, the design variables are updated by comparing the local effective SEDs and the current reference interval of SED.

Numerical examples show that the ratio between the tension modulus and the compression modulus of the bi-modulus material in a structure has a significant effect on the final topology design, which is different from that in the same structure with isotropic material. In the optimal structure, it can be found that the material points with the higher modulus are reserved as much as possible. When the ratio is far more than unity, the material can be considered as tension-only material. If the ratio is far less than unity, the material can be considered as compression-only material. As a result, the topology optimization of continuum structures with tension-only or compression-only materials can also be solved by the proposed method.

The value of this paper is twofold: the bi-modulus material layout optimization in a continuum can be solved by the method proposed in this paper, and the layout difference between the structure with bi-modulus material and the same structure but with isotropic material shows that traditional topology optimization result could not be suitable for a real bi-modulus layout design project.

An important objective of 3‐D graphical finite element postprocessing is the facility to indicate to the engineer the accuracy of analysis results. The inclusion of mesh quality sensors permits a subjective evaluation of the adequacy of a single analysis being interpreted. For graphical approaches, both strain energy density gradients and discontinuities of unsmoothed responses and their gradients have proved to be effective sensors. Interactive graphical tools which can display discontinuity information effectively are described; these are essentially different from the ordinary methods used for the viewing of smoothed results.

The purpose of this paper was to investigate the feasibility on design and production of a three-dimensional honeycomb based on selective laser melting (SLM) technique for use in aeronautical application.

Various polyhedrons were investigated using their mechanical property, i.e. strain energy density (SED), by means of finite element (FE) analysis for the suitability of use in aerospace application; the highest SED polyhedron was selected as a candidate polyhedron. From the FE analysis, the truncated octahedron (three-dimensional honeycomb) structure was considered to be the potential candidate. Polyhedron size and beam thickness of the open-cellular three-dimensional honeycomb structure were modelled and analysed to observe how the geometric properties influence the stiffness of the structure. One selected model of open-cellular honeycomb (unit cell size: 2.5 mm and beam thickness: 0.15 mm) was fabricated using SLM. The SLM prototypes were assessed by their mechanical properties, including compressive strength, stiffness and strength per weight ratio. To investigate the feasibility in production of airfoil section sandwich structure, NACA 0016 airfoil section with three-dimensional honeycomb core was constructed and also fabricated using SLM.

According to the result, the three-dimensional honeycomb has elastic modulus of 63.18 MPa and compressive strength of 1.1 MPa, whereas strength per weight ratio is approximately 5.0 × 103 Nm/kg. The FE result presented good agreement to the mechanical testing result. The geometric parameter of the three-dimensional honeycomb structure influences the stiffness, especially the beam thickness, i.e. increase of beam thickness obviously produces the stiffer structure. In addition, the sandwich structure of airfoil was also successfully manufactured.

This work demonstrated the production of sandwich structure of airfoil using SLM for aeronautical engineering. This investigation has shown the potential applications of the three-dimensional structure, e.g. aircraft interior compartment components and structure of unmanned aerial vehicles.

The purpose of this paper is to develop a progressive damage framework to predict the fatigue life of cord-reinforced rubber composite under cyclic loadings. Special attention has been paid to failure mechanisms, like cord–rubber interfacial debonding, and rubber matrix damage.

The constitutive modeling is based on the continuum damage mechanics (CDMs) and the thermodynamics of irreversible process. The damage in rubber is described by an istropic law, whereas elasto-plastic continuum model has been proposed for cord–rubber interphase layer. The numerical framework is implemented into commercial finite element code Abaqus/Standard via user subroutine (UMAT).

One of the most important findings obtained from reviewing various techniques is that meso-level fatigue damage modeling based on developed framework can simulate competitive damage scenarios, e.g. debonding, delamination or matrix failure.

A systematic framework for predicting failure in cord-reinforced rubber composite is formulated within the context of CDMs that can also be applied for industrial components, such as tires and airsprings.

The main aim of this study is to investigate the mixed-mode I/II failure and the cracking manner of three-dimensional (3D)-printed components made by the fused deposition modeling technique in an experimental and theoretical manner.

Acrylonitrile butadiene styrene (ABS) material and a modified printing method (that increases the adhesion and integrity between the layers and strands) are used for manufacturing the semicircular bending (SCB) test samples. In addition to precracking, the effect of additional stress concentration on the stress field is studied by introducing three small holes to the SCB fracture samples. The critical mixed-mode I/II failure loads obtained from the experiments are predicted using different stress/strain-based fracture theories, including maximum tangential stress (MTS), maximum tangential strain (MTSN), generalized form of MTS and MTSN and combination of them with equivalent material concept (EMC). The effects of plastic deformation, as well as the structural stress concentration, are considered for a more realistic prediction of mixed-mode fracture load.

The stress-based criteria are more suitable than the strain-based theories. Among the investigated fracture models, the EMC–generalized maximum tangential stress theory provided the best agreement with the experimental results obtained from 3D-printed SCB tests.

The influences of stress risers and applicability of different failure theories in cracked layered 3D-printed parts are studied on the fracture behavior of tested specimens under mixed-mode I/II.

This study presents finite element (FE) and generalized regression neural network (GRNN) approaches for modeling multiple crack growth problems and predicting crack-growth directions under the influence of multiple crack parameters.

To determine the crack-growth direction in aluminum specimens, multiple crack parameters representing some degree of crack propagation complexity, including crack length, inclination angle, offset and distance, were examined. FE method models were developed for multiple crack growth simulations. To capture the complex relationships among multiple crack-growth variables, GRNN models were developed as nonlinear regression models. Six input variables and one output variable comprising 65 training and 20 test datasets were established.

The FE model could conveniently simulate the crack-growth directions. However, several multiple crack parameters could affect the simulation accuracy. The GRNN offers a reliable method for modeling the growth of multiple cracks. Using 76% of the total dataset, the NN model attained an R2 value of 0.985.

The models are presented for static multiple crack growth problems. No material anisotropy is observed.

In practical crack-growth analyses, the NN approach provides significant benefits and savings.

The proposed GRNN model is simple to develop and accurate. Its performance was superior to that of other NN models. This model is also suitable for modeling multiple crack growths with arbitrary geometries. The proposed GRNN model demonstrates its prediction capability with a simpler learning process, thus producing efficient multiple crack growth predictions and assessments.

The purpose of the present work is to develop the combination of the radial point interpolation method (RPIM) with a bi-directional evolutionary structural optimization (BESO) algorithm and extend it to the analysis of benchmark examples and automotive industry applications.

A BESO algorithm capable of detecting variations in the stress level of the structure, and thus respond to those changes by reinforcing the solid material, is developed. A meshless method, the RPIM, is used to iteratively obtain the stress field. The obtained optimal topologies are then recreated and numerically analyzed to validate its proficiency.

The proposed algorithm is capable to achieve accurate benchmark material distributions. Implementation of the BESO algorithm combined with the RPIM allows developing innovative lightweight automotive structures with increased performance.

Computational cost of the topology optimization analysis is constrained by the nodal density discretizing the problem domain. Topology optimization solutions are usually complex, whereby they must be fabricated by additive manufacturing techniques and experimentally validated.

In automotive industry, fuel consumption, carbon emissions and vehicle performance is influenced by structure weight. Therefore, implementation of accurate topology optimization algorithms to design lightweight (cost-efficient) components will be an asset in industry.

Meshless methods applications in topology optimization are not as widespread as the finite element method (FEM). Therefore, this work enhances the state-of-the-art of meshless methods and demonstrates the suitability of the RPIM to solve topology optimization problems. Innovative lightweight automotive structures are developed using the proposed methodology.

This paper aims to deal with the study of interaction between multiple cracks in an aluminum alloy under static loading. Self-similar as well as non-self-similar crack growth has been observed which depends on the relative crack positions defined by crack offset distance and crack tip distance. On the basis of experimental observations, the conditions for crack coalescence, crack shielding, crack interaction, crack initiation, etc. are discussed with respect to crack position parameters. Considering crack tip distance, crack offset distance, crack size and crack inclination with loading axis as input parameter and crack initiation direction as output parameter, an artificial neural network (ANN) model is developed. The model results were then compared with the experimental results. It was observed that the model predicts the crack initiation direction under monotonic loading within a scatter band of ±0.5°.

The study is based on the experimental observations. Growth studies are made from the growth initiation from two cracks in a rectangular aluminium plate under static loading. The present study is focused on the influence of crack position defined by crack offset distance and crack tip distance on growth direction. In addition to this, ANN has been used to predict crack growth direction in multiple crack geometry under static loading. The predicted results have been compared with the experimental data.

The influence of the interaction between multiple cracks on crack extension angle greatly depends on the relative position of cracks defined by crack tip distance S, crack offset distance H and crack inclinations with respect to loading direction. The intensity of the crack interaction can be described according to degree of crack extension angle and relative crack position factors. It is also observed that the progress of the outer and inner crack tip direction is different which mainly depends on the relative crack position.

It is limited to static loading only. Under fatigue loading findings may differ.

It is important to investigate the growth behaviour under multiple cracks and also to know the effect of crack statistics on the growth behaviour to estimate the component life. The study also focused on the development of a high quality predictive method.

The results show trends that vary with crack geometry condition and the ANN and empirical solution provides a possible solution to assess crack initiation angle under multiple crack geometry.