Extended isogeometric analysis for cohesive fracture

The objective of this study is to present an extended isogeometric formulation for cohesive fracture. The approach exploits the higher order interelement continuity property of nonuniform rational B-splines (NURBS), in particular the higher accuracy that results for the stress prediction, which yields an improved estimate for the direction of crack propagation compared to customary Lagrangian interpolations. Shifting is used to ensure compatibility with the surrounding discretization, where, different from extended finite element methods, the affected elements stretch over several rows perpendicular to the crack path. To avoid fine meshes around the crack tip in case of cohesive fracture, a blending function is used in the extension direction of the crack path. To comply with standard finite element data structures, Bézier extraction is used. The absence of the Kronecker-delta property in the higher order interpolations of isogeometric analysis impedes the enrichment scheme and compatibility enforcement. These issues are studied comprehensively at the hand of several examples, while crack propagation analyses show the viability of the approach.     

On Suitability of the Averaged Strain Energy Density Criterion in Predicting Mixed Mode I/Ii Brittle Fracture of Blunt V-Notches with Negative Mode I Contributions

Strength of Materials - The main goal of the present research is to check the suitability of the well-known brittle fracture criterion, namely the averaged strain energy density (ASED), in...     

Accelerating fuzzy genetic algorithm for the optimization of steel structures

In this paper, the combination of a genetic algorithm and fuzzy logic is used for different types of optimization problems (sizing, topology and geometry) in steel structures. The primary objective is to introduce a new fitness function that uses a real value for the overall satisfaction parameter. By considering a real value instead of a random value for the overall satisfaction parameter, the probability of reaching the global optimum increases. In addition, to decrease the Computation time and to accelerate the convergence rate in the optimization process, a penalty function is added to the fitness function. Also, in spite of the previous methods, fuzzy GA is applied from the first generation of optimization problems. Furthermore, for this process, a similar bilinear membership function is used for the objective function and the constraints. The efficiency and robustness of the proposed approach is demonstrated by several illustrative examples and the results are compared to those of previous studies.     

Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty

Measuring and controlling emissions across the logistics network is an important challenge for today’s firms according to increasing concern about the environmental impact of business activities. This paper proposes a bi-objective credibility-based fuzzy mathematical programming model for designing the strategic configuration of a green logistics network under uncertain conditions. The model aims to minimize the environmental impacts and the total costs of network establishment simultaneously for the sake of providing a sensible balance between them. A popular but credible environmental impact assessment index, i.e., CO₂ equivalent index is used to model the environmental impact across the concerned logistics network. Since transportation mode and production technology play important roles on the concerned objectives, the proposed model integrates their respective decisions with those of strategic network design ones. In addition, to solve the proposed bi-objective fuzzy optimization model, an interactive fuzzy solution approach based upon credibility measure is developed. An industrial case study is also provided to show the applicability of the proposed model as well as the usefulness of its solution method.     

Cooperative spectrum sensing against noise uncertainty using Neyman–Pearson lemma on fuzzy hypothesis test

In this paper, we consider the problem of cooperative spectrum sensing in the presence of the noise power uncertainty. We propose a new spectrum sensing method based on the fuzzy hypothesis test (FHT) that utilizes membership functions as hypotheses for the modeling and analyzing such uncertainty. In particular, we apply the Neyman–Pearson lemma on the FHT and propose a threshold-based local detector at each secondary user (SU) in which the threshold depends on the noise power uncertainty. In the proposed scheme, a centralized manner in the cooperative spectrum sensing is deployed in which each SU sends its one bit decision to a fusion center. The fusion center makes a final decision about the absence/presence of a primary user (PU). The performance of the PU's signal detection is evaluated by the probability of signal detection for a specific signal to noise ratio when the probability of false alarm is set to a fixed value. The performance of the proposed algorithm is compared numerically with two classical threshold-based energy detectors. Simulation results show that the proposed algorithm considerably outperforms the methods with a bi-thresholds energy detector and a simple energy detector in the presence of the noise power uncertainty.     

Experimental and numerical investigation of thermal loads in Inocnel 718 machining

Inducing high thermal loads in machining of difficult-to-cut materials changes the mechanical properties of a machined surface/subsurface. In particular, a thermally affected layer leads to tensile residual stresses and microstructure changes. Nickel-based alloys are hard materials and frequently used in different industries. Since the generation of thermal loads in machining Inconel 718 is evident, in this paper an experimental and numerical investigation were performed to evaluate thermal loads and the depth of the affected layer in the machining of Inconel 718 superalloy. First, the effect of cutting parameters was studied on the average machined surface temperature by experimental tests. Then, the results of experiments were used to validate a 3D numerical model. Using the calibration strategy, the heat transfer coefficient at the chip–tool interface was found to be dependent on the cutting conditions. Next, the effect of the initial workpiece hardness and tool geometry, including tool nose radius and edge radius, was evaluated on thermal loads and the depth of the recrystallized layer. The critical strain criterion was used to estimate the depth of the recrystallized layer and then, the numerical results were compared with experimentally measured depth of the affected layer at different machining parameters.     

Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory

In this article, dynamic buckling analysis of an embedded curved microbeam reinforced by functionally graded carbon nanotubes is carried out. The structure is subjected to thermal, magnetic and harmonic mechanical loads. Timoshenko beam theory is employed to simulate the structure. Furthermore, the temperature-dependent surrounding elastic foundation is modeled by normal springs and a shear layer. Using strain gradient theory, the small scale effects are taken into account. The extended rule of mixture is employed to estimate the equivalent properties of the composite material. The governing equations and different boundary conditions are derived based on the energy method and Hamilton’s principle. Dynamic stability regions of the system are obtained using differential quadrature method. The aim of this paper is to investigate the influence of different parameters such as small scale effect, boundary conditions, elastic foundation, volume fraction and distribution types of carbon nanotubes, magnetic field, temperature and central angle of the curved microbeam on the dynamic stability region of the system. The results indicate that by increasing the volume fraction of CNTs, the frequency of the system increases and thus the dynamic stability region occurs at higher frequencies.     

Fracture analysis of dissimilar Al‐Al friction stir welded joints under tensile/shear loading

In this research, fracture of dissimilar friction stir welded (FSWed) joint made of Al 7075‐T6 and Al 6061‐T6 aluminum alloys is investigated in the cracked semi‐circular bend (CSCB) specimen under mixed mode I/II loading. Due to the elastic‐plastic behavior of the welded material and the existence of significant plastic deformations around the crack tip at the propagation instance, fracture prediction of the FSWed specimens needs some failure criteria in the context of the elastic‐plastic fracture mechanics which are very complicated and time‐consuming. For this purpose, the Equivalent Material Concept (EMC) is used herein by which the tensile behavior of the welded material is equated with that of a virtual brittle material. By combining EMC with the 2 brittle fracture criteria, namely the maximum tangential stress (MTS) and mean stress (MS) criteria, the load‐carrying capacity (LCC) of the FSWed CSCB specimens is predicted. Comparison of the experimental results and theoretical predictions from the 2 criteria showed that both criteria could accurately predict the LCC of the cracked specimens. Moreover, as the contribution of mode II loading increases, the size of the plastic region around the crack tip at failure increases, leading to increasing the LCC.     

Application of EMC‐J criterion to fracture prediction of U‐notched polymeric specimens with nonlinear behaviour

The main purpose of the present research paper is to investigate applicability of a new energy‐based failure prediction model, called EMC‐J criterion, to predict the critical loads of U‐notched polymeric samples having a ductile behaviour and loaded under symmetric 3‐point bending. The evaluated polymeric single edge notch bending samples containing U‐notches failed by considerable plastic deformations around the notch border, making it inappropriate to directly use classic linear elastic‐based formulations. Due to the elastic‐plastic behaviour of the tested polymeric material, EMC‐J criterion is applied to avoid using complex and extremely time‐consuming nonlinear analysis for failure load predictions. Finally, it is shown that EMC‐J criterion can provide a good consistency between the experimental and theoretical results with an average discrepancy of about 10%.     

Notch ductile failure with significant strain‐hardening: The modified equivalent material concept

The equivalent material concept (EMC) assumes that the ductile material has a valid K‐based fracture toughness (K_Ic or K_c). For ductile materials with significant strain‐hardening, no valid K_Ic or K_c is determined by the standard experiments and, hence, EMC seems null. The modified EMC (MEMC) is proposed in this study by which a virtual K_c value is defined and computed for the ductile material with significant strain‐hardening. In this way, Mode I and mixed Mode I/II fracture behaviors of U‐notched aluminum alloy 5083 are assessed in the view points of experiments and theories. Several U‐notched rectangular samples are used for performing the experiments and obtaining the failure loads. Then, the MEMC is coupled with the maximum tangential stress and mean stress criteria and utilized to predict the failure loads theoretically. Finally, it is shown that both the MEMC‐stress‐based criteria can provide very good predictions of the test data.