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The purpose of this study is to simulate the tensile and shear types of fractures using the mixed fracture criteria considering the energy evolution based on the dual bilinear cohesive zone model and investigate the dynamic propagation of tensile and shear fractures induced by an impact load in rock. The propagation of tension and shear at different scales induced by the impact load is also an important aspect of this study.

In this study, based on the well-developed dual bilinear cohesive zone model and combined finite element-discrete element method, the dynamic propagation of tensile and shear fractures induced by the impact load in rock is investigated. Some key technologies, such as the governing partial differential equations, fracture criteria, numerical discretisation and detection and separation, are introduced to form the global algorithm and procedure. By comparing with the tensile and shear fractures induced by the impact load in rock disc in typical experiments, the effectiveness and reliability of the proposed method are well verified.

The dynamic propagation of tensile and shear fractures in the laboratory- and engineering-scale rock disc and rock strata are derived. The influence of mesh sensitivity, impact load velocities and load positions are investigated. The larger load velocities may induce larger fracture width and entire failure. When the impact load is applied near the left support constraint boundary, concentrated shear fractures appear around the loading region, as well as induced shear fracture band, which may induce local instability. The proposed method shows good applicability in studying the propagation of tensile and shear fractures under impact loads.

The proposed method can identify fracture propagation via the stress and energy evolution of rock masses under the impact load, which has potential to be extended into the investigation of the mixed fractures and disturbance of in-situ stresses during dynamic strata mining in deep energy development.

The boundary integral method (BIM) is very attractive to practicing engineers as it reduces the dimensionality of the problem by one, thereby making the procedure computationally inexpensive compared to its peers. The principal feature of this technique is the limitation of all its computations to only the boundaries of the domain. Although the procedure is well developed for the Laplace equation, the Poisson equation offers some computational challenges. Nevertheless, the literature provides a couple of solution methods. This paper revisits an alternate approach that has not gained much traction within the community. The purpose of this paper is to address the main bottleneck of that approach in an effort to popularize it and critically evaluate the errors introduced into the solution by that method.

The primary intent in the paper is to work on the particular solution of the Poisson equation by representing the source term through a Fourier series. The evaluation of the Fourier coefficients requires a rectangular domain even though the original domain can be of any arbitrary shape. The boundary conditions for the homogeneous solution gets modified by the projection of the particular solution on the original boundaries. The paper also develops a new Gauss quadrature procedure to compute the integrals appearing in the Fourier coefficients in case they cannot be analytically evaluated.

The current endeavor has developed two different representations of the source terms. A comprehensive set of benchmark exercises has successfully demonstrated the effectiveness of both the methods, especially the second one. A subsequent detailed analysis has identified the errors emanating from an inadequate number of boundary nodes and Fourier modes, a high difference in sizes between the particular solution and the original domains and the used Gauss quadrature integration procedures. Adequate mitigation procedures were successful in suppressing each of the above errors and in improving the solution accuracy to any desired level. A comparative study with the finite difference method revealed that the BIM was as accurate as the FDM but was computationally more efficient for problems of real-life scale. A later exercise minutely analyzed the heat transfer physics for a fin after validating the simulation results with the analytical solution that was separately derived. The final set of simulations demonstrated the applicability of the method to complicated geometries.

First, the newly developed Gauss quadrature integration procedure can efficiently compute the integrals during evaluation of the Fourier coefficients; the current literature lacks such a tool, thereby deterring researchers to adopt this category of methods. Second, to the best of the author’s knowledge, such a comprehensive error analysis of the solution method within the BIM framework for the Poisson equation does not currently exist in the literature. This particular exercise should go a long way in increasing the confidence of the research community to venture into this category of methods for the solution of the Poisson equation.

The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.

First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.

Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.

This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

The paper's goal is to examine and illustrate the useful uses of submodeling in finite element modeling for topology optimization and stress analysis. The goal of the study is to demonstrate how submodeling – more especially, a 1D approach – can reliably and effectively produce ideal solutions for challenging structural issues. The paper aims to demonstrate the usefulness of submodeling in obtaining converged solutions for stress analysis and optimized geometry for improved fatigue life by studying a cantilever beam case and using beam formulations. In order to guarantee the precision and dependability of the optimization process, the developed approach will also be validated through experimental testing, such as 3-point bending tests and 3D printing. Using 3D finite element models, the 1D submodeling approach is further validated in the final step, showing a strong correlation with experimental data for deflection calculations.

The authors conducted a literature review to understand the existing research on submodeling and its practical applications in finite element modeling. They selected a cantilever beam case as a test subject to demonstrate stress analysis and topology optimization through submodeling. They developed a 1D submodeling approach to streamline the optimization process and ensure result validity. The authors utilized beam formulations to optimize and validate the outcomes of the submodeling approach. They 3D-printed the optimized models and subjected them to a 3-point bending test to confirm the accuracy of the developed approach. They employed 3D finite element models for submodeling to validate the 1D approach, focusing on specific finite elements for deflection calculations and analyzed the results to demonstrate a strong correlation between the theoretical models and experimental data, showcasing the effectiveness of the submodeling methodology in achieving optimal solutions efficiently and accurately.

The findings of the paper are as follows: 1. The use of submodeling, specifically a 1D submodeling approach, proved to be effective in achieving optimal solutions more efficiently and accurately in finite element modeling. 2. The study conducted on a cantilever beam case demonstrated successful stress analysis and topology optimization through submodeling, resulting in optimized geometry for enhanced fatigue life. 3. Beam formulations were utilized to optimize and validate the outcomes of the submodeling approach, leading to the successful 3D printing and testing of the optimized models through a 3-point bending test. 4. Experimental results confirmed the accuracy and validity of the developed submodeling approach in streamlining the optimization process. 5. The use of 3D finite element models for submodeling further validated the 1D approach, with specific finite elements showing a strong correlation with experimental data in deflection calculations. Overall, the findings highlight the effectiveness of submodeling techniques in achieving optimal solutions and validating results in finite element modeling, stress analysis and optimization processes.

The originality and value of the paper lie in its innovative approach to utilizing submodeling techniques in finite element modeling for structural analysis and optimization. By focusing on the reduction of finite element models and the creation of smaller, more manageable models through submodeling, the paper offers designers a more efficient and accurate way to achieve optimal solutions for complex problems. The study's use of a cantilever beam case to demonstrate stress analysis and topology optimization showcases the practical applications of submodeling in real-world scenarios. The development of a 1D submodeling approach, along with the utilization of beam formulations and 3D printing for experimental validation, adds a novel dimension to the research. Furthermore, the paper's integration of 1D and 3D submodeling techniques for deflection calculations and validation highlights the thoroughness and rigor of the study. The strong correlation between the finite element models and experimental data underscores the reliability and accuracy of the developed approach. Overall, the originality and value of this paper lie in its comprehensive exploration of submodeling techniques, its practical applications in structural analysis and optimization and its successful validation through experimental testing.

While performance demands in the natural world are varied, graded lattice structures reveal distinctive mechanical properties with tremendous engineering application potential. For biomechanical functions where mechanical qualities are required from supporting under external loading and permeability is crucial which affects bone tissue engineering, the geometric design in lattice structure for bone scaffolds in loading-bearing applications is necessary. However, when tweaking structural traits, these two factors frequently clash. For graded lattice structures, this study aims to develop a design-optimization strategy to attain improved attributes across different domains.

To handle diverse stress states, parametric modeling is used to produce strut-based lattice structures with spatially varied densities. The tailored initial gradients in lattice structure are subject to automatic property evaluation procedure that hinges on finite element method and computational fluid dynamics simulations. The geometric parameters of lattice structures with numerous objectives are then optimized using an iterative optimization process based on a non-dominated genetic algorithm.

The initial stress-based design of graded lattice structure with spatially variable densities is generated based on the stress conditions. The results from subsequent dual-objective optimization show a series of topologies with gradually improved trade-offs between mechanical properties and permeability.

In this study, a novel structural design-optimization methodology is proposed for mathematically optimizing strut-based graded lattice structures to achieve enhanced performance in multiple domains.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

The purpose of this research is to establish a robust numerical framework for the calibration of macroscopic constitutive parameters, based on the analysis of polycrystalline RVEs with computational homogenisation.

This framework is composed of four building-blocks: (1) the multi-scale model, consisting of polycrystalline RVEs, where the grains are modelled with anisotropic crystal plasticity, and computational homogenisation to link the scales, (2) a set of loading cases to generate the reference responses, (3) the von Mises elasto-plastic model to be calibrated, and (4) the optimisation algorithms to solve the inverse identification problem. Several optimisation algorithms are assessed through a reference identification problem. Thereafter, different calibration strategies are tested. The accuracy of the calibrated models is evaluated by comparing their results against an FE2 model and experimental data.

In the initial tests, the LIPO optimiser performs the best. Good results accuracy is obtained with the calibrated constitutive models. The computing time needed by the FE2 simulations is 5 orders of magnitude larger, compared to the standard macroscopic simulations, demonstrating how this framework is suitable to obtain efficient micro-mechanics-informed constitutive models.

This contribution proposes a numerical framework, based on FE2 and macro-scale single element simulations, where the calibration of constitutive laws is informed by multi-scale analysis. The most efficient combination of optimisation algorithm and definition of the objective function is studied, and the robustness of the proposed approach is demonstrated by validation with both numerical and experimental data.

Currently, massive multiple-input multiple-output (m-MIMO) antennas are typically designed using complex trial-and-error methods. The purpose of this study is to determine an effective optimization method to achieve more efficient antenna design processes.

This paper presents the design stages of a m-MIMO antenna array compatible with 5G smartphones operating in long term evolution (LTE) bands 42, 43 and 46, based on a specific algorithm. Each antenna element in the designed 10-port m-MIMO antenna array is intended to perfectly cover the three specified LTE bands. The optimization methods used for this purpose include the Nelder–Mead simplex algorithm, covariance matrix adaptation evolution strategy, particle swarm optimization and trust region framework (TRF).

Among the primary optimization algorithms, the TRF algorithm met the defined objectives most effectively. The achieved antenna efficiency values exceeded 60.81% in the low band and 68.39% in the high band, along with perfect coverage of the desired bands, demonstrating the success of the design with the TRF algorithm. In addition, the potential electromagnetic field exposure caused by the designed m-MIMO antenna array is elaborated upon in detail using computational human models through specific absorption rate analysis.

The comparison of four different algorithms (two local and two global) for use in the design of a 10-element m-MIMO antenna array with a complex structural configuration and the success of the design implemented with the selected algorithm distinguish this study from others.

This paper aims to investigate the impact of combining grain-oriented electrical steel (GOES) grades on specific iron losses and the flux density distribution within a single-phase magnetic core.

This paper presents the results of finite-element method (FEM) simulations investigating the impact of mixing two different GOES grades on losses of a single-phase magnetic core. The authors used different models: a 3D model with a highly detailed geometry including both saturation and anisotropy, as well as a simplified 2D model to save computation time. The behavior of the flux distribution in the mixed magnetic core is analyzed. Finally, the results from the numerical simulations are compared with experimental results.

The specific iron losses of a mixed magnetic core exhibit a nonlinear decrease with respect to the GOES grade with the lowest losses. Analyzing the magnetic core behavior using 2D and 3D FEM shows that the rolling direction of the GOES grades plays a critical role on the nonlinearity variation of the specific losses.

The novelty of this research lies in achieving an optimum trade-off between the manufacturing cost and the core efficiency by combining conventional and high-performance GOES grade in a single-phase magnetic core.

This paper aims to describe a proposal for an innovative method of normal shock wave–turbulent boundary layer interaction (SBLI) and shock-induced separation control.

The concept is based on the introduction of a tangentially moving wall upstream of the shock wave and in the interaction region. The SBLI control mechanism may be implemented as a closed belt floating on an air cushion, sliding over two cylinders and forming the outer skin of the suction side of the airfoil. The presented exploratory numerical study is conducted with SPARC solver (steady 2D RANS). The effect of the moving wall is presented for the NACA 0012 airfoil operating in transonic conditions.

To assess the accuracy of obtained solutions, validation of the computational model is demonstrated against the experimental data of Harris, Ladson & Hill and Mineck & Hartwich (NASA Langley). The comparison is conducted not only for the reference (impermeable) but also for the perforated (permeable) surface NACA 0012 airfoils. Subsequent numerical analysis of SBLI control by moving wall confirms that for the selected velocity ratios, the method is able to improve the shock-upstream boundary layer and counteract flow separation, significantly increasing the airfoil aerodynamic performance.

The moving wall concept as a means of normal shock wave–turbulent boundary layer interaction and shock-induced separation control has been investigated in detail for the first time. The study quantified the necessary operational requirements of such a system and practicable aerodynamic efficiency gains and simultaneously revealed the considerable potential of this promising idea, stimulating a new direction for future investigations regarding SBLI control.