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Abstract: Abstract This work concerns the stochastic analysis of the bending of a slender cantilever beam subject to an external force with the inclusion of a stochastic effect characterised by white noise. The beam deflection is governed by the classic dynamic Euler–Bernoulli equation. Its response to the stochastic external load is investigated by learning pattern from the simulation data which are collected from numerical computations of ten thousand numerical experiments, which are achieved using a finite difference method coupled with a Monte Carlo method for the uncertainty quantification. Insightful results are presented with visualisation techniques and discussed in detail. Of note, by performing regression analysis to the data, the solution is shown to follow a centred Gaussian process with a strong numerical evidence. The associated autocovariance matrix is computed using the sample data. Then, a mild solution in the probability sense for the deflection at a fixed position and a fixed time is written explicitly in a simple form. The results obtained by the finite difference scheme were also compared to the finite-element scheme and were found to be in good agreement. Unsurprisingly, the finite-element scheme was found to be much more computationally expensive compared to finite difference scheme. Hence, for such a simple structure, the stochastic analysis using the finite difference scheme is preferred. Analysis of the results also showed that some of the regression parameters converge when the number of simulations reaches five hundred and only vary subject to numerical errors of order \(10^{-6}\) if the number of simulations is further increased. While others converge when the number of simulations exceeds two thousand showing that depending on the level of precision required fewer than ten thousand simulations might be required. PubDate: 2023-11-24
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Abstract: Abstract A machine learning method for the discovery of analytic solutions to differential equations is assessed. The method utilizes an inherently interpretable machine learning algorithm, genetic programming-based symbolic regression. An advantage of its interpretability is the output of symbolic expressions that can be used to assess error in algebraic terms, as opposed to purely numerical quantities. Therefore, models output by the developed method are verified by assessing its ability to recover known analytic solutions for two differential equations, as opposed to assessing numerical error. To demonstrate its improvement, the developed method is compared to a conventional, purely data-driven genetic programming-based symbolic regression algorithm. The reliability of successful evolution of the true solution, or an algebraic equivalent, is demonstrated. PubDate: 2023-11-18
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The current paper concerns to develop a new numerical formulation to simulate the tumor growth. The used numerical method is based on the meshless Galerkin technique in which the test and trial functions have been selected from the shape functions of moving Taylor approximation. The main mathematical model to describe the tumor growth is defined as a nonlinear system of equations. Thus, to get acceptable results from the Galerkin weak form, a two-grid algorithm is employed. The first step of the two-grid algorithm computes the corresponding approximated scheme in a coarse mesh by solving a nonlinear algebraic system of equations. Then, the obtained solution in the previous step has been used to solve the corresponding approximated scheme in a fine mesh, such that in the second step, a linear algebraic system of equations is solved. On the other hand, to access more accurate results, the number of nodes in the computational domain must be increased which causes the matrix to become larger. Therefore, the proper orthogonal decomposition is used to reduce size of the algebraic system of equations. Finally, some test problems are tested to confirm the efficiency and accuracy of the proposed numerical formulation. PubDate: 2023-11-13
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Abstract: Abstract A workflow for the numerical prediction of in-flight ice accretion on 3D structures is presented. The method is based on the predictor–corrector approach, which has been so far mainly developed in 2D codes and assessed in straight-wing test cases. The adaptations made for the 3D implementation are thus described. Among other developments, a remeshing technique based on the Dragon method is presented. The new methods are verified against reference numerical data. The whole workflow is validated using several test cases for which experimental measurements of ice shapes are available. Both straight and swept wings are therefore investigated. The numerical results are encouraging for low-sweep angles. Some recommendations are made for improving the results, including the need for new ice-density models. The predictor–corrector method is poorly adapted for cases exhibiting large scallop-like structures, which tends to be reinforced by high sweep angles. In this article, the test cases with highest sweep angle are effectively calculated less accurately. Costly multi-step ice-accretion simulations should be preferred for such conditions, unless a special ice bulk density model is developed. PubDate: 2023-11-07
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Abstract: Abstract For near-field acoustic holography, sparse array measurement for cost reduction can result in inaccuracy due to aliasing error. To attenuate it, there are data-driven methods based on artificial intelligence theories. Among these, the JTCSA-NAH method has not adopted measures for robustness enhancement despite its high accuracy in practice. In this work, the influence of measuring noise on JTCSA-NAH is analyzed followed by the principle of adding Gaussian noise for robustness improvement. Based on the relevant prior conditions, the ICCSA-NAH method, which relies on self-identity constraint data working as the Kalman gain is proposed. Subsequently, numerical example and experiment are carried out, and the results show that compared with JTCSA-NAH method, the mean errors of near-field vibration velocity reconstruction are theoretically and experimentally reduced from 15.19% and 23.64% to 6.03% and 12.45%, respectively, by the ICCSA-NAH method, which verifies the feasibility and superiority of the proposed method. PubDate: 2023-11-06
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Abstract: Abstract The non-contact transmission product permanent magnet coupler (PMC) has been widely used in industry due to its advantages such as low noise and vibration, high efficiency, high reliability, and overload protection. Owing to its complex electromagnetic behaviors, the accurate computation of key performances such as magnetic vector potential and torque is essential for optimizing its transmission efficiency. However, traditional calculation methods are based on analytical or simulation models, either imprecise or computationally intensive, hindering subsequent optimization design modeling. To address the above issue, this paper proposes a novel method based on physical-informed neural networks (PINN) to calculate the PMC performances with high accuracy and low computational cost. PINN integrates prior knowledge into the deep neural network’s loss functions to establish the model and accurately predict the PMC’s performance parameters. Experimental results demonstrate that PINN outperforms traditional calculation methods regarding feasibility, validity, and accuracy. Overall, PINN combines data-driven models with prior knowledge to achieve a data–knowledge dual driven, providing a new approach for optimizing PMC structure design. PubDate: 2023-11-06
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Abstract: Abstract Printed electronics are widely used in wearable tech, IoT, and medical devices, and reliable sintering methods are essential for achieving optimal electrode conductivity. However, existing sintering models are often based on trial-and-error or past experience, highlighting the need for a reliable numerical model to improve the process. Traditional phase-field sintering models are limited by factors such as small mesh size requirements, high computational expenses for large-scale simulations, and high mesh sensitivity. In this article, we introduce a new meshfree phase field model based on the recent hot optimal transform meshfree (HOTM) method to simulate nanoparticle sintering processes efficiently and accurately. We use the Galerkin method to develop variational forms for the Cahn–Hillard and the Allen–Chan equation of the phase-field model. In addition, we apply the Local maximum entropy (LEM) shape function to construct a Node-Material Point framework. Finally, we present two efficiency improvement schemes and MPI parallel computation that enable the model to perform large-scale simulations. After several performance tests, we demonstrate its efficiency and accuracy by presenting both 2D and 3D simulation cases in comparison to actual sintering behaviors of the nanoparticles. PubDate: 2023-10-31
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Abstract: Abstract Generating tangle-free high-quality hexahedral meshes is an ongoing challenge. Tangled meshes, i.e., meshes containing negative Jacobian elements, are unsuitable for finite element (FE) simulations as they lead to erroneous results. Consequently, many untangling methods have been proposed; however, untangling is not always achievable.The present paper addresses this challenge by allowing tangled meshes for FE analysis with the use of the isoparametric tangled finite element method (i-TFEM). The proposed method efficiently handles complex configurations of tangled elements, making it suitable for real-world scenarios. By introducing minor modifications to standard FEM, i-TFEM offers an easy implementation and reduces to standard FEM for non-tangled meshes. Numerical experiments, involving both linear and nonlinear elasticity, demonstrate the accuracy, convergence characteristics, and applicability of the method to real-world tangled meshes. The results emphasize the importance of reevaluating mesh quality indicators for tangled meshes. PubDate: 2023-10-28
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Abstract: Abstract We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can give comparable results to conventional topology optimization techniques, with an added advantage of enabling seamless integration with post-processing software, and a potential of topology optimization with objectives where meshing and Finite Element Analysis (FEA) may be expensive or not suitable. Our approach (DMF-TONN) takes in as inputs the boundary conditions and domain coordinates and finds the optimum density field for minimizing the loss function of compliance and volume fraction constraint violation. The mesh-free nature is enabled by a physics-informed displacement field approximation neural network to solve the linear elasticity partial differential equation and replace the FEA conventionally used for calculating the compliance. We show that using a suitable Fourier Features neural network architecture and hyperparameters, the density field approximation neural network can learn the weights to represent the optimal density field for the given domain and boundary conditions, by directly backpropagating the loss gradient through the displacement field approximation neural network, and unlike prior work there is no requirement of a sensitivity filter, optimality criterion method, or a separate training of density network in each topology optimization iteration. PubDate: 2023-10-28
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Abstract: Abstract Automatic generation of hexahedral meshes for complex geometries is still a challenging problem, the domain-decomposition based method is one of the promising methods for such problems. When generating the meshes of sub-components of a domain, it is often necessary to impose consistent mesh constraints on the interfaces between sub-components. The adoption of mesh matching algorithms can relax such constraints, and improve the efficiency and robustness of mesh generation framework. In this paper, a new mesh matching algorithm based on base-complex structure is proposed. In our method, the base-complex structures of the sub-components to be matched are obtained and optimized first, and then they are used to match the interfaces between the sub-components via dual chord operations on the base-complex structures. After the matching process, an optimization problem is formulated and solved to adjust the positions of corresponding vertices on the interfaces. Compared to the current mesh matching algorithms, instead of performing dual operations directly on mesh elements, the proposed method needs less dual operations and is able to obtain higher quality elements near the interfaces. Finally, the effectiveness of the proposed algorithm is verified by several matching examples. PubDate: 2023-10-26
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Abstract: Abstract This paper provides a compact and efficient 167-line MATLAB code for thermoelastic topology optimization considering transient heat conduction, in view of designing structural components subjected to thermo-mechanical loads. The thermo-mechanical response is determined through finite-element modeling and discretized in time with an implicit finite difference scheme. A density-based topology optimization procedure is developed and applied to a standard compliance minimization problem extended with thermal boundary conditions. The sensitivity analysis is carried out by means of the adjoint variable method in combination with the discretize-then-differentiate approach for computational efficiency. The proposed methodology and its implementation in MATLAB are explained in detail. Furthermore, numerical examples are presented to demonstrate the influence of several parameters with respect to the thermo-mechanical loading and the transient heat conduction analysis. The results show that the thermo-mechanical load ratio significantly affects the optimized topology, as well as the thermal response time related to the transient thermal loading. Finally, the effect of the time-dependent loading is investigated based on a weighted formulation for the objective function to influence the optimization and to obtain a more mechanically or thermally optimized structure. PubDate: 2023-10-24
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Abstract: Abstract In recent years, research and applications of bioinspired structures in advanced engineering fields have gained increased attention from the research community, thanks to their fascinating properties. In this study, we address an efficient computational approach for performing nonlinear static and dynamic analyses of functionally graded plates based on triply periodic minimal surface architectures for the first time. We named a functionally graded triply periodic minimal surface (FG-TPMS) plate. A key idea of modelling FG-TPMS plates is to rely on the four-unknown refined quasi-3D plate theory, von-Kármán assumptions, and NURBS-based isogeometric analysis. The nonlinear behavior of three TPMS structures including Primitive (P), Gyroid (G), and I-graph and Wrapped Package-graph (IWP) under various conditions are intensively studied in this work. To estimate the effective mechanical features of the TPMS architectures, we utilize a two-phase fitting model with respect to the relative density. The influence of several parameters of TPMS structures on the nonlinear static and dynamic characteristics is evaluated. In addition, four types of dynamic loads including rectangular, triangular, half-sine, and explosive blast are also considered here. The key contribution of this study is the development of an efficient and powerful nonlinear numerical model to explore the static and dynamic behavior of TPMS architectures-based FG plates. The present method not only effectively accounts for the thickness stretching effect but also includes the consideration of structural damping, thereby facilitating a more accurate solution to engineering problems under real-world conditions. Furthermore, the current results indicate that FG-TPMS plates exhibit a superior energy absorption capacity compared to isotropic ones of the same weight under geometric nonlinearity conditions. Finally, the findings obtained from this study enhance our understanding of nonlinear behavior as well as provide valuable design strategies for future advanced engineering structures based on TPMS architectures. PubDate: 2023-10-20
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Abstract: Abstract Bayesian optimization (BO) is a popular optimization technique for expensive-to-evaluate black-box functions. We propose a cheap-expensive multi-objective BO strategy for optimizing a permanent magnet synchronous motor (PMSM). The design of an electric motor is a complex, time-consuming process that contains various heterogeneous objectives and constraints; in particular, we have a mix of cheap and expensive objective and constraint functions. The expensive objectives and constraints are usually quantified by a time-consuming finite element method, while the cheap ones are available as closed-form equations. We propose a BO policy that can accommodate cheap-expensive objectives and constraints, using a hypervolume-based acquisition function that combines expensive function approximation from a surrogate with direct cheap evaluations. The proposed method is benchmarked on multiple test functions with promising results, reaching competitive solutions much faster than traditional BO methods. To address the aforementioned design challenges for PMSM, we apply our proposed method, which aims to maximize motor efficiency while minimizing torque ripple and active mass, and considers six other performance indicators as constraints. PubDate: 2023-10-15
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Abstract: Abstract A two-dimensional ordinary state-based peridynamic formulation is proposed for the analysis of elastic–plastic plane structures. Selecting appropriate relation for isotropic extension state, the deviatoric strain energy formulation is derived for plane strain/plane stress cases. Simple formulas to calculate peridynamic equivalent von Mises stress and its equivalent plastic strain are proposed. New yield function and flow rule are introduced. Implicit backward Euler time integration is used to obtain the increment of deviatoric plastic extension. Two example problems of grooved plate specimen and perforated plate under uniform tensile loading are considered to verify the accuracy of the present model in plane strain and plane stress situations respectively. The obtained results had a good agreement with those obtained by finite-element method. Results of displacements, von Mises stress, equivalent plastic strain, and plastic zone area are demonstrated. The effect of influence function on the results is also studied. PubDate: 2023-10-14
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Abstract: Abstract A new peridynamic model for predicting the out-of-plane bending and twisting behavior of composite laminates has been proposed, in which fiber bonds and matrix bonds are distinguished for characterizing anisotropy. The peridynamic formulations are obtained based on the principle of virtual displacements using the Total Lagrange formulation, and the equation of motion is reformulated by the interpolation technique. The critical curvature is adopted as the failure criterion, and a micromodulus reduction method is implemented in the PD algorithm. For multi-layer laminated structures, a new single-layer material point model (SLMPM) is proposed, in which the overall micromodulus is integrated according to all plies in laminates. The capability of the developed PD model was demonstrated by the bending examples of composite laminates with different fiber orientations, and damage analysis was further conducted to demonstrate the strong capability of the proposed PD model in replicating the failure process of composite structures. In addition, the computational efficiency of numerical models can be greatly improved due to the SLMPM. PubDate: 2023-10-12
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Abstract: Abstract Theoretical modeling of sound propagation within lined ducts can help with interpreting the underlying mechanisms of waveguide physics. Herein, we present ESM-FLOW, a meshless, wave-based method in physical space for modeling sound propagation in 3D axisymmetric lined ducts. First, ESM-FLOW is applied to a 3D axisymmetric problem with uniform flow, in which the wall-reflected fields are replaced by a set of equivalent sources (ESs) surrounding the wall. A circumferential Fourier transform is employed to reduce this to a 2D problem in the circumferential modal domain. This enables efficient solving using a 2D equivalent-source method (ESM) scheme with circumferential modal Green’s functions. Clenshaw–Curtis quadrature is used to accurately evaluate the oscillating circumferential integral. The unknown ES amplitudes are solved for through a linear system assembled by replacing the incident and wall-reflected fields with ESs satisfying the wall boundary conditions in the modal domain. Next, rigid-wall modes are derived as inputs for the 3D axisymmetric problem, enabling modal analysis—something with which most boundary-integral formulation (BIF) methods struggle. Finally, a multi-layer ESM-FLOW method is presented to address medium inhomogeneities, in which the non-uniform waveguide is divided into layers with piece-wise constant medium properties. ESM-FLOW is validated by comparison with a finite-element model, and additional simulations are presented to showcase its capabilities. The results demonstrate that ESM-FLOW combines the numerical efficiency and accuracy of typical BIF methods (including backscattering) while overcoming the limitations imposed by uniform media. This makes it highly applicable to the acoustic design of engines and ventilation systems. PubDate: 2023-10-11
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Abstract: In this work, an experimentally validated multiscale modeling framework for additively manufactured shell lattice structures with graded parameters is introduced. It is exemplified in application to the Schwarz primitive triply periodic minimal surface microstructure and 3D printing using masked stereolithography of a photopolymer material. The systematic procedure starts with the characterization of a hyperelastic material model for the 3D printed material. This constitutive model is then employed in the finite element simulation of shell lattices at finite deformations. The computational model is validated with experimental compression tests of printed lattice structures. In this way, the numerical convergence behavior and size dependence of the model are assessed, and the range in which it is reasonable to assume linear elastic behavior is determined. Then, representative volume elements subject to periodic boundary conditions are simulated to homogenize the mechanical behavior of Schwarz primitives with varying aspect ratios and shell thicknesses. Subsequently, the parameterized effective linear elasticity tensor of the metamaterial is represented by a physics-augmented neural network model. With this constitutive model, functionally graded shell lattice structures with varying microstructural parameters are simulated as macroscale continua using finite element and differential quadrature methods. The accuracy, reliability and effectiveness of this multiscale simulation approach are investigated and discussed. Overall, it is shown that this experimentally validated multiscale simulation framework, which is likewise applicable to other shell-like metamaterials, facilitates the design of functionally graded structures through additive manufacturing. Graphical PubDate: 2023-10-11
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Abstract: Abstract The method of combining adaptive Kriging surrogate model with fuzzy simulation can efficiently estimate time-dependent failure possibility (TDFP) under fuzzy uncertainty. However, there still exists potential to improve computational efficiency due to the possible conservative issue in current time-dependent U learning function. Thus, based on the stochastic property of Kriging model, a new learning function is proposed by considering the probability of Kriging model misclassifying the time-dependent state of structure. Comparing with the existing time-dependent U learning function, the proposed learning function cannot only select the fuzzy input point whose time-dependent failure state has been correctly recognized by current Kriging model, but also accurately quantify the time-dependent state misclassification probability of the fuzzy input point with unrecognizable time-dependent state. Using the proposed new learning function, the fuzzy input candidate sample, which contributes most to decrease the probability of the Kriging model misjudging the time-dependent state of structure, and the time candidate sample, which possesses most impact to the time-dependent state of the selected fuzzy input sample, can be selected to efficiently guide updating the Kriging model. Then, the efficiency of estimating TDFP is improved. Several case studies are introduced to verify the superiority of the proposed learning function to existing time-dependent U one in view of efficiency. PubDate: 2023-10-10
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Abstract: Abstract Interfaces in multiphase flows are affected by surface tension, and when temperature gradients occur in the flow domain, tangential surface tensions along the interface also arise. As the behaviour of fluids contacting on a solid surface is also governed by surface tension, the description of the wetting phenomenon is challenging. Peridynamic differential operator (PDDO) can express partial differentials of any order by integral equations. Therefore, the governing equations for multiphase fluid motion, such as the Navier–Stokes equations and energy equations, can be reformulated in terms of integral equations. In this study, a novel non-local method is developed for modelling the multiphase fluid flow motion using the PDDO, and the thermal effect on surface tension force is considered. To describe the surface tension forces in the normal and tangential directions, the non-local form of the continuum surface force (CFS) model is presented. Besides, to overcome the inaccuracy of the unit normal vectors at the three-phase flow intersection region, an additional treatment for this region is presented. Finally, several benchmark multiphase fluid flow cases, such as square droplet deformation, surface wetting, and droplet migration in thermo-capillary flow are presented and validated. The results demonstrate that the developed non-local model can accurately capture the surface tension effect in multiphase fluid flow motion. PubDate: 2023-10-09
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