# Engineering with Computers

Online ISSN: 1435-5663
Print ISSN: 0177-0667
Recent publications
• Jichao Yin
• Hu Wang
• Shuhao Li
• Daozhen Guo
An efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) method is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the combined approximation reduced model (CARM) to reduce the dimension of the model in different aspects. First, the CARM restricts the solution space to avoid large matrix factorization. Second, the PARM is proposed to construct the CARM dynamically to save computational cost. Furthermore, the multi-grid conjugate gradient method is suggested to update PARM adaptively. Finally, several classic numerical examples are tested to show that the proposed method not only significantly improves computational efficiency, but also can solve large-scale problems that are difficult to solve by direct solvers due to the memory limitations.

• Kendrick Tan
• Boshun Gao
• Cheng-Hau Yang
• [...]
Infectious airborne diseases like the recent COVID-19 pandemic render confined spaces high-risk areas. However, in-person activities like teaching in classroom settings and government services are often expected to continue or restart quickly. It becomes important to evaluate the risk of airborne disease transmission while accounting for the physical presence of humans, furniture, and electronic equipment, as well as ventilation. Here, we present a computational framework and study based on detailed flow physics simulations that allow straightforward evaluation of various seating and operating scenarios to identify risk factors and assess the effectiveness of various mitigation strategies. These scenarios include seating arrangement changes, presence/absence of computer screens, ventilation rate changes, and presence/absence of mask-wearing. This approach democratizes risk assessment by automating a key bottleneck in simulation-based analysis—creating an adequately refined mesh around multiple complex geometries. Not surprisingly, we find that wearing masks (with at least 74% inward protection efficiency) significantly reduced transmission risk against unmasked and infected individuals. While the use of face masks is known to reduce the risk of transmission, we perform a systematic computational study of the transmission risk due to variations in room occupancy, seating layout and air change rates. In addition, our findings on the efficacy of face masks further support use of face masks. The availability of such an analysis approach will allow education administrators, government officials (courthouses, police stations), and hospital administrators to make informed decisions on seating arrangements and operating procedures.

In this study, a physics-informed neural energy-force network (PINEFN) framework is first proposed to directly solve the optimum design of truss structures that structural analysis is completely removed from the implementation of the global optimization. Herein, a loss function is constructed to guide the training network based on the complementary energy, constitutive equations, and weight of the structure. Now only neural network (NN) is used in our scheme to minimize the loss function wherein weights and biases of the network are considered as design variables. In this model, spatial coordinates of truss members are examined as input data, while corresponding cross-sectional areas and redundant forces unknown to the network are taken account of output. Accordingly, the predicted outputs obtained by feedforward are employed to establish the loss function relied on physics laws. And then, back-propagation and optimizer are applied to automatically calculate sensitivity and adjust parameters of the network, respectively. This whole process, which is the so-called training, is repeated until convergence. The optimum weight of the structure corresponding to the minimum loss function is indicated as soon as the training process ends without using any structural analyses. Several benchmark examples for sizing optimization of truss structures are examined to determine the reliability, efficiency, and applicability of the proposed model. Obtained outcomes indicated that it not only reduces the computational cost dramatically but also yields higher accuracy and faster convergence speed compared with recent literature.

In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing node control domains. By defining a connectable node cloud, this method uses the integral of the diffusion term and generalized finite-difference operators to derive overdetermined equations of the node control volumes. An empirical method of calculating reliable node control volumes and a triangulation-based method to determine the connectable point cloud are developed. The method focuses only on the volume of the node control domain rather than the specific shape, so the construction of node control domains is virtual and does not increase the computational cost. To our knowledge, this is the first study to construct node control volumes in the meshless framework, termed the node control domain-based meshless method (NCDMM), which can also be regarded as an extended finite-volume method (EFVM). Taking two-phase porous flow problems as an example, discrete NCDMM schemes satisfying local mass conservation are derived by integrating the generalized finite-difference schemes of governing equations on each node control domain. Finally, commonly used low-order finite-volume method (FVM)-based nonlinear solvers for various porous flow models can be directly employed in the proposed NCDMM, significantly facilitating general-purpose application. Theoretically, the proposed NCDMM has the advantages of previous meshless methods for discretizing computational domains with complex geometries, as well as the advantages of traditional low-order FVMs for stably handling a variety of porous flow problems with local mass conservation. Four numerical cases are implemented to test the computational accuracy, efficiency, convergence, and good adaptability to the calculation domain with complex geometry and various boundary conditions.

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling conditions at high accuracy, but come with considerable numerical effort and cost for the evaluation of the mortar integrals to compute the coupling operators. In this paper, we identify bottlenecks in parallel data layout and domain decomposition that hinder an efficient evaluation of the mortar integrals. We then propose a set of computational strategies to restore optimal parallel communication and scalability for the core kernels devoted to the evaluation of mortar terms. We exemplarily study the proposed algorithmic components in the context of three-dimensional large-deformation contact mechanics, both for cases with fixed and dynamically varying interface topology, yet these concepts can naturally and easily be transferred to other mortar applications, e.g. classical meshtying problems. To restore parallel scalability, we employ overlapping domain decompositions of the interface discretization independent from the underlying volumes and then tackle parallel communication for the mortar evaluation by a geometrically motivated reduction of ghosting data. Using three-dimensional contact examples, we demonstrate strong and weak scalability of the proposed algorithms up to 480 parallel processes as well as study and discuss improvements in parallel communication related to mortar finite element methods. For the first time, dynamic load balancing is applied to mortar contact problems with evolving contact zones, such that the computational work is well balanced among all parallel processors independent of the current state of the simulation.

Three approaches for construction of a surrogate model of a result field consisting of multiple physical quantities are presented. The first approach uses direct interpolation of the result space on the input space. In the second and third approaches a Singular Value Decomposition is used to reduce the model size. In the reduced order surrogate models, the amplitudes corresponding to the different basis vectors are interpolated. A quality measure that takes into account different physical parts of the result field is defined. As the quality measure is very cheap to evaluate, it can be used to efficiently optimize hyperparameters of all surrogate models. Based on the quality measure, a criterion is proposed to choose the number of basis vectors for the reduced order models. The performance of the surrogate models resulting from the three different approaches is compared using the quality measure based on a validation set. It is found that the novel criterion can effectively be used to select the number of basis vectors. The choice of construction method significantly influences the quality of the surrogate model.

Enrichment techniques that employ nonconforming mesh are effective in modeling structures with discontinuities because numerical issues regarding mesh quality are avoided. However, the accurate integration of the bilinear and linear forms on the discretized domain, which is required in the standard Galerkin-based finite element method, is computationally expensive due to the complexity of the enriched basis function. In this paper, we present a fast and accurate alternative method of numerical integration using nonlinear regression enabled by a multi-perceptron feedforward neural network. The relationship between an implicitly represented geometry and the quadrature rule derived from the moment fitting method is predicted by the neural network; the neural network-based regression model circumvents complex computation and significantly reduces the overall online time by avoiding expensive function evaluations. Through the selected numerical examples, we demonstrate the efficiency and accuracy of the current method, as well as the flexibility of the trained network to be used in different contexts.

Failure possibility function (FPF) provides the relationship of failure possibility varying with distribution parameters of fuzzy inputs, and it is desired in the possibility-based design optimization under fuzzy uncertainty. However, estimating FPF by direct double-loop fuzzy simulation (DL-FS) requires large computational cost, since failure possibility needs to be repeatedly estimated corresponding to different discrete realizations of distribution parameters. For addressing this issue, an augmented fuzzy simulation (AFS) is proposed to improve the efficiency of estimating FPF. In AFS, the candidate sample pool (CSP) is first generated in an augmented space spanned by fuzzy inputs and their distribution parameters, on which the failure possibility at different distribution parameters can be estimated by the same CSP of AFS. Compared with DL-FS, the proposed AFS only needs one group of FS, which greatly reduces the computational cost and improves the efficiency of estimating FPF. Moreover, a Kriging model is adaptively embedded in the CSP of AFS by adopting U-learning and CSP reduction strategy, in which the convergent Kriging model trained in CSP of AFS is used to replace performance function for recognizing failure samples and estimating FPF. Since the number of the training samples for constructing the convergent Kriging model is much less than the size of CSP of AFS, the method combining adaptive Kriging with AFS can greatly improve the efficiency of estimating FPF, which is verified by the presented examples.

In this article, we are concerned with meshless methods to approximate and simulate the solution of semi-linear stochastic evolution equations. We first study the asymmetric Kansa method and then consider its regularized form. Kansa method is an efficient approach that is easy to implement and adapt and has sufficient accuracy and approximation power. We employ Karhunen–Loéve expansion for having faster and better simulations for the stochastic part. The absolute error, standard deviation, root mean square error, and CPU times for showing the accuracy and speed of our methodology are calculated. From the numerical analysis view, the stability of this methodology for time-dependent problems is investigated by numerical factors in the computational part. Experimentally, the performance of both presented methods is more significant, and proportionally they have better results to previous work in this subject.

An improved nonintrusive parametric model order reduction (pMOR) approach is proposed for the flow field interpolation regarding fluid–structure interaction (FSI) objects. Flow field computation using computational fluid dynamics (CFD) requires excessive computational time and memory. Nonintrusive and data-driven MOR schemes have been proposed to overcome such limitations. The present methodology is implemented by both proper orthogonal decomposition (POD) and a modified Nouveau variational autoencoder (mNVAE). POD attempts to reduce the number of degrees of freedom (DOFs) on the precomputed series of the full-order model parametric result. The reduced DOF yields parametrically independent reduced bases and dependent coefficients. Then, mNVAE is employed for the interpolation of POD coefficients, which will be combined with POD modes for parametrically interpolated flow field generation. The present approach is assessed on the benchmark problem of a two-dimensional plunging airfoil and the highly nonlinear FSI phenomenon of the limit cycle oscillation. The comparison was executed against other POD-based generative neural network approaches. The proposed methodology demonstrates applicability on highly nonlinear FSI objects with improved accuracy and efficiency.

Machine learning (ML)-based data-driven methods have promoted the progress of modeling in many engineering domains. These methods can achieve high prediction and generalization performance for large, high-quality datasets. However, ML methods can yield biased predictions if the observed data (i.e., response variable y) are corrupted by outliers. This paper addresses this problem with a novel, robust ML approach that is formulated as an optimization problem by coupling locally weighted least-squares support vector machines for regression (LWLS-SVMR) with one weight function. The weight is a function of residuals and allows for iteration within the proposed approach, significantly reducing the negative interference of outliers. A new efficient hybrid algorithm is developed to solve the optimization problem. The proposed approach is assessed and validated by comparison with relevant ML approaches on both one-dimensional simulated datasets corrupted by various outliers and multi-dimensional real-world engineering datasets, including datasets used for predicting the lateral strength of reinforced concrete (RC) columns, the fuel consumption of automobiles, the rising time of a servomechanism, and dielectric breakdown strength. Finally, the proposed method is applied to produce a data-driven solver for computational mechanics with a nonlinear material dataset corrupted by outliers. The results all show that the proposed method is robust against non-extreme and extreme outliers and improves the predictive performance necessary to solve various engineering problems.

The discrete model in the traditional finite element method (FEM) inevitably behaves more stiffly than the corresponding continuous model. This results in an unavoidable dispersion error that increases rapidly with the wavenumber. To overcome this problem in acoustic scattering computations, a hybrid smoothed moving least-squares interpolation method (HSMLSIM) is developed to control the dispersion error. In the HSMLSIM, a hybrid stiffness is created by combining a standard FEM model and a node-based locally smoothed FEM model to soften the acoustic stiffness. To accurately calculate the entries of the softened acoustic stiffness, an improved mesh-free interpolation method is adopted for shape function construction. A discrete model that has very close to the actual stiffness of the original model can be achieved using the HSMLSIM. The major benefit of the HSMLSIM is that, for a given mesh, the accuracy is significantly improved compared to that of FEM without introducing extra degrees of freedom. The performance of the proposed method is numerically studied. Numerical experiments are conducted to investigate the properties of the proposed method. The simulation results indicate that the HSMLSIM can effectively suppress the dispersion error and achieve superior computational performance and is, therefore, competitive for acoustic scattering computations.

The difficulties in dealing with steel skeleton frames and low computational efficiency are the major obstacles for applying peridynamics (PD) to model reinforced concrete (RC) structures. This paper proposes a new reinforced concrete model, named PDROD, in which the concrete is modeled by PD theory and the reinforcement is modeled by rod elements. A bonding formulation is derived to characterize the interaction between the concrete and reinforcements, guaranteeing the consistence of load transfer between the two mediums. Thanks to the new bonding model, the discretization of the concrete and reinforcements does not necessarily need to be coincident, facilitating the application of PDROD in modeling RC structures whose skeleton frames are with complex geometries. The PDROD model not only gives full play to the advantages of PD theory in damage problems without additional failure criteria and stiffness degradation model, but also significantly increases the numerical efficiency of computation, which extends the applicability of PD to modeling real-scale RC structures. The accuracy and efficiency of the PDROD model are demonstrated by simulating a series of examples of concrete plates with reinforcing bars. Good agreements have been observed between the results from PDROD and the classical FEM predictions. The challenging benchmarks on the Stuttgart Shear Tests were also simulated to demonstrate the capability of the PDROD model in quasi-brittle fracture problems of large-scale RC structures.

In this paper, a nonlocal operator method combined with an explicit phase field method is applied to model the propagation of quasi-static fracture and show the computational efficiency of the proposed model compared with numerical models based on implicit method in the literature. Based on the energy form of the phase field model, the nonlocal strong form of governing equations are derived. In the implementation, both the mechanical field and phase field are updated with an explicit time integration. Several numerical benchmark problems including L-shape panel, Three-point bending, Notched plate with holes are carried out and compared with other methods, which show good agreement with previous works. Furthermore, a hybrid implicit/explicit model is proposed to improve the computational efficiency of the explicit model. This paper also presents a local damping, which decreases the ratio of kinetic energy to internal energy of the explicit phase field model to apply mass scaling method. The mass scaling for the cases studied here is examined and the computational time is saved.

We propose an efficient implementation of a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In addition to that, significant computational efficiency in memory requirement has been achieved using homogenization strategy. The algorithm has been integrated with versatile computing platform of MATLAB for ease of use and customization. The bottlenecking repetitive solution of the state equation has been solved using an optimized geometric multigrid approach along with CUDA parallelization enabling an order of magnitude faster in computational time than current state of the art implementations. The main novelty lies in the efficient implementation wherein on the fly computation of auxiliary matrices in the multigrid scheme and modification in interpolation schemes using homogenization strategy removes memory limitation of GPUs. Memory hierarchy of GPU has also been exploited for further optimized implementations. All these enable solution of structures involving hundred millions of three dimensional brick elements to be accomplished in a standard desktop computer or a workstation. Performance of the proposed algorithm is illustrated using several examples including design dependent loads. Results obtained indicate the excellent performance and scalability of the proposed approach.

This study presents the bond-based (BB) peridynamics (PD) with stretch and rotation kinematics for modeling the linear elastic deformation of a composite laminate. The laminate experiences only in-plane and transverse shear deformations and disregards the transverse normal deformation. The PD equilibrium equation for a laminate is derived under the assumption of small deformation and is solved by employing implicit techniques. The in-plane PD forces are expressed by considering the PD bond interactions among the points. The forces arising from the interaction of adjacent layers are expressed by considering a pointwise approach that utilizes the PD differential operator (PDDO) in conjunction with the shear-lag theory. The micro-moduli associated with stretch and rotation are directly related to the constitutive relations between stress and strain components in continuum mechanics. It is restricted to only one constraint on the material constants leading to a fixed value of in-plane shear modulus. The accuracy of this approach is demonstrated by capturing the correct deformation in a laminate for varying layups. Finally, its capability for progressive failure is demonstrated by considering a quasi-isotropic laminate with a pre-existing crack. It employs critical stretch, the critical skew (relative rotation) angle and the critical delamination angle in the bond breakage criteria.

Manufacturers have been developing new graphics processing unit (GPU) nodes with large capacity, high bandwidth memory and very high bandwidth intra-node interconnects. This enables moving large amounts of data between GPUs on the same node at low cost. However, small packet bandwidths and latencies have not decreased, which makes global dot products expensive. These characteristics favor a new kind of problem decomposition called “equation decomposition” rather than traditional domain decomposition. In this approach, each GPU is assigned one equation set to solve in parallel so that the frequent and expensive dot product synchronization points in traditional distributed linear solvers are eliminated. In exchange, the method involves infrequent movement of state variables over the high bandwidth, intra-node interconnects. To test this theory, our flagship code Multiphase Flow with Interphase eXchanges (MFiX) was ported to TensorFlow. This new product is known as MFiX-AI and can produce near identical results to the original version of MFiX with significant acceleration in multiphase particle-in-cell (MP-PIC) simulations. The performance of a single node with 4 NVIDIA A100s connected over NVLINK 2.0 was shown to be competitive to 1000 CPU cores (25 nodes) on the JOULE 2.0 supercomputer, leading to an energy savings of up to 90%. This is a substantial performance benefit for small- to intermediate-sized problems. This benefit is expected to grow as GPU nodes become more powerful. Further, MFiX-AI is poised to accept native artificial intelligence/machine learning models for further acceleration and development.

An automatic unstructured mesh generation approach is presented to discretize complex electronic packaging systems for finite element analysis. Various novel schemes are developed to resolve the common issues (models contain geometrical defects, models contain small but necessary features, simulation properties are predefined on models, etc.) to automate the entire mesh generation pipeline. These schemes include employing Boolean operations with a few technical considerations to resolve the geometrical defects of the original model, defining a sizing function that can adapt to small features, and developing a new data structure named the unified topology model to connect a CAD model and the mesh resulting from the model. The proposed approach can generate quality meshes on certain models with geometrical defects, while state-of-the-art open-source tools (Netgen and Gmsh) generate nonconforming meshes on those models. Tests on complex configurations show that the proposed approach can achieve a speed-up of 3–5 times in comparison with state-of-the-art commercial tools (e.g., COMSOL Multiphysics). Simulation results are provided to demonstrate that the proposed approach can create a mesh with satisfactory quality.

Given the limitations of Latin hypercube design in constrained design space, Latin hypervolume designs with good space- filling and noncollapsing properties are developed in this paper. In the proposed method, the value of the design points in each dimension is based on the hypervolume instead of the coordinate axis length, enabling the generated design to have the space-filling property. To address the challenge of precisely obtaining the hypervolume in high-dimensional and irregular design spaces, Monte Carlo sampling is introduced to approximate the hypervolume. In addition, a constrained simulated annealing algorithm is presented for the proposed method, with an acceleration module to speed up the process of searching for a feasible design. The experiments on benchmark numerical examples illustrate that the proposed method is considerably better compared with the other two methods. Moreover, the proposed method is applied to an engineering modeling scenario to analyze the impact of cracks on the physical properties of an aircraft model. The results show that the proposed method generates a more desirable distribution of cracks and is more suitable for complex situations in practical engineering. Source code is available at https:// github. com/ Pang- Yong/ LHVD- OLHVO.

In this paper, the weak form of bond-associated peridynamic differential operator is proposed to solve differential equations. The presented method inherits the advantages of the original peridynamic differential operator and enables directly and efficiently to determine the nonlocal weak form for local differential equations and obtain the corresponding symmetrical tangent stiffness matrix in the smaller size using variational principles. The concept of bond-associated family is introduced to suppress the numerical oscillation and zero-energy modes in this study. Several typical elasticity problems, taken as examples, are presented to show the application and capabilities of this method. The accuracy, convergence, and stability of the proposed method are demonstrated by seven numerical examples including linear and nonlinear, steady and transient state problems, and eigenvalue problems in 1D, 2D, and 3D cases.

Dendrites are one of the most widely observed patterns in nature, and occur across a wide spectrum of physical phenomena—from snow flakes to river basins; from bacterial colonies to lungs and vascular systems; and in solidification and growth patterns in metals and crystals. The ubiquitous occurrence of these “tree-like” structures can be attributed to their excellent space-filling properties, and at times, dendritic structures also spatially manifest fractal-like distributions. As is the case with many fractal-like geometries, the complex multi-level branching structures in dendrites pose a modeling challenge, and a full resolution of dendritic structures is computationally very demanding. In the literature, extensive theoretical models of dendritic formation and evolution, essentially as extensions of the classical moving boundary Stefan problem exist. Much of this understanding is from the analysis of dendrites occurring during the solidification of metallic alloys, as this is critical for understanding microstructure evolution during metal manufacturing processes that involve solidification of a liquid melt. Motivated by the problem of modeling microstructure evolution from liquid melts of pure metals and metallic alloys during metal additive manufacturing, we developed a comprehensive numerical framework for modeling a large variety of dendritic structures that are relevant to metal solidification. In this work, we present a numerical framework encompassing the modeling of Stefan problem formulations relevant to dendritic evolution using a phase-field approach and a finite element method implementation. Using this framework, we model numerous complex dendritic morphologies that are physically relevant to the solidification of pure melts and binary alloys. The distinguishing aspects of this work are—a unified treatment of both pure metals and alloys; novel numerical error estimates of dendritic tip velocity; and the study of error convergence of the primal fields of temperature and the order parameter with respect to numerical discretization. To the best of our knowledge, this is a first of its kind study of numerical convergence of the phase-field equations of dendritic growth in a finite element method setting. Further, using this numerical framework, various types of physically relevant dendritic solidification patterns like single equiaxed, multi-equiaxed, single columnar and multi-columnar dendrites are modeled in two-dimensional and three-dimensional computational domains.

CoKriging is a popular surrogate modeling approach to approximate the input–output relationship using multi-fidelity data from different sources. However, it suffers from the big data issue due to its cubic time complexity and square memory complexity with the data size. This becomes even exacerbated for iterative design optimization. To overcome this limitation, this paper presents a new data sparsification method for multi-fidelity surrogate-based optimization (MFSBO). It includes two key components: reduced design space and data filtering (RDS&DF), which alleviate the surrogate modeling complexity and time for improved efficiency while balancing between exploration and exploitation during optimization. RDS&DF is also combined with an expected improvement reduction (EIR)-based infill technique (Yang et al. in Struct Multidiscip Optim, 2022. https://doi.org/10.1007/s00158-022-03240-x), enabling both parsimony and computational awareness for MFSBO. Two case studies are conducted to examine the proposed method. Results demonstrate that a significant reduction in the modeling and thus optimization time (69.49% and 73.92%) is achieved while retaining the design accuracy.

The impact of liquid droplets on flexible substrates is a common phenomenon in applications, such as plant leaves repelling raindrops and piezoelectric sensors harvest droplet energy. It involves the coupling of free surface flow, elasticity and surface/interface with large deformations that are difficult to simulate using traditional numerical methods. In this study, a novel fluid–flexible structure interaction model is established based on the smoothed particle hydrodynamics (SPH) method. The droplet is described by a weakly compressible (WC) SPH formulation, and the flexible substrate is described by the total Lagrangian (TL) SPH formulation and Mindlin–Reissner shell theory using one layer of particles. Surface tension and wetting effects are simulated by an additional negative pressure term that creates attractive forces among fluid particles, and appropriate kernel functions are selected to eliminate stress instability owing to droplet spreading and retraction. The proposed model is applied to simulate the dynamic process of the droplet impact on hydrophilic and super-hydrophobic cantilever thin plates. The interaction of the droplet and thin plate is investigated under various conditions including stiffness, Weber number, and wettability. Predicted phenomena such as the springboard effect, droplet morphology, plate deformation, and vibration are consistent with experimental observations. The modeling strategy using the TL-SPH shell formulation and free surface WC-SPH formulation showed improved computational efficiency for 3D simulations. Nonlinear behaviors such as droplet spreading, splashing, and large deflection of the substrate, can be effectively reproduced, which demonstrates the potential of SPH in simulating such problem.

A desirable acoustic metasurface requires the scattered acoustic field distribution uniform. Neural networks are effective substitutions to mimic the expensive FE simulations in most research. However, the computational cost required to construct a model with only single high-fidelity (HF) simulation data is still unacceptable. This paper presents a deep learning-based multi-fidelity optimization framework to improve the uniformity of the scattered acoustic field distribution. First, a multi-fidelity composite convolutional neural network (MF-CCNN) method is proposed to predict the high-dimensional scattered acoustic field at a lower data cost. The developed MF-CCNN consists of four convolutional subnets. The first part predicts a low-fidelity (LF) output, whose features are then extracted by the second part and concatenated with the inputs to predict the HF result. Two parallel branches are utilized to map the LF features to the HF output. Then, the physical parameters’ optimization neural network is proposed to minimize the objective under the prediction of MF-CCNN. The proposed method is compared with other state-of-the-art multi-fidelity networks, and the results demonstrate that MF-CCNN reaches the highest accuracy and the mean absolute error is improved by at least 20%. The variance of the obtained scattered acoustic field after optimization is reduced by 3.62%, and the time cost is only 8% of the genetic algorithm (GA), proving the efficiency and accuracy of the proposed framework.

Aiming at the problems such as slow search speed, low optimization accuracy, and premature convergence of standard seagull optimization algorithm, an enhanced hybrid strategy seagull optimization algorithm was proposed. First, chaos mapping is used to generate the initial population to increase the diversity of the population, which lays the foundation for the global search. Then, a nonlinear convergence parameter and inertia weight are introduced to improve the convergence factor and to balance the global exploration and local development of the algorithm, so as to accelerate the convergence speed. Finally, an imitation crossover mutation strategy is introduced to avoid premature convergence of the algorithm. Comparison and verification between MSSOA and its incomplete algorithms are better than SOA, indicating that each improvement is effective and its incomplete algorithms all improve SOA to different degrees in both exploration and exploitation. 25 classic functions and the CEC2014 benchmark functions were tested, and compared with seven well-known meta-heuristic algorithms and its improved algorithm to evaluate the validity of the algorithm. The algorithm can explore different regions of the search space, avoid local optimum and converge to global optimum. Compared with other algorithms, the results of non-parametric statistical analysis and performance index show that the enhanced algorithm in this paper has better comprehensive optimization performance, significantly improves the search speed and convergence precision, and has strong ability to get rid of the local optimal solution. At the same time, in order to prove its applicability and feasibility, it is used to solve two constrained mechanical engineering design problems contain the interpolation curve engineering design and the aircraft wing design. The engineering curve shape with minimum energy, minimum curvature, and the smoother shape of airfoil with low drag are obtained. It is proved that enhanced algorithm in this paper can solve practical problems with constrained and unknown search space highly effectively.

A numerical study of the free-surface flow over a vertical-axis hydrokinetic turbine with different blade-strut configurations is presented in this paper. The set of equations governing this multi-fluid flow consists of the Navier–Stokes equations and an advection equation of the signed distance function which describes the motion of the air–water interface in the context of the level-set method. For this application which involves domain motion, we adopt an arbitrary Lagrangian–Eulerian (ALE) description of the continuum where domain motion occurs independently of the fluid flow. Moreover, the variational multiscale (VMS) method is used for turbulence modelling resulting in the so-called ALE-VMS formulation. The formulation is used to investigate the performance of the turbine in four different computational settings. First, the quarter-struts and tip-struts configurations are simulated under a deep immersion depth. The results of the deep immersion cases show negligible effect from the free surface on the turbine performance. Next, the quarter-struts and tip-struts configurations are simulated under a shallow immersion depth. The results show significant effects of the turbine wake on the deformation of the air–water interface. A reduction in the performance of the turbine is observed in the shallow immersion cases and discussed. The results show robustness of the numerical formulation and provide opportunities for future studies.

This study investigates a non-probabilistic thermo-elastic reliability-based topology optimization (NTE-RBTO) scheme for the lightweight design of composite laminates under thermo-elastic loads with unknown-but-bounded (UBB) parameters. The equivalent constitutive relation of composite laminates is first introduced, and the deterministic topology optimization formulation of composite laminates is derived. In view of the inevitability of multi-source uncertainties during the whole design optimization procedure, the interval model and interval parametric vertex theorem are proposed for the acquisition of the reasonable characterization of uncertain responses in every iterative layout configuration. For reasons of structural safety, an improved non-probabilistic reliability index, the optimization feature distance is adopted, and its design sensitivity with respect to each element pseudo-density under thermal–mechanical coupling loads is calculated. GCMMA, the globally convergent version of MMA (method of moving asymptotes), is employed as the optimization problem solver. The effectiveness and rationality of the proposed method are demonstrated by several numerical examples, eventually.

We propose a novel graph-theoretical method for efficient generation of the topological structure of N-frequency geodesic icosahedron tensegrities. The method only requires the adjacency list of edges of an N-frequency icosahedron, and using a sophisticated approach, creates the major topological entities of the corresponding geodesic icosahedron tensegrity. The graph theory is used to build a bridge between a regular icosahedron and its dual complex tensegrity. The approach proposed is general and perfectly works on icosahedrons with any degree of frequency. The generation of edges is managed in such a way that enables us to group them in different sets as cables and struts. The spherical geodesic tensegrities generated using our method could remarkably extend the complex data sets and large-scale benchmark models required for researchers in the field of tensegrity structures. The whole process and its parts are described and illustrated step by step. Furthermore, the form-finding of 1 to 5-frequency geodesic icosahedron tensegrities is also performed, and sets of self-equilibrium force densities corresponding to their super-stable geometries are provided. The results clearly demonstrate the effectiveness of the proposed method for automated modelling of the icosahedron tensegrities with a chosen frequency.

Code generation technology has been transformative to the field of numerical partial differential equations (PDEs), allowing domain scientists and engineers to automatically compile high-performance solver routines from abstract mathematical descriptions of PDE systems. However, this often assumes a rigid code structure, which is only appropriate to a subset of applications and numerical methods, such as the traditional finite element methods used by the FEniCS code generation system. The present contribution demonstrates how to productively integrate FEniCS into a custom implementation of immersogeometric analysis (IMGA) of thin shell structures interacting with incompressible fluid flows on deforming domains. IMGA is an emerging paradigm for numerical PDEs with complex domain geometries, where non-watertight geometry descriptions are used directly as computational meshes. In particular, we generalize past related work by leveraging code generation to concisely pull back the deforming-domain Navier–Stokes problem to a stationary reference mesh. We also show how code generation enables rapid implementation of different material models for the structure subproblem. We verify our implementation using several benchmark problems, demonstrate its robustness and flexibility by simulating a prosthetic heart valve immersed in a flexible artery, and distribute the full source code online, to be used and modified by the community. Impact of the last item is amplified by the transparent nature of our code-generation-based implementation.

In this paper, the cell-based smoothed finite element method (CS-FEM) is proposed for solving boundary value problems of gradient elasticity in two and three dimensions. The salient features of the CS-FEM are: it does not require an explicit form of the shape functions and alleviates the need for iso-parametric mapping. The main idea is to sub- divide the element into simplicial sub-cells and to use a constant smoothing function in each cell to compute the gradients. This new gradient is then used to compute the bilinear/linear form. The robustness of the method is demonstrated with problems involving smooth and singular solutions in both two and three dimensions. Numerical results show that the proposed framework is able to yield accurate results. The influence of the internal length scale on the stress concentration is studied systematically for a case of a plate with a hole and a plate with an edge crack in two and three dimensions.

This paper proposes an enriched degree of freedom method for absorbing boundary conditions in time-domain finite element method (TD-FEM). In the proposed method, to reduce the reflection of the elastic waves from the artificial boundary, nodes in the absorbing domain are first enriched by the additional degrees of freedom to damp the outgoing elastic waves. Next, based on the motion law of the enriched degree of freedom, a novel damping method is developed to further dampen the oscillation on the enriched degree of freedom. Then, by combining with the modified Newmark algorithm, the proposed method can be employed to efficiently absorb outgoing elastic waves. Finally, some numerical tests are conducted to validate the feasibility and application of the proposed method.

The aim of this work is to propose a new multiphysics mode synthesis (MMS) for the thermomechanical vibration problem. The present thermomechanical model is based on a state-space formulation, which consists of displacement, velocity, and temperature shift. The state-space based thermomechanical formulation is symmetric unlike a conventional non-symmetric formulation for the displacement and temperature shift. In the proposed MMS, the structural variables, the displacement and velocity, are first reduced, which is then applied to the coupling term in the thermal parts. A term of the thermal domain is then reduced while preserving the multiphysics coupling effects, resulting in improved accuracy. The proposed two-step MMS with the thermal physics domain update can be implemented with the coupling term derived using the residual flexibility. The proposed MMS strategy can be also applied to accelerate the computational speed using independent parallel solvers. The performance of the proposed MMS method is evaluated through numerical examples.

In this study, a novel auto-tuned hybrid deep learning approach composed of three base deep learning models, namely, long short-term memory, gated recurrent unit, and support vector regression, is developed to predict the fracture evolution process. The novelty of this framework lies in the auto-determined hyperparameter configurations for each base model based on the Bayesian optimization technique, which guarantees the fast and easy implementation in various practical applications. Moreover, the ensemble modeling technique auto consolidates the predictive capability of each base model to generate the final optimized hybrid model, which offers a better prediction of the overall fracture pattern evolution, as demonstrated by a case study. The comparison of the different prediction strategies exhibits that the direct prediction is a better option than the recursive prediction, in particular for a longer prediction distance. The proposed approach may be applied in various sequential data predictions by adopting the adaptive prediction scheme.

It was in early December 2019 that the terrible news of the outbreak of new coronavirus disease (Covid-19) was reported by the world media, which appeared in Wuhan, China, and is rapidly spreading to other parts of China and several overseas countries. In the field of infectious diseases, modeling, evaluating, and predicting the rate of disease transmission are very important for epidemic prevention and control. Several preliminary mathematical models for Covid-19 are formulated by various international study groups. In this article, the SEIHR(D) compartmental model is proposed to study this epidemic and the factors affecting it, including vaccination. The proposed model can be used to compute the trajectory of the spread of the disease in different countries. Most importantly, it can be used to predict the impact of different inhibition strategies on the development of Covid-19. A computational approach is applied to solve the offered model utilizing the Galerkin method based on the moving least squares approximation constructed on a set of scattered points as a locally weighted least square polynomial fitting. As the method does not need any background meshes, its algorithm can be easily implemented on computers. Finally, illustrative examples clearly show the reliability and efficiency of the new technique and the obtained results are in good agreement with the known facts about the Covid-19 pandemic.

Risk assessment of earth dams is concerned not only with the probability of failure but also with the corresponding consequence, which can be more difficult to quantify when the spatial variability of soil properties is involved. This study presents a risk assessment for an earth dam in spatially variable soils using the random adaptive finite element limit analysis. The random field theory, adaptive finite element limit analysis, and Monte Carlo simulation are employed to implement the entire process. Among these methods, the random field theory is first introduced to describe the soil spatial variability. Then the adaptive finite element limit analysis is adopted to obtain the bound solution and consequence. Finally, the failure probability and risk assessment are counted via the Monte Carlo simulation. In contrary to the deterministic analysis that only a factor of safety is given, the stochastic analysis considering the spatial variability can provide statistical characteristics of the stability and assess the risk of the earth dam failure comprehensively, which can be further used for guiding decision-making and mitigation. Besides, the effects of the correlation structure of strength parameters on the stochastic response and risk assessment of the earth dam are investigated through parametric analysis.

Forecasting water stages is of significance to river and reservoir management. However, conventional models sometimes fail to perform accurately, as water levels are characterized by high nonstationarity. To provide an improved estimation of water stages, this study develops a new prediction framework by coupling stand-alone machine learning models with ensemble algorithms. As base learners, the optimal regression tree (RT) and extreme learning machine (ELM) are integrated into four ensemble strategies, i.e., bagging (BA), boosting (BO), random forest (RF) and random subspace (RS), leading to eight ensemble models. They are then assessed using daily water-stage records at two hydrological stations on the Yangtze River. Their performance is evaluated by statistical criteria: coefficient of determination (CD), Nash–Sutcliffe efficiency (NSE), root mean square error (RMSE) and mean absolute error (MAE). The RT and the ELM generate satisfactory predictions with deficiency in capturing extreme values. The ensemble models generally enhance the prediction efficiency, with their mean CD and NSE augment by up to 6.9% and 7.0%, and mean RMSE and MAE reduction by up to 47.9% and 47.0%. The BO-based models, namely BO-RT and BO-ELM, result in the highest accuracy, with a mean absolute relative error (ARE) of 1.0% and 1.4%. Ensemble learning gains even in multi-step-ahead forecasts, which satisfactorily extends the lead time up to 14 days. This study illustrates the capability of ensemble learning for improved water-level forecasts, which provides reference for modeling related issues such as sediment load and rainfall-runoff.

When considering mesh quality improvement and optimization via node movement, a particularly important goal is to attempt to improve the worst quality in the mesh when that quality is unacceptable. Standard mesh optimization methods often do not address worst case quality and can make it worse. Three fundamental methods for addressing worst case quality in mesh optimization by node movement have appeared in the literature: (1) a shifted barrier approach by Barrera et. al. (Math Comput Simul 46(2):87–102, 1998), (2) a pseudo-barrier approach by Escobar et. al. (Comput Methods Appl Mech Eng 192:2775–2787, 2000), and (3) another barrier approach by Garanzha et. al. (In: IMR 2021-29th international meshing roundtable, 2021). The first two result in ‘simultaneous untangle-optimizers’ while the last addresses worst case quality in terms of the maximum value of the optimization metric. In terms of mesh optimization within the Target Matrix Optimization Paradigm (TMOP), worst case quality is defined by two quantities: the maximum value of the optimization metric ($$\max \mu$$) and the minimum value of the local volume ($$\min \tau$$), both computed over the mesh sample points. In the present paper we show that the methods by the three authors cited above can be applied to the TMOP metrics and used on both linear and high-order element meshes. Unfortunately, the first two methods increase $$\max \tau$$ but do not address $$\max \mu$$. The third method addresses $$\max \mu$$, but fails to address $$\min \tau$$. Using a composition of functions approach, the present work creates new compound metrics that simultaneously increase $$\min \tau$$ and decrease $$\max \mu$$. This goal can also be accomplished by a two-stage optimization procedure in which the first stage untangles the initial mesh and the second stage decreases $$\max \mu$$. Although none of these methods provide a guarantee that the worst case quality will be improved to the point that the quality becomes acceptable, it is shown by numerical examples that they can be very effective.

The prevalence of highly nonlinear and implicit performance functions in structural reliability analysis has increased the computational effort significantly. To solve this problem, an efficiently active learning function, named parameter adaptive expected feasibility function (PAEFF) is proposed using the prediction variance and joint probability density. The PAEFF function first uses the harmonic mean of prediction variances of Kriging model to judge the iteration degree of the current surrogate model, to realize the scaling of the variance in the expected feasibility function. Second, to improve the prediction accuracy of the Kriging model, the joint probability densities are applied to ensure that the sample points to be updated have a higher probability of occurrence. Finally, a new failure probability-based stopping criterion with wider applicability is proposed. Theoretically, the stopping criterion proposed is applicable to all active learning functions. The effectiveness and accuracy of the proposed PAEFF are verified by two mathematical calculations and three engineering examples.

Due to the effects of climate change, coastal engineering structures are more vulnerable to the wave forces caused by natural hazards, especially for the low-lying bridges. To facilitate the structural design and risk assessment of coastal bridges under extreme events, it is imperative to efficiently predict the wave-induced forces with high accuracy. In this study, a novel predictive model for wave-induced forces is established using the ensemble learning technique. Specifically, four state-of-the-art surrogate models, namely the Support Vector Regression (SVR), Kriging (KRG), Polynomial Chaos Expansion (PCE) and Decision Tree (DT), are employed to construct a weighted predictive model, where the weights of individual models are implicitly determined by the artificial neural network (ANN). Depending on the architecture of the ANN model, i.e., with or without a hidden layer, these four surrogate models can be ensembled nonlinearly (ANN1) or linearly (ANN2). Four benchmark functions and three ocean engineering cases are utilized to validate the performance of the established ensemble models, where the correlation coefficient R2, maximum absolute error (MAE) and root mean square error (RMSE) criteria are used as the error metrics. The results show that the proposed ANN-based ensemble strategy is capable of providing robust and accurate approximation for different force components; and can effectively reduce the adverse effect of poorly behaved candidate surrogates by wisely assigning weights to the individual models, thus is beneficial to protect against the use of worst surrogate model. It is envisioned that the proposed ensemble models can be extended to predict wave forces of fickle wave conditions, thus facilitating the associated risk assessment and structural design of ocean infrastructures.

This paper aims to present a modified continuum mathematical model capable on investigation of dynamic behavior and response of perforated microbeam under the effect of moving mass/load for the first time. A size-dependent finite element model with non-classical shape function is exploited to solve the mathematical model and obtain the dynamic response of perforated Timoshenko microbeams under moving loads. To that end, first, equivalent material and geometrical parameters for perforated beam are developed, based on the regular squared perforation configuration. Second, both the stiffness and mass property matrices including the microstructure effect based on modified couple stress theory and Timoshenko first-order shear beam theory are derived for two-node finite element using new shape function. After that, the interaction between the load and beam is modeed and unified with the equation of motion of the beam incorporating mass inertia effects of moving load. The developed procedure is validated and compared. Effects of perforation parameters, moving load velocities, inertia of mass, and the microstructure size parameter on the dynamic response of perforated microbeam structures have been investigated in a wide context. The achieved results are helpful for the design and production of MEMS structures such as frequency filters, resonators, relay switches, accelerometers and mass flow sensors, with perforation.

Perforated beam is essential structural element of Nano-Electro-Mechanical-Systems (NEMS), whose design needs appropriate modelling of size of holes, hole numbers, and scale effects. The current manuscript presents a comprehensive study and develops non-classical closed form solutions to predict the static bending behavior and buckling stability of perforated nanobeams (PNBs) incorporating the surface energy for different four beams theories, for the first time. Equivalent geometrical models for both bulk and surface characteristics are presented. The Gurtin–Murdoch surface elasticity model is modified and adopted to include the perforation in surface characteristics. To consider the warping shear effect on bending as well as critical buckling loads with the presence of surface stress effects, four different beams theories with shear deformation are considered. The non-classical equilibrium equations relevant to each PNB theory are developed in detail. Closed-form solutions are developed considering the different classical and non-classical boundary conditions as well as loading conditions. The proposed methodology is verified by comparing the obtained results with the available analytical solutions for fully filled beams and excellent agreement is observed. Effects of perforation characteristics as well as the surface effects on bending and buckling behaviors are investigated.

In this article, we first present a unified scheme to apply nonlinear dynamic time integration methods. The unified scheme covers many existing time integration methods as exceptional cases. This paper has investigated time integration methods, including the Newmark, Wilson, Houbolt, and ρ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho _{\infty }$$\end{document}-Bathe method. We then implement the multi-point methods as the nonlinear solution schemes along with the direct time integration methods in nonlinear dynamic analysis. Also, a unified scheme for applying single-point and multi-point methods is presented. Finally, we demonstrate with numerical examples that the unified scheme provides a framework for comparing direct time integration methods. We also investigate the performance of multi-point methods as nonlinear solution methods in detail.

In this paper, we present a hybrid dual-variable-horizon peridynamics/continuum mechanics modeling approach and a strength-induced adaptive coupling algorithm to simulate brittle fractures in porous materials. Peridynamics theory is promising for fracture simulation since it allows discontinuities in the displacement field. However, they remain computationally expensive. Besides, there exists the surface effect in peridynamics due to the incomplete neighborhoods near the boundaries, including the outer boundaries and the boundaries of inner pores in porous materials. The proposed approach couples continuum mechanics and peridynamics into a closed equation system and an adaptive algorithm is developed to activate the peridynamics according to a strength criterion. In addition, the surface effect is corrected by introducing an improved peridynamic model with dual and variable horizons. We conduct the simulations using the relevant discretization scheme in each domain, i.e., the discontinuous Galerkin finite-element in the peridynamic domain and the continuous finite-element in the continuum mechanics domain. Two-dimensional numerical examples illustrate that successful fracture simulations of random porous materials can be achieved by this approach. In addition, the impact of distribution and size of pores on the fractures of porous materials is also investigated.

Predicting pediatric spinal deformity (PSD) from X-ray images collected on the patient’s initial visit is a challenging task. This work builds on our previous method and provides a novel bio-informed framework based on a mechanistic machine learning technique with dynamic patient-specific parameters to predict PSD. We provide a geometry-based bone growth model that can be utilized in a range of applications to enhance the bio-informed mechanistic machine learning framework. The proposed technique is utilized to examine and predict spine curvature in PSD cases such as adolescent idiopathic scoliosis. The best fit of a segmented 3D volumetric geometry of the human spine acquired from 2D X-ray images is employed. Using an active contour model based on gradient vector flow snakes, the anteroposterior and lateral views of the X-ray images are segmented to derive the 2D contours surrounding each vertebra. Using minimal user input, the snake parameters are calibrated and automatically computed over the dataset, resulting in fast image segmentation and data collection. The 2D segmented outlines of each vertebra are transformed into a 3D image segmentation result. The Iterative Closest Point mesh registration technique is then used to establish a mesh morphing approach and creates a 3D atlas spine model. Using the comprehensive 3D volumetric model, one can automatically extract spinal geometry data as inputs to the mechanistic machine learning network. Moreover, the proposed bio-informed deep learning network with the modified bone growth model achieves competitive or even superior performance against other state-of-the-art learning-based methods.Please check and confirm if the author names and initials are correct for “Yongjie Jessica Zhang” and “Wing Kam Liu”.We confirm they are correct.

This publication presents required steps for the realization of the pre- and post-processing for the isogeometric analysis and the isogeometric B-Rep analysis, with a focus on the collection of required data. It reveals the essential prerequisites for the preparation and the collection of geometrical information, which are merged with physical information for the creation of numerical models. It addresses both the direct computation on existing CAD drawings and the geometrical design during the preparation of the numerical models. The developments are presented through the example of the open source Rhino plugin Cocodrilo, which shall bring IGA to a larger community, including research and industrial facilities.

Quadrilateral meshes offer certain advantages compared to triangular ones, such as reduced number of elements and alignment with problem-specific directions. We present a pipeline for the generation of quadrilateral meshes on complex geometries. It is based on two key components: robust surface meshing and efficient indirect conversion of a triangular mesh to an all-quad one. The input is a valid geometric surface mesh, i.e., a triangulation that accurately represents the geometry of the model. A right-angled triangular surface mesh is initially created by continuously modifying the input mesh while always preserving its topological validity. The main advantages of our local mesh modification-based approach are to (i) allow the generation of meshes that are globally aligned with a given direction field and (ii) to reliably handle non-manifold feature edges (in multi-volume models) and small features. The final quadrilateral mesh is obtained by merging pairs of triangles into quadrilaterals. We develop a novel bipartite labeling scheme in order to identify and correct inconsistent pairings. The procedure is based on local operations and is much more efficient than previous global strategies for tri-to-quad conversion. The whole pipeline is tested on a large number of models with diverse characteristics.

In this work, a truly explicit time-marching methodology is discussed for the time-domain solution for heat propagation considering the dual-phase-lag (DPL) bioheat model. The proposed technique considers self-adjustable time integration parameters, and it is approached together with automated calculations of domain decomposition and subcycling, providing a very versatile fully adaptive solution algorithm. The discussed domain decomposition procedure automatically divides the domain model into different subdomains (according to the properties of the discretized problem), in which different time-step values are applied, enabling more efficient (yet stable) explicit analyses. Expressions for the adaptive time integration parameters of the method and for the critical time steps of the subdomains of the model are presented and discussed. At the end of the paper, benchmark and applied examples are studied, showing the excellent performance of the proposed approach and the great effectiveness of the discussed fully adaptive formulation.

Top-cited authors
• University of Technology Sydney
• Duy Tan University
• University of Sidi-Bel-Abbes
• Hanoi University of Mining and Geology