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  • Open Access


    Reduced Order Machine Learning Finite Element Methods: Concept, Implementation, and Future Applications

    Ye Lu1, Hengyang Li1, Sourav Saha2, Satyajit Mojumder2, Abdullah Al Amin1, Derick Suarez1, Yingjian Liu3, Dong Qian3, Wing Kam Liu1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1351-1371, 2021, DOI:10.32604/cmes.2021.017719

    Abstract This paper presents the concept of reduced order machine learning finite element (FE) method. In particular, we propose an example of such method, the proper generalized decomposition (PGD) reduced hierarchical deeplearning neural networks (HiDeNN), called HiDeNN-PGD. We described first the HiDeNN interface seamlessly with the current commercial and open source FE codes. The proposed reduced order method can reduce significantly the degrees of freedom for machine learning and physics based modeling and is able to deal with high dimensional problems. This method is found more accurate than conventional finite element methods with a small portion More >

  • Open Access


    Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Elasticity on Unstructured Meshes

    Arash Mehraban1, Henry Tufo1, Stein Sture2, Richard Regueiro2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.3, pp. 1283-1303, 2021, DOI:10.32604/cmes.2021.017476

    Abstract Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity, yet are computationally expensive. To address the computational expense, the paper presents a matrix-free, displacement-based, higher-order, hexahedral finite element implementation of compressible and nearly-compressible (ν → 0.5) linear isotropic elasticity at small strain with p-multigrid preconditioning. The cost, solve time, and scalability of the implementation with respect to strain energy error are investigated for polynomial order p = 1, 2, 3, 4 for compressible elasticity, and p = 2, 3, 4 for nearly-incompressible elasticity, on different number More >

  • Open Access


    Initiation Mechanism of Transverse Cracks in Wind Turbine Blade Trailing Edge

    Jinghua Wang1, Leian Zhang1, Xuemei Huang1,*, Jinfeng Zhang2, Chengwei Yuan1

    Energy Engineering, Vol.119, No.1, pp. 407-418, 2022, DOI:10.32604/EE.2022.016439

    Abstract Transverse crack often occurs in the trailing edge region of the blade when subjected to the excessive edgewise fatigue load. In this paper a refined model was established through local mesh refinement methods in order to investigate the initiation mechanism of crack and its extension in blade trailing edge. The material stress around the crack in trailing edge region under different thicknesses is calculated based on the fracture mechanics theory. The factors affecting the fatigue robustness of blade trailing edge are concluded by investigating the results of finite element analysis and coupons test. Compared with More >

  • Open Access


    Polygonal Finite Element for Two-Dimensional Lid-Driven Cavity Flow

    T. Vu-Huu1, C. Le-Thanh2, H. Nguyen-Xuan3,4, M. Abdel-Wahab3,5,*

    CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 4217-4239, 2022, DOI:10.32604/cmc.2022.020889

    Abstract This paper investigates a polygonal finite element (PFE) to solve a two-dimensional (2D) incompressible steady fluid problem in a cavity square. It is a well-known standard benchmark (i.e., lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier–Stokes (N–S) equation system. The approximation solutions provided in this research are based on our developed equal-order mixed PFE, called Pe1Pe1. It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique. In this More >

  • Open Access


    Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

    Abid. A. Memon1, M. Asif Memon1, Kaleemullah Bhatti1, Kamsing Nonlaopon2,*, Ilyas Khan3

    CMC-Computers, Materials & Continua, Vol.70, No.3, pp. 4341-4355, 2022, DOI:10.32604/cmc.2022.019407

    Abstract This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries. Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation. Because of little maintenance, the heat exchanger of such type is extensively used. Here, we generate simulation of flow and heat transfer using non-isothermal flow interface in the Comsol multiphysics 5.4 which executes the… More >

  • Open Access


    Simulation of Lumbar Spinal Stenosis Using the Finite Element Method

    Din Prathumwan1, Inthira Chaiya2, Kamonchat Trachoo2,*

    CMC-Computers, Materials & Continua, Vol.69, No.3, pp. 3645-3657, 2021, DOI:10.32604/cmc.2021.018241

    Abstract Lumbar spine stenosis (LSS) is a narrowing of the spinal canal that results in pressure on the spinal nerves. This orthopedic disorder can cause severe pain and dysfunction. LSS is a common disabling problem amongst elderly people. In this paper, we developed a finite element model (FEM) to study the forces and the von Mises stress acting on the spine when people bend down. An artificial lumbar spine (L3) was generated from CT data by using the FEM, which is a powerful tool to study biomechanics. The proposed model is able to predict the effect… More >

  • Open Access


    Discontinuous-Galerkin-Based Analysis of Traffic Flow Model Connected with Multi-Agent Traffic Model

    Rina Okuyama1, Naoto Mitsume2, Hideki Fujii1, Hideaki Uchida1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 949-965, 2021, DOI:10.32604/cmes.2021.015773

    Abstract As the number of automobiles continues to increase year after year, the associated problem of traffic congestion has become a serious societal issue. Initiatives to mitigate this problem have considered methods for optimizing traffic volumes in wide-area road networks, and traffic-flow simulation has become a focus of interest as a technique for advance characterization of such strategies. Classes of models commonly used for traffic-flow simulations include microscopic models based on discrete vehicle representations, macroscopic models that describe entire traffic-flow systems in terms of average vehicle densities and velocities, and mesoscopic models and hybrid (or multiscale)… More >

  • Open Access


    Static and Dynamic Analyses of Spliced Column

    Deepak Kumar Singh*

    Sound & Vibration, Vol.55, No.3, pp. 253-262, 2021, DOI:10.32604/sv.2021.011627

    Abstract The analysis of spliced column has been carried out to detect optimum location of providing splices in the column. In the present work, static and dynamic (free vibration) analyses of spliced column have been done by randomising the location of splicing. A symmetrical four storey steel framed building has been modelled, analysed and designed for loads (dead, live and earthquake loads) recommended by Indian Codal provisions using Staad.Pro. The critical column at each floor level is identified based on axial force (AF), bending moment (BM) and shear force (SF). The total 16 models of spliced… More >

  • Open Access


    The Nonlinear Coupling of Oscillating Bubble and Floating Body with Circular Hole

    Ming He, Yunlong Liu*, Shaofei Ren, Wentao Liu

    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 923-942, 2021, DOI:10.32604/cmes.2021.015259

    Abstract The fluid-structure interaction of the oscillating bubble and floating body with circular hole is essentially the nonlinear coupling problem among the incomplete movable boundary, free surface and bubble. This problem is particularly complicated in bubble dynamics. Combined with the volume of fluid method, the Eulerian finite element method is employed to deal with the fluid movement. Based on the improved penalty immersed boundary method, the transient axisymmetric numerical model is established in this paper, considering the fluid-structure interaction effect. The results of simulation are consistent with those of the electric discharge bubble experiment and explosion… More >

  • Open Access


    Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

    Changkye Lee1, Sundararajan Natarajan2, Jack S. Hale3, Zeike A. Taylor4, Jurng-Jae Yee1,*, Stéphane P. A. Bordas3,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 411-436, 2021, DOI:10.32604/cmes.2021.014947

    Abstract This work presents a locking-free smoothed finite element method (S-FEM) for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity. The proposed method overcomes well-known issues of standard finite element methods (FEM) in the incompressible limit: the over-estimation of stiffness and sensitivity to severely distorted meshes. The concepts of cell-based, edge-based and node-based S-FEMs are extended in this paper to three-dimensions. Additionally, a cubic bubble function is utilized to improve accuracy and stability. For the bubble function, an additional displacement degree of freedom is added at the centroid of the element. Several More >

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