Haolun Zhang¹, Mengna Yang¹, Jie Wei², Yufeng Nie^2,*

Digital Engineering and Digital Twin, Vol.2, pp. 49-77, 2024, DOI:10.32604/dedt.2023.044180

Abstract This paper mainly considers the formulation and theoretical analysis of the reduced-order numerical method constructed by proper orthogonal decomposition (POD) for nonlocal diffusion problems with a finite range of nonlocal interactions. We first set up the classical finite element discretization for nonlocal diffusion equations and briefly explain the difference between nonlocal and partial differential equations (PDEs). Nonlocal models have to handle double integrals when using finite element methods (FEMs), which causes the generation of algebraic systems to be more challenging and time-consuming, and discrete systems have less sparsity than those for PDEs. So we establish a reduced-order model (ROM) for… More >

B. Gangadhara Rao^a,*, K. Elangovan^b, K. Hema Chandra Reddy^a, M. Arulprakasajothi^c

Frontiers in Heat and Mass Transfer, Vol.16, pp. 1-8, 2021, DOI:10.5098/hmt.16.15

Abstract In this research, the 3-D coupled thermal electric model analyses on a sandwich bus bar are presented for the comparison of F Class & B Class of insulation. IEC defines the maximum temperature limit at the conductor based on the class of insulation. This paper gives the clarity on the variation on the current density i.e, the size of the conductor by varying the class of insulation. The study is conducted on tin plated 2000 A sandwich busbar system. The sandwich bus bar is made of copper conductors with tin plating and enclosed by an aluminum cover along its length.… More >

Ye Lu¹, Hengyang Li¹, Sourav Saha², Satyajit Mojumder², Abdullah Al Amin¹, Derick Suarez¹, Yingjian Liu³, Dong Qian³, Wing Kam Liu^1,*

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 of degrees of freedom. Different… More >

Changkye Lee¹, Sundararajan Natarajan², Jack S. Hale³, Zeike A. Taylor⁴, Jurng-Jae Yee^1,*, Stéphane P. A. Bordas^3,*

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 numerical studies are performed demonstrating… More >

An Chen^*

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.1, pp. 173-195, 2020, DOI:10.32604/cmes.2020.011871

Abstract In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time. More >

Pengfei Zhu¹, Qinghui Zhang^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 107-127, 2020, DOI:10.32604/cmes.2020.09831

Abstract There are several difficulties in generalized/extended finite element methods (GFEM/XFEM) for moving interface problems. First, the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM. Second, they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes. Furthermore, time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time. This paper is devoted to proposing the stable and robust GFEM/XFEM with effi- cient time stepping schemes for the parabolic interface… More >

An Chen^{1, *}

CMES-Computer Modeling in Engineering & Sciences, Vol.123, No.3, pp. 917-939, 2020, DOI:10.32604/cmes.2020.09224

Abstract In this paper, two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered. These two models can be regarded as the generalization of the classical wave equation in two space dimensions. Combining with the Crank-Nicolson method in temporal direction, efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed, respectively. The corresponding stability and convergence analysis of the numerical methods are discussed. Numerical results are provided to verify the theoretical analysis. More >

Muddasar Khan¹, Cesar Levy¹, Amer Hameed¹, Zulfiqar Khan¹, Khalid Orakzai¹, Musarrat Khan¹, Khuram Shahazad¹, Afzaal M.Malik¹, Shahab Khushnood¹

Structural Durability & Health Monitoring, Vol.6, No.2, pp. 53-68, 2010, DOI:10.3970/sdhm.2010.006.053

Abstract Aluminum metal beverage container is used in packaging foods and chemical industries because of its superior hold, formability, corrosion resistance and join ability. The 80 percent of the container cost is material and aluminum metal is expansive one. The beverage container industry is struggling for potential saving from weight reduction in each container, while meeting the three structural performance standards which have been established to assess the adequacy of the container design. These are axial column load, drop resistance and internal pressure. This paper relates to the internal pressure standard which states that container must withstand at least 90-100PSI or… More >

Xiaolin Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 483-507, 2014, DOI:10.3970/cmes.2014.097.483

Abstract Combining moving least square (MLS) approximations and boundary integral equations, a symmetric and boundary-only meshless method, the Galerkin boundary node method (GBNM), is developed in this paper for two- and threedimensional elasticity problems with mixed boundary conditions. Unlike other MLS-based meshless methods, boundary conditions in this meshless method can be applied directly and easily. In the GBNM, the stiffness matrices so obtained are symmetric. The property of symmetry is an added advantage in coupling the GBNM with the finite element method (FEM). Thus, a symmetric coupling of the GBNM and the FEM is also discussed for elasticity problems. Error analysis… More >

Yuta Kitamura¹, Noriyuki Miyazaki¹, Takahito Kumazaki², Naoto Nagakura³, Yasuhiro Hashimoto³, Isao Masada³

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 151-166, 2010, DOI:10.3970/cmes.2010.068.151

Abstract CaF₂ single crystal is used as high performance optical elements. We developed an analysis system for simulating birefringence of CaF₂ single crystal used as a chamber window of a gas laser light source. The analysis system consists of a stress analysis and a birefringence analysis. In the stress analysis, the finite element method was applied to obtain the mechanical stress caused by a window holder and gas pressure. In the birefringence analysis, the photo-elastic effect gives the change of refractive indices, from which the optical path difference and the fast axis are calculated by using the average stress method. The… More >