Ke Liang^1,*, Zheng Li¹, Zhen Yin¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.011625

Abstract In this work, a finite element based reduced-order technique in the framework of mixed nonlinear kinematics is proposed for the geometrically nonlinear analysis of thin-walled structures [1]. The mixed nonlinear kinematics are established by combining the co-rotational formulation with the updated von Kármán formulation. The co-rotational formulation is selected to calculate the internal force and tangent stiffness of a structure; whereas the third- and fourth-order strain energy derivatives are achieved by the updated von Kármán formulation. For geometrically nonlinear problems with a large deflection, reduced-order models with 1 degree of freedom are constructed using the… More >

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 - 31 January 2024

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… More >