scholarly journals Convergence of the finite element method and the semi-analytical finite element method for prismatic bodies with variable physical and geometric parameters

2021 ◽  
pp. 92-104
Author(s):  
Viktor Bazhenov ◽  
Maksym Horbach ◽  
Ivan Martyniuk ◽  
Oleksandr Maksimyuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Test Problems ◽  
Test Cases ◽  
Approximation Accuracy ◽  
Convergence Of Solutions ◽  
Wide Range ◽  
Prismatic Bodies ◽  
Element Method

In this paper, a numerical study of the convergence of solutions obtained on the basis of the developed approach [1, 3, 4, 5] is carried out. A wide range of test problems for bodies with smoothly and abruptly varying physical and geometric characteristics in elastic and elastic-plastic formulation are considered. The approach developed within the framework of the semi-analytical method to study the stress-strain state of inhomogeneous curvilinear prismatic bodies, taking into account physical and geometric nonlinearity, requires substantiation of its effectiveness in relation to the traditional FEM and confirmation of the reliability of the results obtained on its basis. The main indicators that allow comparing the SAFEM and FEM include the rate of convergence of solutions with an increase in the number of unknowns and the amount of charges associated with solving linear and nonlinear equations. For the considered class of problems, the convergence is determined by such factors as the nature of the change along Z3’ of the geometric and mechanical parameters of the object. The uneven distribution of mechanical characteristics is associated with the presence of the initial heterogeneity of the material, the development of plastic deformations, and the dependence of material properties on temperature. The same factors also affect the convergence of the iterative process, since the conditionality of the SAFEM matrix depends on them. In order to determine the area of effective application of the SAFEM, a wide range of test cases are considered. In all cases, the semi-analytic finite element method is not inferior in approximation accuracy, and in some problems it is 1.5-2 times superior to the traditional method of scheduling elements. finite element method.

A numerical study on the sound transmission loss of HST aluminum extruded panel

2020 ◽  
Vol 68 (5) ◽  
pp. 367-377
Author(s):  
Xu Zheng ◽  
Peilin Ruan ◽  
Le Luo ◽  
Yi Qiu ◽  
Zhiyong Hao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Performance Optimization ◽  
High Speed ◽  
Transmission Loss ◽  
Numerical Study ◽  
Sound Transmission ◽  
Sound Transmission Loss ◽  
Wide Range ◽  
Element Method

Aluminum is a light, strong, and corrosion-resistant material. Its extruded form, the aluminum extruded panel, consists of two aluminum plates with truss core, which can be applied in a wide range of engineering areas. In this work, the structure-acoustic coupling finite element method (FEM) is employed to analyze the sound transmission through high-speed train (HST) aluminum extruded panels. The automatically matched layer (AML) is used to simulate the non-reflective boundary condition. It is found that the predicted sound transmission loss (STL) is in good agreement with the experimental results and the prediction accuracy of the finite element method can be further verified. Based on this proposed method, a parametric study is carried out to investigate how the structure parameters affect the STL. The results suggest that the rib angle exhibits a greater effect on STL in the above-middle frequency area where the modal density is high. The increase in the height between the panels will lead to a higher STL overall value of the aluminum extruded panel and make the STL dips move toward higher frequencies, while the increase of the rib thickness will drive the STL dips to an opposite direction. Finally, the STLs of the aluminum extruded panel in different regions of the train body are comprehensively analyzed. The highest overall value of STL is found in the flat-top region, whereas the lowest value appears in the curve-top region. Overall, the results in this article can provide valuable implications for the noise performance optimization of HST.

scholarly journals Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

1991 ◽  
Vol 33 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Tang ◽  
R. O. Weber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Galerkin Finite Element Method ◽  
Linear Diffusion ◽  
Galerkin Finite Element ◽  
Fisher’S Equation ◽  
Nonlinear Reaction ◽  
Fisher's Equation ◽  
Element Method

AbstractFisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

Numerical Study of Hydrodynamic Forces on a Submarine Piggyback Pipeline Under Wave Action

2012 ◽  
Author(s):  
Xiaofei Cheng ◽  
Yongxue Wang ◽  
Bing Ren ◽  
Guoyu Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Hydrodynamic Forces ◽  
Wave Action ◽  
Numerical Results ◽  
Physical Model Test ◽  
Element Method

In the paper, a 2D numerical model is established to simulate the hydrodynamic forces on a submarine piggyback pipeline under regular wave action. The two-dimensional Reynolds-averaged Navier-Stokes equations with a κ-ω turbulence model closure are solved by using a three-step Taylor-Galerkin finite element method (FEM). A Computational Lagrangian-Eulerian Advection Remap Volume of Fluid (CLEAR-VOF) method is employed to simulate free surface problems, which is inherently compatible with unstructured meshes and finite element method. The numerical results of in-line force and lift (transverse) force on the piggyback pipeline for e/D = G/D = 0.25 and KC = 25.1 are compared with physical model test results, which are conducted in a marine environmental flume in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. It is indicated that the numerical results coincide with the experimental results and that the numerical model can be used to predict the hydrodynamic forces on the piggyback pipeline under wave action. Based on the numerical model, the surface pressure distribution and the motion of vortices around the piggyback pipeline for e/D = G/D = 0.25, KC = 25.1 are investigated, and a characteristic vortex pattern around the piggyback pipeline denoted “anti-phase-synchronized” pattern is recognized.

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