The Hybrid Boundary Element Method: An Alliance Between Mechanical Consistency and Simplicity

1989 ◽  
Vol 42 (11S) ◽  
pp. S54-S63 ◽  
Author(s):  
N. A. Dumont
Keyword(s):  
Finite Element Method ◽  
Boundary Element ◽  
Complete Solution ◽  
Computational Effort ◽  
Element Formulation ◽  
Numerical Examples ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Force Displacement ◽  
Element Method

The most important features of a new numerical method are outlined. The mechanical, or variational consistency of the hybrid finite element method is extended to the conventional boundary element formulation, giving rise to naturally established symmetric force-displacement relations. The computational effort for the complete solution of a given problem, according to this method, is in some cases only a small fraction of the effort needed with traditional methods. This paper also outlines briefly the types of analyses which may be advantageously performed with this new method, many of which are already being implemented by the author and co-workers. Some numerical examples are provided.

A Hybrid Finite Element Formulation for Mid-Frequency Analysis of Systems With Excitation Applied on Short Members

2000 ◽  
Author(s):  
Xi Zhao ◽  
Nickolas Vlahopoulos
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Input Power ◽  
Element Formulation ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Element Method

Abstract A hybrid finite element method for computing mid-frequency vibrations is presented. In the mid-frequency region a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths within their dimensions. The former are considered long members and they are modeled by the Energy Finite Element Analysis (EFEA). The latter are considered short and they are modeled by the Finite Element Analysis (FEA). In this paper the excitation is considered to be applied on the short members. The hybrid formulation computes the response of the entire system. The characteristics of the long members affect the behavior of the short members and the amount of power flow between the members of the system. The resonant characteristics of the short members and the boundary conditions imposed by the long members determine the amount of input power into the system. The interaction between members is described by a set of equations between the FEA and the EFEA primary variables at the interfaces between long and short members. The equations for the short and the long members and the interface equations are solved simultaneously. A theoretical formulation and a numerical implementation for systems that contain one wave type is presented. Analytical solutions for several co-linear beam configurations are compared to numerical results produced by the hybrid finite element method. Good correlation is observed for all analyses.

Free Vibration of Spherical Shells Using a Hybrid Finite Element Method

2015 ◽  
Vol 15 (04) ◽  
pp. 1450062 ◽  
Author(s):  
Mohamed Menaa ◽  
Aouni A. Lakis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Theoretical Data ◽  
Free Vibration Analysis ◽  
Element Formulation ◽  
Spherical Shells ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Element Method

In this study, free vibration analysis of spherical shell is carried out. The structural model is based on a combination of thin shell theory and the classical finite element method. Free vibration equations using the hybrid finite element formulation are derived and solved numerically. Therefore, the number of elements chosen is function of the complexity of the structure. Convergence is rapid. It is not necessary to choose a large number of elements to obtain good results. The results are validated using numerical and theoretical data available in the literature. The analysis is accomplished for spherical shells of different geometries, boundary conditions and radius to thickness ratios. This proposed hybrid finite element method can be used efficiently for design and analysis of spherical shells employed in high speed aircraft structures.

scholarly journals Hybrid Finite Element Method and Variational Theory of Complex Rays for Helmholtz Problems

2016 ◽  
Vol 24 (04) ◽  
pp. 1650015 ◽  
Author(s):  
Hao Li ◽  
Pierre Ladevèze ◽  
Hervé Riou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Variational Theory ◽  
Numerical Examples ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Vibration Problems ◽  
Complex Rays ◽  
Element Method

In this paper, we consider the Weak Trefftz Discontinuous Galerkin (WTDG) method, which enables one to use at the same time the Finite Element Method (FEM) or Variational Theory of Complex Rays (VTCR) discretizations (polynoms and waves), for vibration problems. It has already been developed such that the FEM and the VTCR can be used in different adjacent subdomains in the same problem. Here, it is revisited and extended in order to allow one to use the two discretizations in the same subdomain, at the same time. Numerical examples illustrate the performances of such an approach.

scholarly journals Modelling Plates and Shells by Means of the Rigid Finite Element Method

2015 ◽  
Vol 62 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Andrzej Nowak ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibrations ◽  
The Finite Element Method ◽  
Hybrid Finite Element Method ◽  
Hybrid Finite Element ◽  
Rigid Finite Element Method ◽  
Plates And Shells ◽  
Single Set ◽  
Element Method

Abstract The rigid finite element method (RFEM) has been used mainly for modelling systems with beam-like links. This paper deals with modelling of a single set of electrodes consisting of an upper beam with electrodes, which are shells with complicated shapes, and an anvil beam. Discretisation of the whole system, both the beams and the electrodes, is carried out by means of the rigid finite element method. The results of calculations concerned with free vibrations of the plates are compared with those obtained from a commercial package of the finite element method (FEM), while forced vibrations of the set of electrodes are compared with those obtained by means of the hybrid finite element method (HFEM) and experimental measurements obtained on a special test stand.

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