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"Boundary element methods."
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Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method
This study extends the calculation of unknown quantities at boundary points to the computation of internal displacements and stresses. The methodological approach is broadly consistent with boundary point calculations. However, the computation of internal unknowns does not involve spatial singularities; the internal stress boundary integral equation is first derived. Subsequently, the obtained boundary integral equation is numerically processed, requiring discretization in both time and space, followed by assembly and solution. When solving the elements in the influence coefficient matrices, the displacement influence coefficient matrix S and the traction influence coefficient matrix D exhibit only wavefront singularities. These wavefront singularities are treated analytically in the time domain, and the spatial integrals are handled using Gaussian numerical integration. The correctness of the algorithm and theory is verified through two classical numerical examples. A theoretically sound and accurate three-dimensional elastodynamic time domain boundary element method and its corresponding computational program are established, providing a reliable tool for guiding engineering design.
Journal Article
Estimation of Stress Intensity Factor by Using a New Fast Multipole Dual-Boundary Element Method
Cracks and defects are inevitable during the long-term use of structures. This study focuses on determining the stress intensity factors of multi-cracked structures by using a new fast multipole dual boundary element method. Numerical examples show that the results of the present method agree well with analytic solutions. When the crack distribution changes, the most unfavorable conditions also change. The shape of the defect has an effect on the stress intensity factors of nearby cracks. Among triangular, rectangular, hexagonal, and circular defects, when the area of the defect is identical, the triangular pore is more likely to induce crack propagation, while the circular pore is more secure. The above results can be used as a reference for structural design and optimization.
Journal Article
The Fundamentals of Boundary Element Methods
The boundary element method is one of the most popular methods of numerical modeling for various problems in mechanics and physics. A big attraction for scientists is the possibility to consider not the region for which a problem needs to be solved but to consider the region's border instead. The boundary element method allows for significant simplification of the decision process, increasing the accuracy and reliability of the results.
eBook
Research on dynamic characteristics and radiation noise of a helicopter main reducer based on finite element and boundary element method
In order to solve the problem of radiation noise of helicopter reducer with symmetrical structure, a simulation method is proposed to predict the noise of gearbox of a helicopter reducer from steady dynamic response to the acoustic radiation calculation. Primarily, taking the influence of time-varying stiffness into consideration, the lumped mass model of gear-rotor-bearing system is established. The dynamic load of transmission system is solved by New-Mark-β method, which is regarded as excitation of the gearbox. Then finite element model of housing is established, the radiated noise of the housing is predict by finite element and boundary element method, the influence of multi-source excitation on the radiated noise of the gearbox is analyzed. Finally, the radiated noise of the reducer under different working conditions is explored. All conclusions of this research could provide theoretical reference for vibration and noise reduction of helicopter reducer.
Journal Article
Dynamic Fracture Analysis of Plates Loaded in Tension and Bending Using the Dual Boundary Element Method
The purpose of this paper is to solve dynamic fracture problems of plates under both tension and bending using the boundary element method (BEM). The dynamic problems were solved in the Laplace-transform domain, which avoided the calculation of the domain integrals resulting from the inertial terms. The dual boundary element method, in which both displacement and traction boundary integral equations are utilized, was applied to the modelling of cracks. The dynamic fracture analysis of a plate under combined tension and bending loads was conducted using the BEM formulations for the generalized plane stress theory and Mindlin plate bending theory. Dynamic stress intensity factors were estimated based on the crack opening displacements.
Journal Article
Dynamic Damage Quantification of Slab Tracks—Finite Element Models on Winkler Soil and Finite-Element Boundary-Element Models on Continuous Soil
Train passages over intact or damaged slab tracks on different soils were calculated by two methods. The finite element method (FEM) uses a Winkler soil under the track model by adding a thin “soil layer”. The combined finite-element boundary-element method has a continuous soil model that is included by the boundary element method. The basic results are the distributions of the track (rail, track plate, and base layer) displacements along the track for a single axle load. These solutions were superposed to a complete train load and transformed to time histories. The influence of track and soil parameters was analysed. The main interest was the influence of the track damage. A gap between the track plate and base layer of different lengths was studied for changes in amplitudes and widths of deflection. A best fit to measured track displacements was found so that the track damage could be identified and quantified. The FEM model with the Winkler soil cannot be fitted to the amplitude and width with the same soil parameters. Therefore, the FEBEM model is preferable for these railway track problems.
Journal Article
A Fast Optimization Algorithm of FEM/BEM Simulation for Periodic Surface Acoustic Wave Structures
The accurate analysis of periodic surface acoustic wave (SAW) structures by combined finite element method and boundary element method (FEM/BEM) is important for SAW design, especially in the extraction of couple-of-mode (COM) parameters. However, the time cost is very large. With the aim to accelerate the calculation of SAW FEM/BEM analysis, some optimization algorithms for the FEM and BEM calculation have been reported, while the optimization for the solution to the final FEM/BEM equations which is also with a large amount of calculation is hardly reported. In this paper, it was observed that the coefficient matrix of the final FEM/BEM equations for the periodic SAW structures was similar to a Toeplitz matrix. A fast algorithm based on the Trench recursive algorithm for the Toeplitz matrix inversion was proposed to speed up the solution of the final FEM/BEM equations. The result showed that both the time and memory cost of FEM/BEM was reduced furtherly.
Journal Article
A Boundary Element Model for Structural Health Monitoring Based on the S0 Lamb Wave Mode
The aim of this paper was to carry out numerical simulations of structural health monitoring applications for plate structures using the boundary element method (BEM). The fundamental symmetric Lamb mode (S0) is chosen for the SHM applications. The propagation, reflection and diffraction of the S0 mode Lamb wave are modelled using a boundary element formulation based on the plane stress theory. Piezoelectric (PZT) actuators are mounted on plate surfaces to excite the S0 mode wave. A semi-analytical method is adopted to couple the PZT actuators and the host plate. Numerical results show that BEM is a very efficient simulation method for the structural health monitoring of plates.
Journal Article