Figure - available from: Engineering with Computers
This content is subject to copyright. Terms and conditions apply.
Taipei 101 with a sphere-shaped damper [50]

Taipei 101 with a sphere-shaped damper [50]

Source publication
Article
Full-text available
This paper proposes an enriched degree of freedom method for absorbing boundary conditions in time-domain finite element method (TD-FEM). In the proposed method, to reduce the reflection of the elastic waves from the artificial boundary, nodes in the absorbing domain are first enriched by the additional degrees of freedom to damp the outgoing elast...

Similar publications

Article
Full-text available
This work investigates the Flamant-Boussinesq problem for a half-space made of a homogeneous and isotropic dielectric material. The dynamical flexoelectric effect and the dynamical flexocoupling between displacement and polarization, due to mechanical and electrical states, are taken in consideration. The mechanical loading is taken as a wave of a...
Article
Full-text available
In the course of designing and certifying civil aircraft, a significant number of dynamic tests are necessary. If the test specimen is too large in volume or weight, it will place higher demands on the loading capacity of the test equipment. The main focus in the design process of dynamic test specimens is to ensure consistency in the dynamic chara...
Preprint
Full-text available
The aim of the paper is to study the problem $$ \begin{cases} u_{tt}-\Delta u+P(x,u_t)=f(x,u) \qquad &\text{in $(0,\infty)\times\Omega$,} u=0 &\text{on $(0,\infty)\times \Gamma_0$,} u_{tt}+\partial_\nu u-\Delta_\Gamma u+Q(x,u_t)=g(x,u)\qquad &\text{on $(0,\infty)\times \Gamma_1$,} u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x) & \text{in $\bar{\Omega}$,} \end...
Article
Full-text available
Thermoelastic damping effects are very important intrinsic losses in microelectromechanical system/nanoelectromechanical system based sensors and filters, which limit the maximum achievable quality factor. Thermoelasticity arises due to coupling between the temperature field and elastic field of the material and its interaction within the material...
Article
Full-text available
A fully discrete computational technique involving the implicit finite difference technique and cubic Hermite splines is proposed to solve the non-linear conformable damped Burgers’ equation with variable coefficients numerically. The proposed scheme is capable of solving the equation having singularity at t=0. The space direction is discretized us...

Citations

... The first type of numerical methods is the discontinuum-based methods, such as the finite discrete element method (FDEM) [1], discontinuous deformation analysis (DDA) [2], and the numerical manifold method (NMM) [3,4]. It is worth mentioning that a reliable non-reflection boundary [5,6] must be developed to simulate actual seismic motion accurately and avoid the effects of reflected waves in numerical simulations. For instance, Jiao et al. [7] introduced the viscous boundary [8] in DDA to prevent the reflection of outward propagating waves back into the model and investigated the wave propagation problems. ...
Article
Full-text available
A thorough understanding of the seismic response of geotechnical structures has always been an aspiration for all engineers. Recently, the non-local general particle dynamics (NLGPD), which considers the variation of material density, has exhibited excellent promise in modelling extremely large deformation and dynamic problems. To extend the capacity of NLGPD to carry out seismic response analysis, four non-reflection boundaries are newly added in the framework of NLGPD in this paper. The viscous boundary allows wave energy to be absorbed by dashpot, in which a stress input method is proposed to input the seismic motion. The viscous-spring boundary can capture the elasticity recovery ability of the far-field medium. The free-field boundary achieves the free-field motion at lateral boundaries in the process of absorbing wave, and the corresponding relation between the points of the main model and the free-field column is determined. The static-dynamic unified boundary is introduced to model the transformation process from fixed boundary conditions in a static state to free field boundary conditions in dynamic analysis. Several representative numerical examples are solved to validate the feasibility of the proposed method. The numerical results show that the NLGPD method provides robustness and broad applicability for the seismic response analysis.
... where u(x) is the displacement at a specific point, N i (x) is the interpolation function associated with each node, u i represents the nodal displacement values, and n denotes the total number of nodes. For the enriched degree of freedom method (EDM), one prominent approach for enriching degrees of freedom (DOFs) into computational models is the extended finite element method (XFEM) [6,[42][43][44][45]. XFEM enhances the node by incorporating Heaviside functions, particularly useful for solving crack-related problems. ...
... Therefore, the EDM can also alter the stiffness of the computational model by introducing novel enrichment functions. In this regard, we proposed a method for addressing absorbing boundary problems using the EDM in the previous studies [6,45]. When assembling the element stiffness matrix considering the enriched DOFs in the EDM, the element stiffness matrix K v can be written as: ...
... For the EDM, as shown in Eq. (28), it is evident that within an element, the presence of even a single enriched DOF can influence every conventional DOF. The EDM attenuates the outgoing elastic waves by adding the damping force to the enriched DOF [6,45]. Therefore, when the EDM is employed to implement the absorbing boundary problems, the damping force on an enriched DOF can affect the force acting on every conventional DOFs within an element. ...
Article
Absorbing boundaries are essential in engineering simulations, especially for elastodynamic problems, to ensure accuracy, reliability and numerical stability. In this paper, the added degree of freedom method (ADM) is developed as a novel approach to address absorbing boundary challenges in finite element analysis. In ADM, additional degrees of freedom (DOFs) are introduced within the absorbing domain to attenuate outgoing elastic waves. For the proposed ADM to implement the absorbing boundary, the stiffness and mass properties of both the added DOFs and conventional DOFs within the absorbing domain are adjusted. This adjustment aims to reduce the propagation speed of elastic waves within the medium, and to prolong the duration of interaction between elastic waves and the surrounding medium. Consequently, the vibrations of nodes can be effectively attenuated by applying damping forces to the added DOFs. The numerical results show that the ADM has the ability to absorb one-dimensional and two-dimensional elastic waves across a broad range of frequencies. Therefore, the proposed ADM offers an innovative solution for modeling absorbing boundaries in various scientific and engineering applications, addressing the challenges of simulating wave propagation within finite computational domains.
... The XFEM is a numerical approach used to solve problems involving discontinuities. By incorporating additional degrees of freedom and enrichment functions into the model, the XFEM can represent various geometries and types of discontinuities, including cracks, interfaces, and voids, without remeshing [35][36][37][38][39][40][41]. ...
... Additionally, to model the SHPB test system and to reduce the computational cost, absorbing boundary conditions are employed in the XFEM to model the buffer bar and to shorten the transmission bar. Drawing from the authors' previous research [35,38,56], the enriched degrees of freedom method can be used by the XFEM to model the infinite domain, and this method is summarized in a concise manner below. ...
... Chen et. al[38] demonstrated that introducing an additional DOF to the model can modify the stiffness. Nonetheless, a sudden change in stiffness can result in the reflection of elastic waves. ...
Article
Rock strata often contain weak interlayers, and it is vital to understand how rocks respond to dynamic loads for predicting natural disasters such as earthquakes and landslides. In this paper, a combined numerical and experimental analysis is carried out to investigate the dynamic properties and failure behaviours of specimens with and without a weak interlayer. Specifically, split Hopkinson pressure bar tests are employed, and numerical simulations of these tests are developed in the framework of the extended finite element method. Additionally, the feasibility of the proposed numerical method for modelling the split Hopkinson pressure bar is verified by comparison with laboratory tests. The results demonstrate that the existence of a material interface or a weak interlayer in the specimen can cause stress concentrations under dynamic stress waves and that the failure behaviours of the specimen can also be changed. Evidently, the failure pattern in the intact specimen consists of a compression‒shear failure pattern and a tensile failure pattern. The failure pattern in the specimen containing a persistent flaw is the compression‒shear failure pattern, and the failure pattern in the specimen containing a weak interlayer consists of a compression‒shear failure pattern and a tensile failure pattern, in which the number of tensile cracks increases with increasing thickness of weak interlayers in the specimen.
... To remove the unwanted elastic waves reflected from the model's boundary, many absorbing boundaries were proposed such as the viscous absorbing boundary [62], the continued-fraction absorbing boundary conditions [63], the Rayleigh-type damping method coupled with the viscoelastic boundary [64], the stiffness reduction method [65], the enriched degree of freedom method [66] and the perfectly matched layer (PML) [67][68][69][70][71]. Among these methods, the PML has advantages in addressing the absorbing boundary condition problem [72]. ...
Article
In this paper, the effects of crack lengths and wavelengths on dynamic cracking behaviours are investigated using the improved extended finite element method (XFEM), in which the absorbing boundary condition is coupled into the XFEM. Subsequently, to study the evolution of the displacement and the energy affected by the cracks, numerical tests in a plate containing a crack are conducted under dynamic loads with different wavelengths. Finally, the effects of the crack lengths and wavelengths on the dynamic cracking behaviors are investigated by analysing the evolution of the dynamic stress intensity factor and the energy release rate. The numerical results show that a sudden drop in energy can be found when the angle between the incident dynamic load and the crack varies from a vertical angle to an acute angle. Additionally, it is found that the crack length rarely affects the dynamic cracking behaviours, while the wavelength does significantly affect the dynamic cracking behaviours. When the wavelength is smaller than the critical wavelength, tensile-shear cracking behavior occurs. Otherwise, the cracking behaviour consists of a compression-shear cracking pattern and a tension-shear cracking pattern.
Article
In this paper, we studied the finite volume formulations for solving the diffraction grating problem that is truncated by the perfectly matched layer (PML) technique. Based on a reliable the a-posteriori error estimate, an adaptive PML finite volume method is discussed for the numerical approximation of the diffraction grating problem. The PML parameters are obtained numerically by sharp a-posteriori error estimates of the PML finite volume method such as the thickness of the layer and the medium property. It is worth mentioning in the a-posteriori error estimates that we derive the error representation formula and use a [Formula: see text]-orthogonality property of the residual similar to the Galerkin orthogonality used in the finite element method. Furthermore, the lower bound is established to demonstrate the efficiency of the a-posteriori error estimates. Numerical experiments are given to illustrate the accuracy and robustness of our adaptive algorithm.