scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

scholarly journals Development of boundary-element time-step scheme in solving 3D poroelastodynamics problems

2018 ◽  
Vol 183 ◽  
pp. 01042 ◽  
Author(s):  
Igor Vorobtsov ◽  
Aleksandr Belov ◽  
Andrey Petrov
Keyword(s):  
Boundary Element ◽  
Solid Phase ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Discrete Analogue ◽  
Boundary Integral ◽  
Step Method ◽  
Time Step ◽  
Element Scheme ◽  
Runge Kutta

The development of time-step boundary-element scheme for the three dimensional boundaryvalue problems of poroelastodynamics is presented. The poroelastic continuum is described using Biot’s mathematical model. Poroelastic material is assumed to consist of a solid phase constituting an elastic formdefining skeleton and carrying most of the loading, and two fluid phases filling the pores. Dynamic equations of the poroelastic medium are written for unknown functions of displacement of the elastic skeleton and pore pressures of the filling materials. Green’s matrices and, based on it, boundary integral equations are written in Laplace domain. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. Boundary element scheme is based on time-step method of numerical inversion of Laplace transform. A modification of the time-step scheme on the nodes of Runge-Kutta methods is considered. The Runge-Kutta scheme is exemplified with 2-and 3-stage Radau schemes. The results of comparing the two schemes in analyzing a numerical example are presented.

Added Wave Resistance Computations Using Desingularized Source and Panel Methods

2015 ◽  
Author(s):  
Xinshu Zhang ◽  
Wei Li ◽  
Yunxiang You
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Wave Resistance ◽  
Boundary Integral ◽  
Time Step ◽  
Panel Methods ◽  
Calm Water ◽  
Constant Strength ◽  
Hull Forms ◽  
Large Amplitude Motion

A three-dimensional time-domain approach has been developed to compute large-amplitude motion response and the second-order added wave resistance for ships traveling in waves. The proposed method is an extension of a well established linear approach developed in a previous paper [1]. The numerical model is developed based on boundary integral equation, which is solved at each time step by distributing desingularized sources above the calm water surface and employing constant-strength panels on body surface. The nonlinear Froude-Krylov and wave diffraction forces are computed. Equations of motion are solved with including the effects of Euler angles. A broad range of different hull forms, including two Wigley hulls, a Series 60 hull, and a S-175 hull, are employed to validate the present computational model. By comparing the obtained numerical results to experiments, it is demonstrated that the present model using double-body basis flow can well predict added wave resistance.

Application of the peridynamic differential operator to the solution of sloshing problems in tanks

2018 ◽  
Vol 36 (1) ◽  
pp. 45-83 ◽  
Author(s):  
Soheil Bazazzadeh ◽  
Arman Shojaei ◽  
Mirco Zaccariotto ◽  
Ugo Galvanetto
Keyword(s):  
Fluid Flow ◽  
Differential Operator ◽  
Domain Boundary ◽  
Time Algorithm ◽  
Field Variable ◽  
Integration Scheme ◽  
Inviscid Fluid ◽  
Time Step ◽  
Content Type ◽  
Jump Discontinuities

PurposeThe purpose of this paper is to apply the Peridynamic differential operator (PDDO) to incompressible inviscid fluid flow with moving boundaries. Based on the potential flow theory, a Lagrangian formulation is used to cope with non-linear free-surface waves of sloshing water in 2D and 3D rectangular and square tanks.Design/methodology/approachIn fact, PDDO recasts the local differentiation operator through a nonlocal integration scheme. This makes the method capable of determining the derivatives of a field variable, more precisely than direct differentiation, when jump discontinuities or gradient singularities come into the picture. The issue of gradient singularity can be found in tanks containing vertical/horizontal baffles.FindingsThe application of PDDO helps to obtain the velocity field with a high accuracy at each time step that leads to a suitable geometry updating for the procedure. Domain/boundary nodes are updated by using a second-order finite difference time algorithm. The method is applied to the solution of different examples including tanks with baffles. The accuracy of the method is scrutinized by comparing the numerical results with analytical, numerical and experimental results available in the literature.Originality/valueBased on the investigations, PDDO can be considered a reliable and suitable approach to cope with sloshing problems in tanks. The paper paves the way to apply the method for a wider range of problems such as compressible fluid flow.

Wave-Current Interaction with a Large Three-Dimensional Body by THOBEM

1997 ◽  
Vol 41 (04) ◽  
pp. 273-285
Author(s):  
D. J. Kim ◽  
M. H. Kim
Keyword(s):  
Free Surface ◽  
Surface Condition ◽  
Three Dimensional ◽  
Higher Order ◽  
Boundary Integral ◽  
Open Boundary ◽  
Wave System ◽  
Viscous Effects ◽  
Regular Perturbation ◽  
Time Step

The effects of uniform steady currents (or small forward velocity) on the interaction of a large three-dimensional body with waves are investigated by a time-domain higher-order boundary element method (THOBEM). The current speed is assumed to be small so that the viscous effects and the steady wave system generated by currents are insignificant. Using regular perturbation with two small parameters є and δ associated with wave slope and current velocity, respectively, the boundary value problem is decomposed into the zeroth-order steady double-body-flow problem at 0(δ) with a rigid-wall free-surface condition and the first-order unsteady wave problem with the modified free-surface and body-boundary conditions expanded up to O(eδ). Higher-order boundary integral equation methods are then used to solve the respective problems with the Rankine sources distributed over the entire boundary. The free surface is integrated at each time step by Adams-Bashforth-Moulton method. The Sommerfeld/Orlanski radiation condition is numerically implemented to absorb all the wave energy at the open boundary. To solve the so-called corner problem, discontinuous elements are used at the intersection of free-surface and radiation boundaries Using the developed numerical method, wave forces, wave field and run-up, mean drift forces and wave drift damping are calculated.

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