scholarly journals Eigenstrain Boundary Integral Equations with Local Eshelby Matrix for Stress Analysis of Ellipsoidal Particles

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hang Ma ◽  
Cheng Yan ◽  
Qing-hua Qin
Keyword(s):  
Numerical Simulation ◽  
Computational Model ◽  
Large Scale ◽  
High Efficiency ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Boundary Integral ◽  
Ellipsoidal Particles ◽  
Reinforced Materials

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

A Scalable Time-Parallel Solution of Periodic Rotor Dynamics in X3D

2021 ◽  
Author(s):  
Mrinalgouda Patil ◽  
Anubhav Datta
Keyword(s):  
Harmonic Balance ◽  
Large Scale ◽  
Structural Model ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Flight Test ◽  
Solution Procedure ◽  
Balance Method ◽  
Computational Time ◽  
Near Resonance

A time-parallel algorithm is developed for large-scale three-dimensional rotor dynamic analysis. A modified harmonic balance method with a scalable skyline solver forms the kernel of this algorithm. The algorithm is equipped with a solution procedure suitable for large-scale structures that have lightly damped modes near resonance. The algorithm is integrated in X3D, implemented on a hybrid shared and distributed memory architecture, and demonstrated on a three-dimensional structural model of a UH-60A-like fully articulated rotor. Flight-test data from UH-60A Airloads Program transition flight C8513 are used for validation. The key conclusion is that the new solver converges to the time marching solution more than 50 times faster and achieves a performance greater than 1 teraFLOPS. The significance of this conclusion is that the principal barrier of computational time for trim solution using high-fidelity three-dimensional structures can be overcome with the scalable harmonic balance method demonstrated in this paper.

Numerical Implementation

1994 ◽  
Author(s):  
Nhan Phan-Thien ◽  
Sangtae Kim
Keyword(s):  
Boundary Element ◽  
Numerical Integration ◽  
Integral Equations ◽  
Large Scale ◽  
Boundary Integral Equations ◽  
Numerical Technique ◽  
Boundary Integral ◽  
Practical Implementation ◽  
Computing Environment ◽  
The Individual

Analytical solutions to a set of boundary integral equations are rare, even with simple geometries and boundary conditions. To make any reasonable progress, a numerical technique must be used. There are basically four issues that must be discussed in any numerical scheme dealing with integral equations. The first and most basic one is how numerical integration can be effected, together with an effective way of dealing with singular kernels of the type encountered in elastostatics. Numerical integration is usually termed numerical quadrature, meaning mathematical formulae for numerical integration. The second issue is the boundary discretization: when integration over the whole boundary is replaced by a sum of the integrations over the individual patches on the boundary. Each patch would be a finite element, or in our case, a boundary element on the surface. Obviously a high-order integration scheme can be devised for the whole domain, thus eliminating the need for boundary discretization. Such a scheme would be problem dependent and therefore would not be very useful to us. The third issue has to do with the fact that we are constrained by the very nature of the numerical approximation process to search for solutions within a certain subspace of L2, say the space of piecewise constant functions in which the unknowns are considered to be constant over a boundary element. It is the order of this subspace, together with the order and the nature of the interpolation of the geometry, that gives rise to the names of various boundary element schemes. Finally, one is faced with the task of solving a set of linear algebraic equations, which is usually dense (the system matrix is fully populated) and potentially ill-conditioned. A direct solver such as Gauss elimination may be very efficient for small- to medium-sized problems but will become stuck in a large-scale simulation, where the only feasible solution strategy is an iterative method. In fact, iterative solution strategies lead naturally to a parallel algorithm under a suitable parallel computing environment. This chapter will review various issues involved in the practical implementation of the CDL-BIEM on a serial computer and on a distributed computing environment.

Boundary Element Method Analysis of Three-Dimensional Thermoelastic Fracture Problems Using the Energy Domain Integral

2005 ◽  
Vol 73 (6) ◽  
pp. 959-969 ◽  
Author(s):  
R. Balderrama ◽  
A. P. Cisilino ◽  
M. Martinez
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Auxiliary Function ◽  
Boundary Integral ◽  
Crack Advance ◽  
Domain Integral ◽  
Energy Domain ◽  
Element Method

A boundary element method (BEM) implementation of the energy domain integral (EDI) methodology for the numerical analysis of three-dimensional fracture problems considering thermal effects is presented in this paper. The EDI is evaluated from a domain representation naturally compatible with the BEM, since stresses, strains, temperatures, and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations. Special emphasis is put on the selection of the auxiliary function that represents the virtual crack advance in the domain integral. This is found to be a key feature to obtain reliable results at the intersection of the crack front with free surfaces. Several examples are analyzed to demonstrate the efficiency and accuracy of the implementation.

Numerical Simulation of Turbulent Driven Secondary Flow in a 90° Bend Pipe

2013 ◽  
Vol 765-767 ◽  
pp. 514-519
Author(s):  
Min Chen ◽  
Zhi Guo Zhang
Keyword(s):  
Numerical Simulation ◽  
Large Scale ◽  
Three Dimensional ◽  
Curvature Flow ◽  
Bend Pipe ◽  
Curved Pipe ◽  
Numerical Result ◽  
Bent Pipe ◽  
Flow Through ◽  
Strong Curvature

The numerical simulation of the developing turbulent flow through a three-dimensional curved pipe with strong curvature is presented. This numerical simulation is to investigate the flow structure of pipe-flow through a 90° bent pipe with the aid of RNG k-ε turbulence model, which had been well validated for high screwed curvature flow. Dean Motion downstream of the bend are found and presented. And the numerical result demonstrates that Dean motions co-exist with large scale swirling motions inside the bend pipe. Snapshot of velocity and pressure reveals that the structures found upstream of the bend persist after the bend and survive the strong secondary motions induced by the pipe curvature.

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.

scholarly journals Study on Fluorine Pollution in a Slag Yard

2019 ◽  
Vol 9 (5) ◽  
pp. 847
Author(s):  
Lide Wei ◽  
Changfu Wei ◽  
Sugang Sui
Keyword(s):  
Numerical Simulation ◽  
Experimental Investigation ◽  
Numerical Simulations ◽  
Solute Transport ◽  
Large Scale ◽  
Three Dimensional ◽  
Simulation Method ◽  
Laboratory Studies ◽  
Survey Results ◽  
Simulation Results

This paper suggests a large-scale three-dimensional numerical simulation method to investigate the fluorine pollution near a slag yard. The large-scale three-dimensional numerical simulation method included an experimental investigation, laboratory studies of solute transport during absorption of water by soil, and large-scale three-dimensional numerical simulations of solute transport. The experimental results showed that the concentrations of fluorine from smelting slag and construction waste soil were well over the discharge limit of 0.1 kg/m3 recommended by Chinese guidelines. The key parameters of the materials used for large-scale three-dimensional numerical simulations were determined based on an experimental investigation, laboratory studies, and soil saturation of survey results and back analyses. A large-scale three-dimensional numerical simulation of solute transport was performed, and its results were compared to the experiment results. The simulation results showed that the clay near the slag had a high saturation of approximately 0.9, consistent with the survey results. Comparison of the results showed that the results of the numerical simulation of solute transport and the test results were nearly identical, and that the numerical simulation results could be used as the basis for groundwater environmental evaluation.

scholarly journals Seismic performance analysis and assessment of a precast bridge computational model

DYNA ◽  
2020 ◽  
Vol 87 (212) ◽  
pp. 80-89
Author(s):  
José Benjumea ◽  
Mehdi Saiidi ◽  
Ahmad Itani
Keyword(s):  
Performance Analysis ◽  
Computational Model ◽  
Seismic Performance ◽  
Earthquake Engineering ◽  
Large Scale ◽  
Three Dimensional ◽  
Shake Table ◽  
Bridge Model ◽  
Precast Elements ◽  
The University

A large-scale, two-span bridge model constructed by assembling precast elements was tested under a series of bi-axial ground motionssimulated on a shake table at the Earthquake Engineering Laboratory at the University of Nevada, Reno. The response of the bridge wasestimated before the tests using a three-dimensional computational model developed in OpenSees software. After the tests, key measuredseismic responses were compared to those predicted by the computational model to assess the modeling assumptions. Relatively largeerrors for the displacements, base shears, and hysteretic response of the bridge were observed. The influence of the earthquake loading,materials, connectivity of the precast elements, and boundary conditions in the computational model on the errors are discussed in thispaper. Future modeling directions are proposed to reduce these errors.

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