A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis

A Shape Optimisation with the Isogeometric Boundary Element Method and Adjoint Variable Method for the Three-Dimensional Helmholtz Equation

This paper explores an isogeometric boundary element method (IGA-BEM) for sloshing problems in cylindrical tanks with single and multiply connected domains. Instead of the Lagrange basis functions used in the standard BEM, the nonuniform rational B-splines (NURBS) basis functions are introduced to approximate the geometries of the problem boundaries and the unknown variables. Compared with the Lagrange basis functions, NURBS basis functions can accurately reconstruct the geometric boundary of analysis domain with almost no error, and all the data information for NURBS basis functions can be directly obtained from the computer-aided design (cad) or computer-aided engineering (cae) commercial software, which implies the modeling process of IGA-BEM is more simple than that of the standard BEM. NURBS makes it possible for the IGA-BEM to realize the seamless connection between cad and cae software with relative higher calculation accuracy than the standard BEM. Based on the weighted residual method as well as the divergence theorem, the IGA-BEM is developed for the single and multiply connected domains, whose boundaries are separately defined in the parameter space by different knot vectors. The natural sloshing frequencies of the liquid sloshing in a circular cylindrical tank with a coaxial or an off-center circular pipe, an elliptical cylindrical tank with an elliptical pipe, a circular cylindrical tank with multiple pipes are estimated with the introduced method by assuming an ideal (inviscid and incompressible) liquid, irrotational small-amplitude sloshing, and the linear free-surface condition. The comparison between the results obtained by the proposed method and those in the existing literatures shows very good agreements, which verifies the proposed model well. Meanwhile, the effects of radius ratio, liquid depth, number, and location of internal pipe (pipes) on the natural sloshing frequency and sloshing mode are analyzed carefully, and some conclusions are outlined finally.

Shape optimization by conventional and extended isogeometric boundary element method with PSO for two-dimensional Helmholtz acoustic problems

NURBS-enhanced boundary element method based on independent geometry and field approximation for 2D potential problems

Isogeometric symmetric FE-BE coupling method for acoustic-structural interaction

An isogeometric boundary element method is applied to simulate wave scattering problems governed by the Helmholtz equation. The NURBS (non-uniform rational B-splines) widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The singular integrals existing in Burton-Miller formulation are evaluated directly and accurately using Hadamard’s finite part integration. Fast multipole method is applied to accelerate the solution of the system of equations. It is demonstrated that the isogeometric boundary element method based on NURBS performs better than the conventional approach based on Lagrange basis functions in terms of accuracy, and the use of the fast multipole method both retains the accuracy for isogeometric boundary element method and reduces the computational cost.

The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The clear benefit of the approach is that no mesh needs to be generated prior to running the analysis. This is achieved by utilising the isogeometric concept whereby computer-aided design data are used to construct not only the geometry discretisation but also the displacement and traction approximations. In this manner, significant savings can be made in the engineering design and analysis process. This paper also demonstrates that, compared with a standard boundary-element method implementation using quadratic Lagrangian shape functions, superior accuracy is achieved using the present approach for the same number of degrees of freedom. It further illustrates practical applications of the method, comparing against results obtained with a standard boundary-element method and finite-element method for verification. In addition, a propeller is analysed as a sample to show the ability of the present method to handle complex three-dimensional geometries.

Seamless integration of computer-aided geometric modeling and acoustic simulation: Isogeometric boundary element methods based on Catmull-Clark subdivision surfaces

The computation of the acoustic scattering from objects in the ocean is useful to analyze the characteristics of the targets, which can be numerically modelled by acoustic boundary element method (BEM). The BEM has a defect of fictitious frequency problem, Burton-Miller method is studied to overcome the singular problems. In this paper, the Hadamard finite-part integral method based on collocation method is studied to overcome the singularity. It is found that, the near singularity is also quite significant and deteriorates largely the accuracy of BEM. A method based on polar transformation is proposed in this paper to overcome such a defect. Once the problems of singularity and near-singularity are solved, the conventional BEM model is established to serve as a foundation for fast BEM.It is well known that conventional BEM yields a full matrix, which is of O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) memory complexity. Furthermore, the time complexity could be up to O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), if Gaussian elimination method is adopted to solve the linear equation of BEM. Many fast methods are proposed to solve the problems, such as the GMRES iterative solver, fast multipole method and H-matrix (Hierarchical Matrices) method. H-matrix method is applied to overcome the faults of conventional BEM, by using the low-rank approximations to compress blocks of the matrix, which is a pure algebraic method. The ACA (Adaptive Cross Approximation) method is proposed to compute the outer-product form of low-rank matrices, instead of SVD (Singular Value Decomposition), which consumes high CPU time and is of no usability. ACA-BEM is used to predict the acoustic scattering from objects in the ocean, especially the large-scale problems. The directivities of a rigid sphere and a rigid ellipsoid are computed by ACA BEM, the time consumed is very short. For a problem of more than 20,000 DOFs, it can be solved within 2 minutes. Therefore, ACA BEM can be used to solve large-scale acoustic scattering problems very efficiently.

Fast algorithm for multi-frequency numerical integration in the simulation of acoustic scattering from rigid object by the boundary element method is presented. Normal derivative of the free-space Greens function is partially approximated with the unknown variable by a set of shape functions. As a result, the numerical integral is independent of frequency and need be calculated only at the first frequency step. Singular integral can be computed using the same procedure as that applied in the conventional boundary element method. Computational efficiency and accuracy of the new technique are demonstrated by an example. Numerical results obtained using the new technique are compared with the corresponding analytical solutions and numerical results obtained using the conventional boundary element method. The new technique works well and saves a lot of computational time in the process of generation of coefficient matrices for multi-frequency analysis.

Corrosion of reinforcing steel-bar (rebar) is modelled phenomenologically as corrosion losses of three phases. Corresponding to these phases, high AE activities are characteristically observed twice during the corrosion process. It is shown that the 1st AE activity corresponds to the onset of the corrosion in rebar and at the 2nd period of high activity AE events result from concrete cracking due to the expansion of rebar caused by corrosion products. The expansion caused by corrosion products generates micro-cracks in concrete as corrosion-induced cracks, of which mechanisms can be investigated experimentally by AE. To this end, SiGMA (Simplified Green’s functions for Moment tensor Analysis) is applied to the corrosion process in reinforced concrete. To compare with cracking mechanisms identified by SiGMA, a numerical analysis by the two-dimensional boundary element method (BEM) is performed for stress analysis and applied boundary nodes were determined from a diffusion analysis of chloride contents by the finite element method (FEM). Thus, fracture mechanisms of corrosion-induced cracks are quantitatively evaluated by AE-SiGMA and BEM. For on-site measurement of the corrosion in reinforced concrete, hybrid nondestructive evaluation (NDE) is going to be developed. Here, acoustic emission (AE) measurement is conducted, along with measuring half-cell potentials and polarization resistances at the surface of concrete. In order to identify the corroded area along rebar, the potential inversion by BEM (PiBEM) analysis is applied. Thus, plausible areas of the corrosion in rebar are identified.

In water depths up to 61m offshore pipelines are buried in excavated trenches to minimize their impact on the local environment and to reduce the possibility of accidental damage. For many practical reasons it is not unusual to have several pipelines buried in very close proximity to one another. A two-dimensional boundary element method which can be used to predict the seabed pressure field and the surface wave induced forces on a single buried pipe or any cluster configuration is presented. Of particular interest for design practice is the introduction of non-linear stream function wave theory into the formulation. A comparison of the boundary element model predictions with the analytical solution for a single buried pipeline, and a finite element model, which was validated using small scale laboratory tests is presented and discussed. The use of linear and non-linear ocean surface wave theories is examined and predictions of wave induced forces on several cluster configurations is presented. The two-dimensional boundary element approach is shown to be efficient and very suitable for this type of offshore application.

A two-dimensional boundary element method with a constant element type was adopted to study the sound field of a building near a roadway. First, a factor analysis of the computed results has been done, which include the element length, the Hankel functions’ calculation accuracy, and numerical integration accuracy. Then, boundary element method is applied to calculate building attenuation with different building aspect ratios and different frequencies with balconies, followed by drawing of the sound field distribution diagram. The calculation results revealed the following: (1) a wider building results in a more severe sound attenuation; (2) balconies on different floors produce a reduction of approximately 15 dB for broadband spectral characteristics of A-weight road traffic noise, and the maximum values appear at the bottoms of balconies; (3) for the points in the balconies, higher sound frequencies are correlated to larger insertion loss, with the insertion loss increasing from 3 dB to &gt;10 dB when the sound frequency increases from 20 to 4000 Hz; (4) calculations of three typical frequencies indicate that the insertion loss of 500 Hz (main frequency of heavy vehicles) is 6 dB less than that of 800 Hz (main frequency of light vehicles), i.e. the flow control of heavy vehicles could conspicuously improve the ambient acoustic environment of buildings near a roadway.

Isogeometric boundary element method for isotropic damage elastic mechanical problems

In this paper, we propose a two-dimensional (2D) boundary element method (BEM) to explore the coupling properties of two distorted graphene nanoribbons (GNRs) with wrinkles. From the calculation results, it is found that the resonant wavelengths are redshifted compared with a single GNR, and the scattering intensity is greatly increased, due to the coupling between the two GNRs. In the non-degenerate structure, the coupling resonance modes of the two GNRs are the superposition of the resonance modes of every single GNR, and the resonant wavelength and scattering intensity of different modes change differently with the gap between the two GNRs and their heights. When the coupling effect becomes stronger, some modes will split. We explain the results through the charge and current distribution of the GNRs. This work will help to understand the coupling mechanism of surface plasmon resonances of GNRs.